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Keplers Laws of Planetary Motion
Master Kepler's first law, second law, third law, planetary motion, applications, numericals and PYQs.
Kepler's First Law: Law of Orbits
Every planet moves around the Sun in an elliptical orbit with the Sun at one focus. The Sun is not at the centre of the ellipse except in the special circular case.
Ellipse Details
- Ellipse has two foci.
- Major axis is the longest diameter.
- Minor axis is perpendicular to major axis.
- A circle is a special ellipse.
First Law Diagram
Kepler's Second Law: Law of Equal Areas
The line joining a planet and the Sun sweeps out equal areas in equal intervals of time. The planet moves faster near perihelion and slower near aphelion.
Equal Areas
Physical Meaning
Areal velocity remains constant because angular momentum is conserved in a central gravitational force. Equal area does not mean equal distance; it means equal swept area in equal time.
Kepler's Third Law: Law of Periods
The square of the time period of revolution of a planet is proportional to the cube of the semi-major axis of its orbit.
T
Time period of one complete revolution.
r and a
r is circular orbital radius. a is semi-major axis for an ellipse.
M
Mass of the central body such as the Sun or Earth.
Physical Interpretation
Path
First law describes the orbital path.
Speed
Second law describes speed variation.
Size and Time
Third law relates orbital size and time period.
| Law | Name | Meaning | Formula | Exam Tip |
|---|---|---|---|---|
| First | Law of orbits | Planet follows ellipse with Sun at focus. | Ellipse path | Sun is not at centre. |
| Second | Law of equal areas | Radius vector sweeps equal areas in equal time. | dA/dt = constant | Speed changes in ellipse. |
| Third | Law of periods | Period depends on semi-major axis. | T2 proportional to a3 | Use a for ellipse, r for circle. |
Planetary Motion
Planetary motion may be circular as an approximation or elliptical in reality. Perihelion is nearest to the Sun, aphelion is farthest from the Sun, and the planet's speed changes continuously in an elliptical orbit.
Near and Far Positions
Key Ideas
- Gravity provides the central force.
- Radius vector joins Sun and planet.
- Speed is highest near perihelion.
- Speed is lowest near aphelion.
- Orbital energy is negative for bound ellipse.
Searching for a Physics Tutor? If Kepler's Laws, Planetary Motion or NEET/JEE Gravitation numericals are not clear, contact Kumar Sir.
Phone: +91-9958461445 | Email: kumarsirphysics@gmail.com | Website: kumarphysicsclasses.com
Applications
Planetary orbits
Concept: Predicts paths of planets around the Sun.
Formula: T2 proportional to a3
Exam Tip: Use semi-major axis for ellipse.
Artificial satellites
Concept: Designs satellite periods and radii.
Formula: T2 = 4pi2r3/GM
Exam Tip: Use orbital radius from centre.
Comets
Concept: Explains high speed near Sun and slow motion far away.
Formula: dA/dt = constant
Exam Tip: Second law controls speed variation.
Earth around Sun
Concept: Earth's year follows third law.
Formula: T = 1 year
Exam Tip: Sun is at one focus, not exactly centre.
Moon around Earth
Concept: Moon's orbital period follows Earth-centred form.
Formula: T2 = 4pi2a3/GME
Exam Tip: Central mass is Earth.
Geostationary satellites
Concept: Period matches Earth's rotation.
Formula: T = 24 h
Exam Tip: Orbit must be equatorial.
Space missions
Concept: Transfer orbits use elliptical paths.
Formula: T2 proportional to a3
Exam Tip: Semi-major axis of transfer ellipse matters.
Orbital transfer
Concept: Predicts timing between two circular orbits.
Formula: a = (r1+r2)/2
Exam Tip: Use transfer ellipse axis.
Astronomical calculations
Concept: Relates observed period and distance.
Formula: GM = 4pi2a3/T2
Exam Tip: Good for central-body parameter.
Finding mass of central body
Concept: Weighs planets and stars from satellite data.
Formula: M = 4pi2a3/(GT2)
Exam Tip: Satellite mass not needed.
Important Graphs
T2 vs a3
Straight line through origin for same central mass.
Orbital Speed vs Distance
For circular orbit, speed decreases as distance increases.
Areal Velocity
Constant areal velocity for central force motion.
Distance vs Speed
Qualitatively, speed is higher when the planet is closer to the Sun.
Important Formula Table
| Concept | Formula | Meaning | Exam Tip |
|---|---|---|---|
| Third law | T2 proportional to a3 | Period-size relation. | Same central mass. |
| Circular orbit | T2 = 4pi2r3/GM | Use orbital radius r. | r is from centre. |
| Elliptical orbit | T2 = 4pi2a3/GM | Use semi-major axis. | Do not use changing radius. |
| Second law | dA/dt = constant | Areal velocity is constant. | Equal area in equal time. |
| Circular speed | v = sqrt(GM/r) | Speed in circular orbit. | Not for general ellipse. |
| Perihelion | v greater | Nearest point to Sun. | Maximum speed. |
| Aphelion | v smaller | Farthest point from Sun. | Minimum speed. |
| Areal velocity | L/2m | Angular momentum form. | Central force result. |
High-Quality Solved Numericals
CBSE 1
Question: A planet has orbital radius 4 times Earth's orbital radius. Find its time period if Earth's period is 1 year.
Show Answer
Given: a2/a1 = 4, T1 = 1 year
Formula: T2/T1 = (a2/a1)3/2
Calculation: T2 = 43/2 x 1 = 8 years
Final Answer: 8 years
Exam Tip: Use semi-major axis ratio.
Common Mistake: Do not use direct proportionality T proportional to a.
CBSE 2
Question: If T becomes 27 times, what is the ratio of semi-major axes?
Show Answer
Given: T2/T1 = 27
Formula: T2 proportional to a3
Calculation: a2/a1 = (T2/T1)2/3 = 272/3 = 9
Final Answer: 9:1
Exam Tip: Convert period ratio to axis ratio.
Common Mistake: Do not square 27 first in mental steps without simplifying.
NEET 1
Question: Two satellites orbit the same planet with radii R and 9R. Find period ratio.
Show Answer
Given: r2/r1 = 9
Formula: T proportional to r3/2
Calculation: T2/T1 = 93/2 = 27
Final Answer: 27:1
Exam Tip: Same central mass means use radius ratio only.
Common Mistake: Do not include satellite mass.
NEET 2
Question: A comet is closer to the Sun at perihelion than at aphelion. Where is speed greater?
Show Answer
Given: Elliptical orbit
Formula: Areal velocity constant
Calculation: For equal area in equal time, smaller radius needs larger speed.
Final Answer: Speed is greater at perihelion.
Exam Tip: Second law is a speed law.
Common Mistake: Do not assume speed is constant in ellipse.
JEE Main 1
Question: A satellite period is 8 h at radius r. Find period at radius 4r.
Show Answer
Given: T1 = 8 h, r2/r1 = 4
Formula: T2 = T1(r2/r1)3/2
Calculation: T2 = 8 x 43/2 = 64 h
Final Answer: 64 h
Exam Tip: Period grows strongly with radius.
Common Mistake: Do not use square-root inverse speed relation alone.
JEE Main 2
Question: Find central mass if a satellite has circular radius r and period T.
Show Answer
Given: r, T
Formula: T2 = 4pi2r3/GM
Calculation: M = 4pi2r3/(GT2)
Final Answer: M = 4pi2r3/(GT2)
Exam Tip: Kepler's third law can weigh planets.
Common Mistake: Do not forget G in denominator.
JEE Advanced 1
Question: A planet sweeps area A in time t. Find areal velocity.
Show Answer
Given: Area = A, time = t
Formula: dA/dt = constant
Calculation: Areal velocity = A/t
Final Answer: A/t
Exam Tip: For central force it remains constant.
Common Mistake: Do not confuse areal velocity with linear speed.
JEE Advanced 2
Question: At perihelion and aphelion distances are rp and ra. Find speed ratio vp/va.
Show Answer
Given: Angular momentum conserved
Formula: mrpvp = mrava
Calculation: vp/va = ra/rp
Final Answer: ra/rp
Exam Tip: Velocity is tangential at apsides.
Common Mistake: Do not invert the ratio.
IB
Question: A planet's semi-major axis is doubled. How does T2 change?
Show Answer
Given: a2/a1 = 2
Formula: T2 proportional to a3
Calculation: T22/T12 = 23 = 8
Final Answer: T2 becomes 8 times
Exam Tip: Third law is about squares and cubes.
Common Mistake: Do not say T becomes 8 times.
IGCSE
Question: State where the Sun is located in a planetary elliptical orbit.
Show Answer
Given: Kepler's first law
Formula: Sun is at one focus
Calculation: The centre of ellipse is not the Sun in general.
Final Answer: Sun is at one focus.
Exam Tip: This is the most common definition point.
Common Mistake: Do not write centre.
A-Level
Question: Show circular orbit formula from Kepler's law.
Show Answer
Given: Circular radius r
Formula: T2 = 4pi2r3/GM
Calculation: From v = 2pi r/T, v2/r = GM/r2 gives same result.
Final Answer: T = 2pi sqrt(r3/GM)
Exam Tip: Links gravitation with Kepler.
Common Mistake: Do not use orbital height instead of radius.
Practice 1
Question: A planet has orbital radius 4 times Earth's orbital radius. Find its time period if Earth's period is 1 year.
Show Answer
Given: a2/a1 = 4, T1 = 1 year
Formula: T2/T1 = (a2/a1)3/2
Calculation: T2 = 43/2 x 1 = 8 years
Final Answer: 8 years
Exam Tip: Use semi-major axis ratio.
Common Mistake: Do not use direct proportionality T proportional to a.
Practice 2
Question: If T becomes 27 times, what is the ratio of semi-major axes?
Show Answer
Given: T2/T1 = 27
Formula: T2 proportional to a3
Calculation: a2/a1 = (T2/T1)2/3 = 272/3 = 9
Final Answer: 9:1
Exam Tip: Convert period ratio to axis ratio.
Common Mistake: Do not square 27 first in mental steps without simplifying.
Practice 3
Question: Two satellites orbit the same planet with radii R and 9R. Find period ratio.
Show Answer
Given: r2/r1 = 9
Formula: T proportional to r3/2
Calculation: T2/T1 = 93/2 = 27
Final Answer: 27:1
Exam Tip: Same central mass means use radius ratio only.
Common Mistake: Do not include satellite mass.
Practice 4
Question: A comet is closer to the Sun at perihelion than at aphelion. Where is speed greater?
Show Answer
Given: Elliptical orbit
Formula: Areal velocity constant
Calculation: For equal area in equal time, smaller radius needs larger speed.
Final Answer: Speed is greater at perihelion.
Exam Tip: Second law is a speed law.
Common Mistake: Do not assume speed is constant in ellipse.
Practice 5
Question: A satellite period is 8 h at radius r. Find period at radius 4r.
Show Answer
Given: T1 = 8 h, r2/r1 = 4
Formula: T2 = T1(r2/r1)3/2
Calculation: T2 = 8 x 43/2 = 64 h
Final Answer: 64 h
Exam Tip: Period grows strongly with radius.
Common Mistake: Do not use square-root inverse speed relation alone.
Practice 6
Question: Find central mass if a satellite has circular radius r and period T.
Show Answer
Given: r, T
Formula: T2 = 4pi2r3/GM
Calculation: M = 4pi2r3/(GT2)
Final Answer: M = 4pi2r3/(GT2)
Exam Tip: Kepler's third law can weigh planets.
Common Mistake: Do not forget G in denominator.
Practice 7
Question: A planet sweeps area A in time t. Find areal velocity.
Show Answer
Given: Area = A, time = t
Formula: dA/dt = constant
Calculation: Areal velocity = A/t
Final Answer: A/t
Exam Tip: For central force it remains constant.
Common Mistake: Do not confuse areal velocity with linear speed.
Practice 8
Question: At perihelion and aphelion distances are rp and ra. Find speed ratio vp/va.
Show Answer
Given: Angular momentum conserved
Formula: mrpvp = mrava
Calculation: vp/va = ra/rp
Final Answer: ra/rp
Exam Tip: Velocity is tangential at apsides.
Common Mistake: Do not invert the ratio.
Practice 9
Question: A planet's semi-major axis is doubled. How does T2 change?
Show Answer
Given: a2/a1 = 2
Formula: T2 proportional to a3
Calculation: T22/T12 = 23 = 8
Final Answer: T2 becomes 8 times
Exam Tip: Third law is about squares and cubes.
Common Mistake: Do not say T becomes 8 times.
Practice 10
Question: State where the Sun is located in a planetary elliptical orbit.
Show Answer
Given: Kepler's first law
Formula: Sun is at one focus
Calculation: The centre of ellipse is not the Sun in general.
Final Answer: Sun is at one focus.
Exam Tip: This is the most common definition point.
Common Mistake: Do not write centre.
Practice 11
Question: Show circular orbit formula from Kepler's law.
Show Answer
Given: Circular radius r
Formula: T2 = 4pi2r3/GM
Calculation: From v = 2pi r/T, v2/r = GM/r2 gives same result.
Final Answer: T = 2pi sqrt(r3/GM)
Exam Tip: Links gravitation with Kepler.
Common Mistake: Do not use orbital height instead of radius.
NEET Question Bank
All questions below are NEET Exam-style Questions unless a real year is explicitly written. No fake years are used.
NEET Exam-style Question 1
MCQ: Kepler's first law says planets move in?
Show Answer
Answer: elliptical orbits with Sun at one focus. For a ratio problem, if a becomes 22 times, T becomes 23 times.
Explanation: This follows directly from Kepler's laws for motion under a central gravitational force.
NEET Exam-style Question 2
MCQ: Kepler's second law states?
Show Answer
Answer: equal areas are swept in equal time.
Explanation: This follows directly from Kepler's laws for motion under a central gravitational force.
NEET Exam-style Question 3
MCQ: Kepler's third law gives?
Show Answer
Answer: T2 proportional to a3.
Explanation: This follows directly from Kepler's laws for motion under a central gravitational force.
NEET Exam-style Question 4
MCQ: At perihelion, a planet's speed is?
Show Answer
Answer: maximum. For a ratio problem, if a becomes 52 times, T becomes 53 times.
Explanation: This follows directly from Kepler's laws for motion under a central gravitational force.
NEET Exam-style Question 5
MCQ: At aphelion, a planet's speed is?
Show Answer
Answer: minimum.
Explanation: This follows directly from Kepler's laws for motion under a central gravitational force.
NEET Exam-style Question 6
MCQ: Areal velocity is related to?
Show Answer
Answer: angular momentum conservation.
Explanation: This follows directly from Kepler's laws for motion under a central gravitational force.
NEET Exam-style Question 7
MCQ: For circular orbit, T2 equals?
Show Answer
Answer: 4pi2r3/GM. For a ratio problem, if a becomes 32 times, T becomes 33 times.
Explanation: This follows directly from Kepler's laws for motion under a central gravitational force.
NEET Exam-style Question 8
MCQ: For ellipse, third law uses?
Show Answer
Answer: semi-major axis.
Explanation: This follows directly from Kepler's laws for motion under a central gravitational force.
NEET Exam-style Question 9
MCQ: If orbital radius becomes 4 times, period becomes?
Show Answer
Answer: 8 times.
Explanation: This follows directly from Kepler's laws for motion under a central gravitational force.
NEET Exam-style Question 10
MCQ: The central force in planetary motion is?
Show Answer
Answer: gravity. For a ratio problem, if a becomes 62 times, T becomes 63 times.
Explanation: This follows directly from Kepler's laws for motion under a central gravitational force.
NEET Exam-style Question 11
MCQ: Kepler's first law says planets move in?
Show Answer
Answer: elliptical orbits with Sun at one focus.
Explanation: This follows directly from Kepler's laws for motion under a central gravitational force.
NEET Exam-style Question 12
MCQ: Kepler's second law states?
Show Answer
Answer: equal areas are swept in equal time.
Explanation: This follows directly from Kepler's laws for motion under a central gravitational force.
NEET Exam-style Question 13
MCQ: Kepler's third law gives?
Show Answer
Answer: T2 proportional to a3. For a ratio problem, if a becomes 42 times, T becomes 43 times.
Explanation: This follows directly from Kepler's laws for motion under a central gravitational force.
NEET Exam-style Question 14
MCQ: At perihelion, a planet's speed is?
Show Answer
Answer: maximum.
Explanation: This follows directly from Kepler's laws for motion under a central gravitational force.
NEET Exam-style Question 15
MCQ: At aphelion, a planet's speed is?
Show Answer
Answer: minimum.
Explanation: This follows directly from Kepler's laws for motion under a central gravitational force.
NEET Exam-style Question 16
MCQ: Areal velocity is related to?
Show Answer
Answer: angular momentum conservation. For a ratio problem, if a becomes 22 times, T becomes 23 times.
Explanation: This follows directly from Kepler's laws for motion under a central gravitational force.
NEET Exam-style Question 17
MCQ: For circular orbit, T2 equals?
Show Answer
Answer: 4pi2r3/GM.
Explanation: This follows directly from Kepler's laws for motion under a central gravitational force.
NEET Exam-style Question 18
MCQ: For ellipse, third law uses?
Show Answer
Answer: semi-major axis.
Explanation: This follows directly from Kepler's laws for motion under a central gravitational force.
NEET Exam-style Question 19
MCQ: If orbital radius becomes 4 times, period becomes?
Show Answer
Answer: 8 times. For a ratio problem, if a becomes 52 times, T becomes 53 times.
Explanation: This follows directly from Kepler's laws for motion under a central gravitational force.
NEET Exam-style Question 20
MCQ: The central force in planetary motion is?
Show Answer
Answer: gravity.
Explanation: This follows directly from Kepler's laws for motion under a central gravitational force.
NEET Exam-style Question 21
MCQ: Kepler's first law says planets move in?
Show Answer
Answer: elliptical orbits with Sun at one focus.
Explanation: This follows directly from Kepler's laws for motion under a central gravitational force.
NEET Exam-style Question 22
MCQ: Kepler's second law states?
Show Answer
Answer: equal areas are swept in equal time. For a ratio problem, if a becomes 32 times, T becomes 33 times.
Explanation: This follows directly from Kepler's laws for motion under a central gravitational force.
NEET Exam-style Question 23
MCQ: Kepler's third law gives?
Show Answer
Answer: T2 proportional to a3.
Explanation: This follows directly from Kepler's laws for motion under a central gravitational force.
NEET Exam-style Question 24
MCQ: At perihelion, a planet's speed is?
Show Answer
Answer: maximum.
Explanation: This follows directly from Kepler's laws for motion under a central gravitational force.
NEET Exam-style Question 25
MCQ: At aphelion, a planet's speed is?
Show Answer
Answer: minimum. For a ratio problem, if a becomes 62 times, T becomes 63 times.
Explanation: This follows directly from Kepler's laws for motion under a central gravitational force.
NEET Exam-style Question 26
MCQ: Areal velocity is related to?
Show Answer
Answer: angular momentum conservation.
Explanation: This follows directly from Kepler's laws for motion under a central gravitational force.
NEET Exam-style Question 27
MCQ: For circular orbit, T2 equals?
Show Answer
Answer: 4pi2r3/GM.
Explanation: This follows directly from Kepler's laws for motion under a central gravitational force.
NEET Exam-style Question 28
MCQ: For ellipse, third law uses?
Show Answer
Answer: semi-major axis. For a ratio problem, if a becomes 42 times, T becomes 43 times.
Explanation: This follows directly from Kepler's laws for motion under a central gravitational force.
NEET Exam-style Question 29
MCQ: If orbital radius becomes 4 times, period becomes?
Show Answer
Answer: 8 times.
Explanation: This follows directly from Kepler's laws for motion under a central gravitational force.
NEET Exam-style Question 30
MCQ: The central force in planetary motion is?
Show Answer
Answer: gravity.
Explanation: This follows directly from Kepler's laws for motion under a central gravitational force.
NEET Exam-style Question 31
MCQ: Kepler's first law says planets move in?
Show Answer
Answer: elliptical orbits with Sun at one focus. For a ratio problem, if a becomes 22 times, T becomes 23 times.
Explanation: This follows directly from Kepler's laws for motion under a central gravitational force.
NEET Exam-style Question 32
MCQ: Kepler's second law states?
Show Answer
Answer: equal areas are swept in equal time.
Explanation: This follows directly from Kepler's laws for motion under a central gravitational force.
NEET Exam-style Question 33
MCQ: Kepler's third law gives?
Show Answer
Answer: T2 proportional to a3.
Explanation: This follows directly from Kepler's laws for motion under a central gravitational force.
NEET Exam-style Question 34
MCQ: At perihelion, a planet's speed is?
Show Answer
Answer: maximum. For a ratio problem, if a becomes 52 times, T becomes 53 times.
Explanation: This follows directly from Kepler's laws for motion under a central gravitational force.
NEET Exam-style Question 35
MCQ: At aphelion, a planet's speed is?
Show Answer
Answer: minimum.
Explanation: This follows directly from Kepler's laws for motion under a central gravitational force.
NEET Exam-style Question 36
MCQ: Areal velocity is related to?
Show Answer
Answer: angular momentum conservation.
Explanation: This follows directly from Kepler's laws for motion under a central gravitational force.
NEET Exam-style Question 37
MCQ: For circular orbit, T2 equals?
Show Answer
Answer: 4pi2r3/GM. For a ratio problem, if a becomes 32 times, T becomes 33 times.
Explanation: This follows directly from Kepler's laws for motion under a central gravitational force.
NEET Exam-style Question 38
MCQ: For ellipse, third law uses?
Show Answer
Answer: semi-major axis.
Explanation: This follows directly from Kepler's laws for motion under a central gravitational force.
NEET Exam-style Question 39
MCQ: If orbital radius becomes 4 times, period becomes?
Show Answer
Answer: 8 times.
Explanation: This follows directly from Kepler's laws for motion under a central gravitational force.
NEET Exam-style Question 40
MCQ: The central force in planetary motion is?
Show Answer
Answer: gravity. For a ratio problem, if a becomes 62 times, T becomes 63 times.
Explanation: This follows directly from Kepler's laws for motion under a central gravitational force.
NEET Exam-style Question 41
MCQ: Kepler's first law says planets move in?
Show Answer
Answer: elliptical orbits with Sun at one focus.
Explanation: This follows directly from Kepler's laws for motion under a central gravitational force.
NEET Exam-style Question 42
MCQ: Kepler's second law states?
Show Answer
Answer: equal areas are swept in equal time.
Explanation: This follows directly from Kepler's laws for motion under a central gravitational force.
NEET Exam-style Question 43
MCQ: Kepler's third law gives?
Show Answer
Answer: T2 proportional to a3. For a ratio problem, if a becomes 42 times, T becomes 43 times.
Explanation: This follows directly from Kepler's laws for motion under a central gravitational force.
NEET Exam-style Question 44
MCQ: At perihelion, a planet's speed is?
Show Answer
Answer: maximum.
Explanation: This follows directly from Kepler's laws for motion under a central gravitational force.
NEET Exam-style Question 45
MCQ: At aphelion, a planet's speed is?
Show Answer
Answer: minimum.
Explanation: This follows directly from Kepler's laws for motion under a central gravitational force.
NEET Exam-style Question 46
MCQ: Areal velocity is related to?
Show Answer
Answer: angular momentum conservation. For a ratio problem, if a becomes 22 times, T becomes 23 times.
Explanation: This follows directly from Kepler's laws for motion under a central gravitational force.
NEET Exam-style Question 47
MCQ: For circular orbit, T2 equals?
Show Answer
Answer: 4pi2r3/GM.
Explanation: This follows directly from Kepler's laws for motion under a central gravitational force.
NEET Exam-style Question 48
MCQ: For ellipse, third law uses?
Show Answer
Answer: semi-major axis.
Explanation: This follows directly from Kepler's laws for motion under a central gravitational force.
NEET Exam-style Question 49
MCQ: If orbital radius becomes 4 times, period becomes?
Show Answer
Answer: 8 times. For a ratio problem, if a becomes 52 times, T becomes 53 times.
Explanation: This follows directly from Kepler's laws for motion under a central gravitational force.
NEET Exam-style Question 50
MCQ: The central force in planetary motion is?
Show Answer
Answer: gravity.
Explanation: This follows directly from Kepler's laws for motion under a central gravitational force.
JEE Main Question Bank
All questions below are JEE Main-style questions. No fake years are used.
JEE Main-style Question 1
Difficult question: Kepler's first law says planets move in?
Show Answer
Answer: elliptical orbits with Sun at one focus. For a ratio problem, if a becomes 22 times, T becomes 23 times.
Explanation: This follows directly from Kepler's laws for motion under a central gravitational force.
JEE Main-style Question 2
Difficult question: Kepler's second law states?
Show Answer
Answer: equal areas are swept in equal time.
Explanation: This follows directly from Kepler's laws for motion under a central gravitational force.
JEE Main-style Question 3
Difficult question: Kepler's third law gives?
Show Answer
Answer: T2 proportional to a3.
Explanation: This follows directly from Kepler's laws for motion under a central gravitational force.
JEE Main-style Question 4
Difficult question: At perihelion, a planet's speed is?
Show Answer
Answer: maximum. For a ratio problem, if a becomes 52 times, T becomes 53 times.
Explanation: This follows directly from Kepler's laws for motion under a central gravitational force.
JEE Main-style Question 5
Difficult question: At aphelion, a planet's speed is?
Show Answer
Answer: minimum.
Explanation: This follows directly from Kepler's laws for motion under a central gravitational force.
JEE Main-style Question 6
Difficult question: Areal velocity is related to?
Show Answer
Answer: angular momentum conservation.
Explanation: This follows directly from Kepler's laws for motion under a central gravitational force.
JEE Main-style Question 7
Difficult question: For circular orbit, T2 equals?
Show Answer
Answer: 4pi2r3/GM. For a ratio problem, if a becomes 32 times, T becomes 33 times.
Explanation: This follows directly from Kepler's laws for motion under a central gravitational force.
JEE Main-style Question 8
Difficult question: For ellipse, third law uses?
Show Answer
Answer: semi-major axis.
Explanation: This follows directly from Kepler's laws for motion under a central gravitational force.
JEE Main-style Question 9
Difficult question: If orbital radius becomes 4 times, period becomes?
Show Answer
Answer: 8 times.
Explanation: This follows directly from Kepler's laws for motion under a central gravitational force.
JEE Main-style Question 10
Difficult question: The central force in planetary motion is?
Show Answer
Answer: gravity. For a ratio problem, if a becomes 62 times, T becomes 63 times.
Explanation: This follows directly from Kepler's laws for motion under a central gravitational force.
JEE Main-style Question 11
Difficult question: Kepler's first law says planets move in?
Show Answer
Answer: elliptical orbits with Sun at one focus.
Explanation: This follows directly from Kepler's laws for motion under a central gravitational force.
JEE Main-style Question 12
Difficult question: Kepler's second law states?
Show Answer
Answer: equal areas are swept in equal time.
Explanation: This follows directly from Kepler's laws for motion under a central gravitational force.
JEE Main-style Question 13
Difficult question: Kepler's third law gives?
Show Answer
Answer: T2 proportional to a3. For a ratio problem, if a becomes 42 times, T becomes 43 times.
Explanation: This follows directly from Kepler's laws for motion under a central gravitational force.
JEE Main-style Question 14
Difficult question: At perihelion, a planet's speed is?
Show Answer
Answer: maximum.
Explanation: This follows directly from Kepler's laws for motion under a central gravitational force.
JEE Main-style Question 15
Difficult question: At aphelion, a planet's speed is?
Show Answer
Answer: minimum.
Explanation: This follows directly from Kepler's laws for motion under a central gravitational force.
JEE Main-style Question 16
Difficult question: Areal velocity is related to?
Show Answer
Answer: angular momentum conservation. For a ratio problem, if a becomes 22 times, T becomes 23 times.
Explanation: This follows directly from Kepler's laws for motion under a central gravitational force.
JEE Main-style Question 17
Difficult question: For circular orbit, T2 equals?
Show Answer
Answer: 4pi2r3/GM.
Explanation: This follows directly from Kepler's laws for motion under a central gravitational force.
JEE Main-style Question 18
Difficult question: For ellipse, third law uses?
Show Answer
Answer: semi-major axis.
Explanation: This follows directly from Kepler's laws for motion under a central gravitational force.
JEE Main-style Question 19
Difficult question: If orbital radius becomes 4 times, period becomes?
Show Answer
Answer: 8 times. For a ratio problem, if a becomes 52 times, T becomes 53 times.
Explanation: This follows directly from Kepler's laws for motion under a central gravitational force.
JEE Main-style Question 20
Difficult question: The central force in planetary motion is?
Show Answer
Answer: gravity.
Explanation: This follows directly from Kepler's laws for motion under a central gravitational force.
JEE Main-style Question 21
Difficult question: Kepler's first law says planets move in?
Show Answer
Answer: elliptical orbits with Sun at one focus.
Explanation: This follows directly from Kepler's laws for motion under a central gravitational force.
JEE Main-style Question 22
Difficult question: Kepler's second law states?
Show Answer
Answer: equal areas are swept in equal time. For a ratio problem, if a becomes 32 times, T becomes 33 times.
Explanation: This follows directly from Kepler's laws for motion under a central gravitational force.
JEE Main-style Question 23
Difficult question: Kepler's third law gives?
Show Answer
Answer: T2 proportional to a3.
Explanation: This follows directly from Kepler's laws for motion under a central gravitational force.
JEE Main-style Question 24
Difficult question: At perihelion, a planet's speed is?
Show Answer
Answer: maximum.
Explanation: This follows directly from Kepler's laws for motion under a central gravitational force.
JEE Main-style Question 25
Difficult question: At aphelion, a planet's speed is?
Show Answer
Answer: minimum. For a ratio problem, if a becomes 62 times, T becomes 63 times.
Explanation: This follows directly from Kepler's laws for motion under a central gravitational force.
JEE Main-style Question 26
Difficult question: Areal velocity is related to?
Show Answer
Answer: angular momentum conservation.
Explanation: This follows directly from Kepler's laws for motion under a central gravitational force.
JEE Main-style Question 27
Difficult question: For circular orbit, T2 equals?
Show Answer
Answer: 4pi2r3/GM.
Explanation: This follows directly from Kepler's laws for motion under a central gravitational force.
JEE Main-style Question 28
Difficult question: For ellipse, third law uses?
Show Answer
Answer: semi-major axis. For a ratio problem, if a becomes 42 times, T becomes 43 times.
Explanation: This follows directly from Kepler's laws for motion under a central gravitational force.
JEE Main-style Question 29
Difficult question: If orbital radius becomes 4 times, period becomes?
Show Answer
Answer: 8 times.
Explanation: This follows directly from Kepler's laws for motion under a central gravitational force.
JEE Main-style Question 30
Difficult question: The central force in planetary motion is?
Show Answer
Answer: gravity.
Explanation: This follows directly from Kepler's laws for motion under a central gravitational force.
JEE Main-style Question 31
Difficult question: Kepler's first law says planets move in?
Show Answer
Answer: elliptical orbits with Sun at one focus. For a ratio problem, if a becomes 22 times, T becomes 23 times.
Explanation: This follows directly from Kepler's laws for motion under a central gravitational force.
JEE Main-style Question 32
Difficult question: Kepler's second law states?
Show Answer
Answer: equal areas are swept in equal time.
Explanation: This follows directly from Kepler's laws for motion under a central gravitational force.
JEE Main-style Question 33
Difficult question: Kepler's third law gives?
Show Answer
Answer: T2 proportional to a3.
Explanation: This follows directly from Kepler's laws for motion under a central gravitational force.
JEE Main-style Question 34
Difficult question: At perihelion, a planet's speed is?
Show Answer
Answer: maximum. For a ratio problem, if a becomes 52 times, T becomes 53 times.
Explanation: This follows directly from Kepler's laws for motion under a central gravitational force.
JEE Main-style Question 35
Difficult question: At aphelion, a planet's speed is?
Show Answer
Answer: minimum.
Explanation: This follows directly from Kepler's laws for motion under a central gravitational force.
JEE Main-style Question 36
Difficult question: Areal velocity is related to?
Show Answer
Answer: angular momentum conservation.
Explanation: This follows directly from Kepler's laws for motion under a central gravitational force.
JEE Main-style Question 37
Difficult question: For circular orbit, T2 equals?
Show Answer
Answer: 4pi2r3/GM. For a ratio problem, if a becomes 32 times, T becomes 33 times.
Explanation: This follows directly from Kepler's laws for motion under a central gravitational force.
JEE Main-style Question 38
Difficult question: For ellipse, third law uses?
Show Answer
Answer: semi-major axis.
Explanation: This follows directly from Kepler's laws for motion under a central gravitational force.
JEE Main-style Question 39
Difficult question: If orbital radius becomes 4 times, period becomes?
Show Answer
Answer: 8 times.
Explanation: This follows directly from Kepler's laws for motion under a central gravitational force.
JEE Main-style Question 40
Difficult question: The central force in planetary motion is?
Show Answer
Answer: gravity. For a ratio problem, if a becomes 62 times, T becomes 63 times.
Explanation: This follows directly from Kepler's laws for motion under a central gravitational force.
JEE Main-style Question 41
Difficult question: Kepler's first law says planets move in?
Show Answer
Answer: elliptical orbits with Sun at one focus.
Explanation: This follows directly from Kepler's laws for motion under a central gravitational force.
JEE Main-style Question 42
Difficult question: Kepler's second law states?
Show Answer
Answer: equal areas are swept in equal time.
Explanation: This follows directly from Kepler's laws for motion under a central gravitational force.
JEE Main-style Question 43
Difficult question: Kepler's third law gives?
Show Answer
Answer: T2 proportional to a3. For a ratio problem, if a becomes 42 times, T becomes 43 times.
Explanation: This follows directly from Kepler's laws for motion under a central gravitational force.
JEE Main-style Question 44
Difficult question: At perihelion, a planet's speed is?
Show Answer
Answer: maximum.
Explanation: This follows directly from Kepler's laws for motion under a central gravitational force.
JEE Main-style Question 45
Difficult question: At aphelion, a planet's speed is?
Show Answer
Answer: minimum.
Explanation: This follows directly from Kepler's laws for motion under a central gravitational force.
JEE Main-style Question 46
Difficult question: Areal velocity is related to?
Show Answer
Answer: angular momentum conservation. For a ratio problem, if a becomes 22 times, T becomes 23 times.
Explanation: This follows directly from Kepler's laws for motion under a central gravitational force.
JEE Main-style Question 47
Difficult question: For circular orbit, T2 equals?
Show Answer
Answer: 4pi2r3/GM.
Explanation: This follows directly from Kepler's laws for motion under a central gravitational force.
JEE Main-style Question 48
Difficult question: For ellipse, third law uses?
Show Answer
Answer: semi-major axis.
Explanation: This follows directly from Kepler's laws for motion under a central gravitational force.
JEE Main-style Question 49
Difficult question: If orbital radius becomes 4 times, period becomes?
Show Answer
Answer: 8 times. For a ratio problem, if a becomes 52 times, T becomes 53 times.
Explanation: This follows directly from Kepler's laws for motion under a central gravitational force.
JEE Main-style Question 50
Difficult question: The central force in planetary motion is?
Show Answer
Answer: gravity.
Explanation: This follows directly from Kepler's laws for motion under a central gravitational force.
JEE Advanced Question Bank
These focus on Kepler's third law, areal velocity, angular momentum conservation, elliptical orbit concepts, satellite motion and central force.
JEE Advanced-style Question 1
Advanced question: Kepler's first law says planets move in?
Show Answer
Answer: elliptical orbits with Sun at one focus. For a ratio problem, if a becomes 22 times, T becomes 23 times.
Explanation: This follows directly from Kepler's laws for motion under a central gravitational force.
JEE Advanced-style Question 2
Advanced question: Kepler's second law states?
Show Answer
Answer: equal areas are swept in equal time.
Explanation: This follows directly from Kepler's laws for motion under a central gravitational force.
JEE Advanced-style Question 3
Advanced question: Kepler's third law gives?
Show Answer
Answer: T2 proportional to a3.
Explanation: This follows directly from Kepler's laws for motion under a central gravitational force.
JEE Advanced-style Question 4
Advanced question: At perihelion, a planet's speed is?
Show Answer
Answer: maximum. For a ratio problem, if a becomes 52 times, T becomes 53 times.
Explanation: This follows directly from Kepler's laws for motion under a central gravitational force.
JEE Advanced-style Question 5
Advanced question: At aphelion, a planet's speed is?
Show Answer
Answer: minimum.
Explanation: This follows directly from Kepler's laws for motion under a central gravitational force.
JEE Advanced-style Question 6
Advanced question: Areal velocity is related to?
Show Answer
Answer: angular momentum conservation.
Explanation: This follows directly from Kepler's laws for motion under a central gravitational force.
JEE Advanced-style Question 7
Advanced question: For circular orbit, T2 equals?
Show Answer
Answer: 4pi2r3/GM. For a ratio problem, if a becomes 32 times, T becomes 33 times.
Explanation: This follows directly from Kepler's laws for motion under a central gravitational force.
JEE Advanced-style Question 8
Advanced question: For ellipse, third law uses?
Show Answer
Answer: semi-major axis.
Explanation: This follows directly from Kepler's laws for motion under a central gravitational force.
JEE Advanced-style Question 9
Advanced question: If orbital radius becomes 4 times, period becomes?
Show Answer
Answer: 8 times.
Explanation: This follows directly from Kepler's laws for motion under a central gravitational force.
JEE Advanced-style Question 10
Advanced question: The central force in planetary motion is?
Show Answer
Answer: gravity. For a ratio problem, if a becomes 62 times, T becomes 63 times.
Explanation: This follows directly from Kepler's laws for motion under a central gravitational force.
JEE Advanced-style Question 11
Advanced question: Kepler's first law says planets move in?
Show Answer
Answer: elliptical orbits with Sun at one focus.
Explanation: This follows directly from Kepler's laws for motion under a central gravitational force.
JEE Advanced-style Question 12
Advanced question: Kepler's second law states?
Show Answer
Answer: equal areas are swept in equal time.
Explanation: This follows directly from Kepler's laws for motion under a central gravitational force.
JEE Advanced-style Question 13
Advanced question: Kepler's third law gives?
Show Answer
Answer: T2 proportional to a3. For a ratio problem, if a becomes 42 times, T becomes 43 times.
Explanation: This follows directly from Kepler's laws for motion under a central gravitational force.
JEE Advanced-style Question 14
Advanced question: At perihelion, a planet's speed is?
Show Answer
Answer: maximum.
Explanation: This follows directly from Kepler's laws for motion under a central gravitational force.
JEE Advanced-style Question 15
Advanced question: At aphelion, a planet's speed is?
Show Answer
Answer: minimum.
Explanation: This follows directly from Kepler's laws for motion under a central gravitational force.
JEE Advanced-style Question 16
Advanced question: Areal velocity is related to?
Show Answer
Answer: angular momentum conservation. For a ratio problem, if a becomes 22 times, T becomes 23 times.
Explanation: This follows directly from Kepler's laws for motion under a central gravitational force.
JEE Advanced-style Question 17
Advanced question: For circular orbit, T2 equals?
Show Answer
Answer: 4pi2r3/GM.
Explanation: This follows directly from Kepler's laws for motion under a central gravitational force.
JEE Advanced-style Question 18
Advanced question: For ellipse, third law uses?
Show Answer
Answer: semi-major axis.
Explanation: This follows directly from Kepler's laws for motion under a central gravitational force.
JEE Advanced-style Question 19
Advanced question: If orbital radius becomes 4 times, period becomes?
Show Answer
Answer: 8 times. For a ratio problem, if a becomes 52 times, T becomes 53 times.
Explanation: This follows directly from Kepler's laws for motion under a central gravitational force.
JEE Advanced-style Question 20
Advanced question: The central force in planetary motion is?
Show Answer
Answer: gravity.
Explanation: This follows directly from Kepler's laws for motion under a central gravitational force.
JEE Advanced-style Question 21
Advanced question: Kepler's first law says planets move in?
Show Answer
Answer: elliptical orbits with Sun at one focus.
Explanation: This follows directly from Kepler's laws for motion under a central gravitational force.
JEE Advanced-style Question 22
Advanced question: Kepler's second law states?
Show Answer
Answer: equal areas are swept in equal time. For a ratio problem, if a becomes 32 times, T becomes 33 times.
Explanation: This follows directly from Kepler's laws for motion under a central gravitational force.
JEE Advanced-style Question 23
Advanced question: Kepler's third law gives?
Show Answer
Answer: T2 proportional to a3.
Explanation: This follows directly from Kepler's laws for motion under a central gravitational force.
JEE Advanced-style Question 24
Advanced question: At perihelion, a planet's speed is?
Show Answer
Answer: maximum.
Explanation: This follows directly from Kepler's laws for motion under a central gravitational force.
JEE Advanced-style Question 25
Advanced question: At aphelion, a planet's speed is?
Show Answer
Answer: minimum. For a ratio problem, if a becomes 62 times, T becomes 63 times.
Explanation: This follows directly from Kepler's laws for motion under a central gravitational force.
JEE Advanced-style Question 26
Advanced question: Areal velocity is related to?
Show Answer
Answer: angular momentum conservation.
Explanation: This follows directly from Kepler's laws for motion under a central gravitational force.
JEE Advanced-style Question 27
Advanced question: For circular orbit, T2 equals?
Show Answer
Answer: 4pi2r3/GM.
Explanation: This follows directly from Kepler's laws for motion under a central gravitational force.
JEE Advanced-style Question 28
Advanced question: For ellipse, third law uses?
Show Answer
Answer: semi-major axis. For a ratio problem, if a becomes 42 times, T becomes 43 times.
Explanation: This follows directly from Kepler's laws for motion under a central gravitational force.
JEE Advanced-style Question 29
Advanced question: If orbital radius becomes 4 times, period becomes?
Show Answer
Answer: 8 times.
Explanation: This follows directly from Kepler's laws for motion under a central gravitational force.
JEE Advanced-style Question 30
Advanced question: The central force in planetary motion is?
Show Answer
Answer: gravity.
Explanation: This follows directly from Kepler's laws for motion under a central gravitational force.
JEE Advanced-style Question 31
Advanced question: Kepler's first law says planets move in?
Show Answer
Answer: elliptical orbits with Sun at one focus. For a ratio problem, if a becomes 22 times, T becomes 23 times.
Explanation: This follows directly from Kepler's laws for motion under a central gravitational force.
JEE Advanced-style Question 32
Advanced question: Kepler's second law states?
Show Answer
Answer: equal areas are swept in equal time.
Explanation: This follows directly from Kepler's laws for motion under a central gravitational force.
JEE Advanced-style Question 33
Advanced question: Kepler's third law gives?
Show Answer
Answer: T2 proportional to a3.
Explanation: This follows directly from Kepler's laws for motion under a central gravitational force.
JEE Advanced-style Question 34
Advanced question: At perihelion, a planet's speed is?
Show Answer
Answer: maximum. For a ratio problem, if a becomes 52 times, T becomes 53 times.
Explanation: This follows directly from Kepler's laws for motion under a central gravitational force.
JEE Advanced-style Question 35
Advanced question: At aphelion, a planet's speed is?
Show Answer
Answer: minimum.
Explanation: This follows directly from Kepler's laws for motion under a central gravitational force.
JEE Advanced-style Question 36
Advanced question: Areal velocity is related to?
Show Answer
Answer: angular momentum conservation.
Explanation: This follows directly from Kepler's laws for motion under a central gravitational force.
JEE Advanced-style Question 37
Advanced question: For circular orbit, T2 equals?
Show Answer
Answer: 4pi2r3/GM. For a ratio problem, if a becomes 32 times, T becomes 33 times.
Explanation: This follows directly from Kepler's laws for motion under a central gravitational force.
JEE Advanced-style Question 38
Advanced question: For ellipse, third law uses?
Show Answer
Answer: semi-major axis.
Explanation: This follows directly from Kepler's laws for motion under a central gravitational force.
JEE Advanced-style Question 39
Advanced question: If orbital radius becomes 4 times, period becomes?
Show Answer
Answer: 8 times.
Explanation: This follows directly from Kepler's laws for motion under a central gravitational force.
JEE Advanced-style Question 40
Advanced question: The central force in planetary motion is?
Show Answer
Answer: gravity. For a ratio problem, if a becomes 62 times, T becomes 63 times.
Explanation: This follows directly from Kepler's laws for motion under a central gravitational force.
JEE Advanced-style Question 41
Advanced question: Kepler's first law says planets move in?
Show Answer
Answer: elliptical orbits with Sun at one focus.
Explanation: This follows directly from Kepler's laws for motion under a central gravitational force.
JEE Advanced-style Question 42
Advanced question: Kepler's second law states?
Show Answer
Answer: equal areas are swept in equal time.
Explanation: This follows directly from Kepler's laws for motion under a central gravitational force.
JEE Advanced-style Question 43
Advanced question: Kepler's third law gives?
Show Answer
Answer: T2 proportional to a3. For a ratio problem, if a becomes 42 times, T becomes 43 times.
Explanation: This follows directly from Kepler's laws for motion under a central gravitational force.
JEE Advanced-style Question 44
Advanced question: At perihelion, a planet's speed is?
Show Answer
Answer: maximum.
Explanation: This follows directly from Kepler's laws for motion under a central gravitational force.
JEE Advanced-style Question 45
Advanced question: At aphelion, a planet's speed is?
Show Answer
Answer: minimum.
Explanation: This follows directly from Kepler's laws for motion under a central gravitational force.
JEE Advanced-style Question 46
Advanced question: Areal velocity is related to?
Show Answer
Answer: angular momentum conservation. For a ratio problem, if a becomes 22 times, T becomes 23 times.
Explanation: This follows directly from Kepler's laws for motion under a central gravitational force.
JEE Advanced-style Question 47
Advanced question: For circular orbit, T2 equals?
Show Answer
Answer: 4pi2r3/GM.
Explanation: This follows directly from Kepler's laws for motion under a central gravitational force.
JEE Advanced-style Question 48
Advanced question: For ellipse, third law uses?
Show Answer
Answer: semi-major axis.
Explanation: This follows directly from Kepler's laws for motion under a central gravitational force.
JEE Advanced-style Question 49
Advanced question: If orbital radius becomes 4 times, period becomes?
Show Answer
Answer: 8 times. For a ratio problem, if a becomes 52 times, T becomes 53 times.
Explanation: This follows directly from Kepler's laws for motion under a central gravitational force.
JEE Advanced-style Question 50
Advanced question: The central force in planetary motion is?
Show Answer
Answer: gravity.
Explanation: This follows directly from Kepler's laws for motion under a central gravitational force.
IB / IGCSE / A-Level Questions
25 IB Questions
- IB question 1: State or apply a key result from Kepler's laws.
Show Answer
Use the appropriate law: path is ellipse, areal velocity is constant, or T2 proportional to a3. Explain with the given orbit data. - IB question 2: State or apply a key result from Kepler's laws.
Show Answer
Use the appropriate law: path is ellipse, areal velocity is constant, or T2 proportional to a3. Explain with the given orbit data. - IB question 3: State or apply a key result from Kepler's laws.
Show Answer
Use the appropriate law: path is ellipse, areal velocity is constant, or T2 proportional to a3. Explain with the given orbit data. - IB question 4: State or apply a key result from Kepler's laws.
Show Answer
Use the appropriate law: path is ellipse, areal velocity is constant, or T2 proportional to a3. Explain with the given orbit data. - IB question 5: State or apply a key result from Kepler's laws.
Show Answer
Use the appropriate law: path is ellipse, areal velocity is constant, or T2 proportional to a3. Explain with the given orbit data. - IB question 6: State or apply a key result from Kepler's laws.
Show Answer
Use the appropriate law: path is ellipse, areal velocity is constant, or T2 proportional to a3. Explain with the given orbit data. - IB question 7: State or apply a key result from Kepler's laws.
Show Answer
Use the appropriate law: path is ellipse, areal velocity is constant, or T2 proportional to a3. Explain with the given orbit data. - IB question 8: State or apply a key result from Kepler's laws.
Show Answer
Use the appropriate law: path is ellipse, areal velocity is constant, or T2 proportional to a3. Explain with the given orbit data. - IB question 9: State or apply a key result from Kepler's laws.
Show Answer
Use the appropriate law: path is ellipse, areal velocity is constant, or T2 proportional to a3. Explain with the given orbit data. - IB question 10: State or apply a key result from Kepler's laws.
Show Answer
Use the appropriate law: path is ellipse, areal velocity is constant, or T2 proportional to a3. Explain with the given orbit data. - IB question 11: State or apply a key result from Kepler's laws.
Show Answer
Use the appropriate law: path is ellipse, areal velocity is constant, or T2 proportional to a3. Explain with the given orbit data. - IB question 12: State or apply a key result from Kepler's laws.
Show Answer
Use the appropriate law: path is ellipse, areal velocity is constant, or T2 proportional to a3. Explain with the given orbit data. - IB question 13: State or apply a key result from Kepler's laws.
Show Answer
Use the appropriate law: path is ellipse, areal velocity is constant, or T2 proportional to a3. Explain with the given orbit data. - IB question 14: State or apply a key result from Kepler's laws.
Show Answer
Use the appropriate law: path is ellipse, areal velocity is constant, or T2 proportional to a3. Explain with the given orbit data. - IB question 15: State or apply a key result from Kepler's laws.
Show Answer
Use the appropriate law: path is ellipse, areal velocity is constant, or T2 proportional to a3. Explain with the given orbit data. - IB question 16: State or apply a key result from Kepler's laws.
Show Answer
Use the appropriate law: path is ellipse, areal velocity is constant, or T2 proportional to a3. Explain with the given orbit data. - IB question 17: State or apply a key result from Kepler's laws.
Show Answer
Use the appropriate law: path is ellipse, areal velocity is constant, or T2 proportional to a3. Explain with the given orbit data. - IB question 18: State or apply a key result from Kepler's laws.
Show Answer
Use the appropriate law: path is ellipse, areal velocity is constant, or T2 proportional to a3. Explain with the given orbit data. - IB question 19: State or apply a key result from Kepler's laws.
Show Answer
Use the appropriate law: path is ellipse, areal velocity is constant, or T2 proportional to a3. Explain with the given orbit data. - IB question 20: State or apply a key result from Kepler's laws.
Show Answer
Use the appropriate law: path is ellipse, areal velocity is constant, or T2 proportional to a3. Explain with the given orbit data. - IB question 21: State or apply a key result from Kepler's laws.
Show Answer
Use the appropriate law: path is ellipse, areal velocity is constant, or T2 proportional to a3. Explain with the given orbit data. - IB question 22: State or apply a key result from Kepler's laws.
Show Answer
Use the appropriate law: path is ellipse, areal velocity is constant, or T2 proportional to a3. Explain with the given orbit data. - IB question 23: State or apply a key result from Kepler's laws.
Show Answer
Use the appropriate law: path is ellipse, areal velocity is constant, or T2 proportional to a3. Explain with the given orbit data. - IB question 24: State or apply a key result from Kepler's laws.
Show Answer
Use the appropriate law: path is ellipse, areal velocity is constant, or T2 proportional to a3. Explain with the given orbit data. - IB question 25: State or apply a key result from Kepler's laws.
Show Answer
Use the appropriate law: path is ellipse, areal velocity is constant, or T2 proportional to a3. Explain with the given orbit data.
25 IGCSE Questions
- IGCSE question 1: State or apply a key result from Kepler's laws.
Show Answer
Use the appropriate law: path is ellipse, areal velocity is constant, or T2 proportional to a3. Explain with the given orbit data. - IGCSE question 2: State or apply a key result from Kepler's laws.
Show Answer
Use the appropriate law: path is ellipse, areal velocity is constant, or T2 proportional to a3. Explain with the given orbit data. - IGCSE question 3: State or apply a key result from Kepler's laws.
Show Answer
Use the appropriate law: path is ellipse, areal velocity is constant, or T2 proportional to a3. Explain with the given orbit data. - IGCSE question 4: State or apply a key result from Kepler's laws.
Show Answer
Use the appropriate law: path is ellipse, areal velocity is constant, or T2 proportional to a3. Explain with the given orbit data. - IGCSE question 5: State or apply a key result from Kepler's laws.
Show Answer
Use the appropriate law: path is ellipse, areal velocity is constant, or T2 proportional to a3. Explain with the given orbit data. - IGCSE question 6: State or apply a key result from Kepler's laws.
Show Answer
Use the appropriate law: path is ellipse, areal velocity is constant, or T2 proportional to a3. Explain with the given orbit data. - IGCSE question 7: State or apply a key result from Kepler's laws.
Show Answer
Use the appropriate law: path is ellipse, areal velocity is constant, or T2 proportional to a3. Explain with the given orbit data. - IGCSE question 8: State or apply a key result from Kepler's laws.
Show Answer
Use the appropriate law: path is ellipse, areal velocity is constant, or T2 proportional to a3. Explain with the given orbit data. - IGCSE question 9: State or apply a key result from Kepler's laws.
Show Answer
Use the appropriate law: path is ellipse, areal velocity is constant, or T2 proportional to a3. Explain with the given orbit data. - IGCSE question 10: State or apply a key result from Kepler's laws.
Show Answer
Use the appropriate law: path is ellipse, areal velocity is constant, or T2 proportional to a3. Explain with the given orbit data. - IGCSE question 11: State or apply a key result from Kepler's laws.
Show Answer
Use the appropriate law: path is ellipse, areal velocity is constant, or T2 proportional to a3. Explain with the given orbit data. - IGCSE question 12: State or apply a key result from Kepler's laws.
Show Answer
Use the appropriate law: path is ellipse, areal velocity is constant, or T2 proportional to a3. Explain with the given orbit data. - IGCSE question 13: State or apply a key result from Kepler's laws.
Show Answer
Use the appropriate law: path is ellipse, areal velocity is constant, or T2 proportional to a3. Explain with the given orbit data. - IGCSE question 14: State or apply a key result from Kepler's laws.
Show Answer
Use the appropriate law: path is ellipse, areal velocity is constant, or T2 proportional to a3. Explain with the given orbit data. - IGCSE question 15: State or apply a key result from Kepler's laws.
Show Answer
Use the appropriate law: path is ellipse, areal velocity is constant, or T2 proportional to a3. Explain with the given orbit data. - IGCSE question 16: State or apply a key result from Kepler's laws.
Show Answer
Use the appropriate law: path is ellipse, areal velocity is constant, or T2 proportional to a3. Explain with the given orbit data. - IGCSE question 17: State or apply a key result from Kepler's laws.
Show Answer
Use the appropriate law: path is ellipse, areal velocity is constant, or T2 proportional to a3. Explain with the given orbit data. - IGCSE question 18: State or apply a key result from Kepler's laws.
Show Answer
Use the appropriate law: path is ellipse, areal velocity is constant, or T2 proportional to a3. Explain with the given orbit data. - IGCSE question 19: State or apply a key result from Kepler's laws.
Show Answer
Use the appropriate law: path is ellipse, areal velocity is constant, or T2 proportional to a3. Explain with the given orbit data. - IGCSE question 20: State or apply a key result from Kepler's laws.
Show Answer
Use the appropriate law: path is ellipse, areal velocity is constant, or T2 proportional to a3. Explain with the given orbit data. - IGCSE question 21: State or apply a key result from Kepler's laws.
Show Answer
Use the appropriate law: path is ellipse, areal velocity is constant, or T2 proportional to a3. Explain with the given orbit data. - IGCSE question 22: State or apply a key result from Kepler's laws.
Show Answer
Use the appropriate law: path is ellipse, areal velocity is constant, or T2 proportional to a3. Explain with the given orbit data. - IGCSE question 23: State or apply a key result from Kepler's laws.
Show Answer
Use the appropriate law: path is ellipse, areal velocity is constant, or T2 proportional to a3. Explain with the given orbit data. - IGCSE question 24: State or apply a key result from Kepler's laws.
Show Answer
Use the appropriate law: path is ellipse, areal velocity is constant, or T2 proportional to a3. Explain with the given orbit data. - IGCSE question 25: State or apply a key result from Kepler's laws.
Show Answer
Use the appropriate law: path is ellipse, areal velocity is constant, or T2 proportional to a3. Explain with the given orbit data.
25 A-Level Questions
- A-Level question 1: State or apply a key result from Kepler's laws.
Show Answer
Use the appropriate law: path is ellipse, areal velocity is constant, or T2 proportional to a3. Explain with the given orbit data. - A-Level question 2: State or apply a key result from Kepler's laws.
Show Answer
Use the appropriate law: path is ellipse, areal velocity is constant, or T2 proportional to a3. Explain with the given orbit data. - A-Level question 3: State or apply a key result from Kepler's laws.
Show Answer
Use the appropriate law: path is ellipse, areal velocity is constant, or T2 proportional to a3. Explain with the given orbit data. - A-Level question 4: State or apply a key result from Kepler's laws.
Show Answer
Use the appropriate law: path is ellipse, areal velocity is constant, or T2 proportional to a3. Explain with the given orbit data. - A-Level question 5: State or apply a key result from Kepler's laws.
Show Answer
Use the appropriate law: path is ellipse, areal velocity is constant, or T2 proportional to a3. Explain with the given orbit data. - A-Level question 6: State or apply a key result from Kepler's laws.
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Use the appropriate law: path is ellipse, areal velocity is constant, or T2 proportional to a3. Explain with the given orbit data. - A-Level question 7: State or apply a key result from Kepler's laws.
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Use the appropriate law: path is ellipse, areal velocity is constant, or T2 proportional to a3. Explain with the given orbit data. - A-Level question 8: State or apply a key result from Kepler's laws.
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Use the appropriate law: path is ellipse, areal velocity is constant, or T2 proportional to a3. Explain with the given orbit data. - A-Level question 9: State or apply a key result from Kepler's laws.
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Use the appropriate law: path is ellipse, areal velocity is constant, or T2 proportional to a3. Explain with the given orbit data. - A-Level question 10: State or apply a key result from Kepler's laws.
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Use the appropriate law: path is ellipse, areal velocity is constant, or T2 proportional to a3. Explain with the given orbit data. - A-Level question 11: State or apply a key result from Kepler's laws.
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Use the appropriate law: path is ellipse, areal velocity is constant, or T2 proportional to a3. Explain with the given orbit data. - A-Level question 12: State or apply a key result from Kepler's laws.
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Use the appropriate law: path is ellipse, areal velocity is constant, or T2 proportional to a3. Explain with the given orbit data. - A-Level question 13: State or apply a key result from Kepler's laws.
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Use the appropriate law: path is ellipse, areal velocity is constant, or T2 proportional to a3. Explain with the given orbit data. - A-Level question 14: State or apply a key result from Kepler's laws.
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Use the appropriate law: path is ellipse, areal velocity is constant, or T2 proportional to a3. Explain with the given orbit data. - A-Level question 15: State or apply a key result from Kepler's laws.
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Use the appropriate law: path is ellipse, areal velocity is constant, or T2 proportional to a3. Explain with the given orbit data. - A-Level question 16: State or apply a key result from Kepler's laws.
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Use the appropriate law: path is ellipse, areal velocity is constant, or T2 proportional to a3. Explain with the given orbit data. - A-Level question 17: State or apply a key result from Kepler's laws.
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Use the appropriate law: path is ellipse, areal velocity is constant, or T2 proportional to a3. Explain with the given orbit data. - A-Level question 18: State or apply a key result from Kepler's laws.
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Use the appropriate law: path is ellipse, areal velocity is constant, or T2 proportional to a3. Explain with the given orbit data. - A-Level question 19: State or apply a key result from Kepler's laws.
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Use the appropriate law: path is ellipse, areal velocity is constant, or T2 proportional to a3. Explain with the given orbit data. - A-Level question 20: State or apply a key result from Kepler's laws.
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Use the appropriate law: path is ellipse, areal velocity is constant, or T2 proportional to a3. Explain with the given orbit data. - A-Level question 21: State or apply a key result from Kepler's laws.
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Use the appropriate law: path is ellipse, areal velocity is constant, or T2 proportional to a3. Explain with the given orbit data. - A-Level question 22: State or apply a key result from Kepler's laws.
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Use the appropriate law: path is ellipse, areal velocity is constant, or T2 proportional to a3. Explain with the given orbit data. - A-Level question 23: State or apply a key result from Kepler's laws.
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Use the appropriate law: path is ellipse, areal velocity is constant, or T2 proportional to a3. Explain with the given orbit data. - A-Level question 24: State or apply a key result from Kepler's laws.
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Use the appropriate law: path is ellipse, areal velocity is constant, or T2 proportional to a3. Explain with the given orbit data. - A-Level question 25: State or apply a key result from Kepler's laws.
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Use the appropriate law: path is ellipse, areal velocity is constant, or T2 proportional to a3. Explain with the given orbit data.
Assertion Reason Questions
AR 1
Assertion: The Sun is at one focus of a planetary ellipse. Reason: Kepler's first law defines the orbit shape.
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AR 2
Assertion: A planet moves faster near perihelion. Reason: Equal areas must be swept in equal time.
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AR 3
Assertion: Areal velocity is constant. Reason: Angular momentum is conserved in central force motion.
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AR 4
Assertion: T2 is proportional to a3. Reason: All planets orbit the same central mass approximately.
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AR 5
Assertion: The centre of ellipse is not generally the Sun. Reason: The Sun occupies one focus.
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AR 6
Assertion: For circular orbit, a equals r. Reason: A circle is a special ellipse.
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AR 7
Assertion: A comet has changing speed. Reason: Its distance from the Sun changes.
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AR 8
Assertion: Satellite mass does not appear in Kepler's third law. Reason: It cancels in gravitational and centripetal equations.
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AR 9
Assertion: Perihelion speed is greater than aphelion speed. Reason: Angular momentum at apsides gives rv constant.
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AR 10
Assertion: Third law can estimate central mass. Reason: M = 4pi2a3/GT2.
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AR 11
Assertion: The Sun is at one focus of a planetary ellipse. Reason: Kepler's first law defines the orbit shape.
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AR 12
Assertion: A planet moves faster near perihelion. Reason: Equal areas must be swept in equal time.
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AR 13
Assertion: Areal velocity is constant. Reason: Angular momentum is conserved in central force motion.
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AR 14
Assertion: T2 is proportional to a3. Reason: All planets orbit the same central mass approximately.
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AR 15
Assertion: The centre of ellipse is not generally the Sun. Reason: The Sun occupies one focus.
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AR 16
Assertion: For circular orbit, a equals r. Reason: A circle is a special ellipse.
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AR 17
Assertion: A comet has changing speed. Reason: Its distance from the Sun changes.
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AR 18
Assertion: Satellite mass does not appear in Kepler's third law. Reason: It cancels in gravitational and centripetal equations.
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AR 19
Assertion: Perihelion speed is greater than aphelion speed. Reason: Angular momentum at apsides gives rv constant.
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AR 20
Assertion: Third law can estimate central mass. Reason: M = 4pi2a3/GT2.
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AR 21
Assertion: The Sun is at one focus of a planetary ellipse. Reason: Kepler's first law defines the orbit shape.
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AR 22
Assertion: A planet moves faster near perihelion. Reason: Equal areas must be swept in equal time.
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AR 23
Assertion: Areal velocity is constant. Reason: Angular momentum is conserved in central force motion.
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AR 24
Assertion: T2 is proportional to a3. Reason: All planets orbit the same central mass approximately.
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AR 25
Assertion: The centre of ellipse is not generally the Sun. Reason: The Sun occupies one focus.
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AR 26
Assertion: For circular orbit, a equals r. Reason: A circle is a special ellipse.
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AR 27
Assertion: A comet has changing speed. Reason: Its distance from the Sun changes.
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AR 28
Assertion: Satellite mass does not appear in Kepler's third law. Reason: It cancels in gravitational and centripetal equations.
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AR 29
Assertion: Perihelion speed is greater than aphelion speed. Reason: Angular momentum at apsides gives rv constant.
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AR 30
Assertion: Third law can estimate central mass. Reason: M = 4pi2a3/GT2.
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Case Study Questions
Planet Around Sun
Passage: A planet revolves around the Sun in an elliptical orbit with the Sun at one focus.
- Which law gives this path?
- Where is the Sun located?
- Which axis is used in third law?
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Answers: First law, one focus, semi-major axis. Explanation: Kepler's first law gives the shape and third law uses a.
Comet Orbit
Passage: A comet moves very fast near the Sun and slowly far from it.
- Name near point.
- Name far point.
- Which law explains speed change?
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Answers: Perihelion, aphelion, second law. Explanation: Equal areas in equal times require changing speed.
Satellite Around Earth
Passage: A satellite moves around Earth at radius r and period T.
- Write Kepler formula.
- How to find Earth mass?
- Does satellite mass appear?
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Answers: T2=4pi2r3/GM, M=4pi2r3/GT2, no.
Equal Area Law
Passage: A radius vector sweeps two equal shaded sectors in two equal time intervals.
- What stays constant?
- What is conserved?
- Is linear speed constant?
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Answers: Areal velocity, angular momentum, no for ellipse.
Third Law Data Table
Passage: Planet A has a=1 unit and T=1 year. Planet B has a=4 units.
- Find T of B.
- Find T2 ratio.
- Which law is used?
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Answers: T=8 years, T2 ratio=64, third law. Explanation: T ratio = 43/2.
Common Student Mistakes
Sun at Centre
Wrong: the Sun is at the centre of ellipse. Correct: Sun is at one focus.
Radius vs Semi-Major Axis
For elliptical orbit, third law uses semi-major axis a, not an arbitrary instantaneous radius.
Forgetting T2 proportional to a3
Period itself is proportional to a3/2, not a3.
Constant Speed Assumption
In an ellipse, speed is not constant. It is greater near perihelion.
Perihelion and Aphelion
Perihelion means nearest to Sun; aphelion means farthest from Sun.
Blind Circular Formula
v=sqrt(GM/r) is for circular orbit, not all points of an elliptical orbit.
Equal Area Meaning
Equal area law applies to equal time intervals, not equal distances.
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