Escape Velocity and Earth Satellites

Searching for a Physics Tutor? If Escape Velocity, Orbital Velocity, Satellites or NEET/JEE gravitation numericals are not clear, contact Kumar Sir.

Phone: +91-9958461445 | Email: kumarsirphysics@gmail.com | Website: kumarphysicsclasses.com

WhatsApp Kumar SirVisit WebsiteEmail Kumar Sir
v

Escape Velocity and Earth Satellites

Master escape velocity, orbital velocity, satellite motion, time period, geostationary satellite, polar satellite, applications, numericals and PYQs.

CBSENEETJEE MainJEE AdvancedIBIGCSEA-Level
Earth modelescape velocityred satellite

Escape Velocity

Escape velocity is the minimum speed required for a body to escape Earth's gravitational field and reach infinity with zero speed. It is independent of the mass of the escaping body because mass cancels in the energy equation.

1/2 mve2 = GMm/R
ve = sqrt(2GM/R)
ve = sqrt(2gR)

Launch From Earth

Rv escape

Energy Meaning

At surface, gravitational potential energy is -GMm/R. Escape requires kinetic energy equal to GMm/R so that total energy becomes zero at infinity.

Mass Independence

Both kinetic energy and gravitational potential energy contain m, so projectile mass cancels while deriving ve.

Orbital Velocity

Orbital velocity is the speed required for a satellite to move in a circular orbit. Gravity provides the centripetal force.

GMm/r2 = mv2/r
vo = sqrt(GM/r)
Near Earth: vo = sqrt(gR)
ve = sqrt2 vo

Orbit Diagram

rtangent v

Key Comparison

Escape speed near Earth is sqrt2 times orbital speed. This relation is frequently used in NEET and JEE ratio questions.

Exam Tip

Always use orbital radius r from Earth's centre. For height h above surface, r = R + h.

Satellite Motion

A natural satellite is a naturally orbiting body such as the Moon. An artificial satellite is launched by humans. In circular orbit, velocity is tangential and acceleration is toward Earth's centre.

Earth and Satellite

velocityacceleration

Weightlessness

A satellite has gravity acting on it. Weightlessness occurs because the satellite and astronaut are in continuous free fall, so normal reaction becomes zero.

Circular Orbit

Gravity bends the path continuously. Without tangential velocity, the body would fall; with correct speed, it keeps missing Earth.

Time Period of Satellite

The time period is the time taken to complete one revolution.

T = 2pi r/v
T = 2pi sqrt(r3/GM)
For height h: r = R + h, T = 2pi sqrt((R+h)3/GM)

Formula Card

Time period increases as orbital radius increases. Higher satellites move slower but travel larger orbits.

Solved Example

If orbital radius becomes 4 times, how does T change?

Show Answer
T is proportional to r3/2. New T = 43/2T = 8T.

Height Reminder

For a satellite at height h, what is r?

Show Answer
r=R+h. Common mistake: using h alone in formulas.

Geostationary Satellite

A geostationary satellite has time period 24 hours, moves in an equatorial orbit, and appears stationary from Earth. It is widely used for communication.

Height approx 35,786 km above Earth
Orbit radius approx 42,164 km from Earth's centre

Geostationary Orbit

equatorial plane24 hour satellite

Use

Communication, television broadcast, weather monitoring and fixed-region services. It must orbit in the equatorial plane in the same direction as Earth's rotation.

Polar Satellite

A polar satellite passes over the poles, usually in a low altitude orbit. It is useful for Earth observation, weather imaging, mapping, defence and remote sensing.

Polar Orbit

red satellitepolar path

Exam Point

Geostationary satellites stay above the equator. Polar satellites pass near both poles and scan different Earth regions as Earth rotates below them.

Energy of Satellite

For a satellite in circular orbit, kinetic energy is positive, potential energy is negative, and total energy is negative. Binding energy is the energy required to remove the satellite from orbit to infinity.

Kinetic Energy

K = GMm/2r

Potential Energy

U = -GMm/r

Total and Binding Energy

E = -GMm/2r

BE = GMm/2r

QuantitySignMeaning
Kinetic energyPositiveEnergy due to orbital motion.
Potential energyNegativeBound gravitational interaction.
Total energyNegativeSatellite is bound to Earth.
Binding energyPositiveEnergy needed for escape from orbit.

Applications

1. Communication Satellites

Concept: Relay signals over large regions.

Formula: T=24 h for geostationary orbit.

Exam Tip: Equatorial orbit is required.

2. Weather Satellites

Concept: Monitor clouds and storms.

Formula: v=sqrt(GM/r).

Exam Tip: Often polar or geostationary depending purpose.

3. GPS Satellites

Concept: Navigation using timing signals.

Formula: T=2pi sqrt(r3/GM).

Exam Tip: Not geostationary.

4. Remote Sensing

Concept: Observe Earth's surface.

Formula: r=R+h.

Exam Tip: Use orbital radius, not height.

5. Defence Satellites

Concept: Surveillance and secure communication.

Formula: v=sqrt(GM/r).

Exam Tip: Lower orbit gives shorter period.

6. Space Missions

Concept: Launch energy must exceed binding.

Formula: ve=sqrt(2GM/R).

Exam Tip: Escape speed ignores projectile mass.

7. Television Broadcasting

Concept: Fixed dishes use geostationary satellites.

Formula: T=24 h.

Exam Tip: Appears stationary.

8. Internet Satellites

Concept: Networks of satellites provide data links.

Formula: T depends on r3/2.

Exam Tip: Lower orbit reduces delay.

9. Earth Observation

Concept: Imaging land, ocean and atmosphere.

Formula: v=sqrt(GM/(R+h)).

Exam Tip: Polar orbits cover global surface.

10. Navigation

Concept: Position found from multiple satellite signals.

Formula: orbital time follows Kepler relation.

Exam Tip: Needs accurate timing.

Important Graphs

Escape Velocity vs Radius

rve

ve decreases as 1/sqrt(r): steep fall first, then it flattens.

Orbital Velocity vs Radius

rvo

vo also decreases as 1/sqrt(r), with the same curve shape.

Time Period vs Radius

rT

T increases as r3/2, so the graph curves upward.

Satellite Total Energy vs Radius

rE0

E = -GMm/2r is negative and approaches zero from below.

Potential Energy vs Radius

rU0

U = -GMm/r is negative and approaches zero from below.

Important Formula Table

ConceptFormulaMeaningExam Tip
Escape velocityve=sqrt(2GM/R)Minimum speed to escape from surface.Independent of projectile mass.
Escape velocity using gve=sqrt(2gR)Near Earth relation.Use only near surface.
Orbital velocityvo=sqrt(GM/r)Circular orbit speed.Use r from centre.
Relationve=sqrt2 voAt same radius.Common MCQ.
Time periodT=2pi sqrt(r3/GM)One revolution time.T proportional to r3/2.
Radius at height hr=R+hOrbital radius.Never use h alone.
Satellite KEK=GMm/2rPositive energy.Half magnitude of PE.
Satellite PEU=-GMm/rNegative energy.Bound state.
Total energyE=-GMm/2rNegative total.Bound circular orbit.
Binding energyBE=GMm/2rEnergy needed to escape orbit.Positive magnitude.
Geostationary heightabout 35,786 kmAbove Earth surface.Equatorial, 24 h.
Polar satellitePasses over polesEarth observation.Not stationary.

Searching for a Physics Tutor? If Escape Velocity, Orbital Velocity, Satellites or NEET/JEE gravitation numericals are not clear, contact Kumar Sir.

Phone: +91-9958461445 | Email: kumarsirphysics@gmail.com | Website: kumarphysicsclasses.com

WhatsApp Kumar SirVisit WebsiteEmail Kumar Sir

High-Quality Solved Numericals

CBSE Numerical

Question: Find escape speed in terms of g and R.

Show Answer

Given: g=GM/R2. Formula: ve=sqrt(2GM/R). Calculation: GM=gR2, so ve=sqrt(2gR). Final Answer: sqrt(2gR). Exam Tip: Replace GM carefully. Common Mistake: Writing sqrt(gR).

NEET Numerical

Question: If orbital speed near Earth is 7.9 km/s, escape speed is?

Show Answer

Formula: ve=sqrt2 vo. Calculation: 1.414 x 7.9 = 11.2 km/s. Final Answer: 11.2 km/s. Tip: Same radius relation. Mistake: Doubling speed.

JEE Main Numerical

Question: Radius of orbit becomes 4 times. Find new orbital velocity.

Show Answer

v is proportional to 1/sqrt(r). If r becomes 4r, v becomes v/2. Final answer: half.

JEE Advanced Numerical

Question: Energy needed for a circular satellite to escape from orbit radius r.

Show Answer

Total energy in orbit is -GMm/(2r). Escape threshold is 0. Required energy = GMm/(2r). This is binding energy.

IB Numerical

Question: If mass is 100 kg and g=10, R=6.4 x 106 m, estimate escape energy.

Show Answer
E=GMm/R=mgR=100 x 10 x 6.4 x 106=6.4 x 109 J.

IGCSE Numerical

Question: A satellite takes 24 hours and appears fixed. Name it.

Show Answer
Geostationary satellite. It orbits in equatorial plane with Earth's rotation.

A-Level Numerical

Question: If orbital radius doubles, how does time period change?

Show Answer
T proportional to r3/2. New T=23/2T=2sqrt2 T.

NEET Question Bank

Authentic years are mentioned only when known; otherwise these are NEET exam-style questions.

NEET Exam-style Question 1

Escape velocity formula from Earth surface?

Show Answer
sqrt(2GM/R).

NEET Exam-style Question 2

Escape velocity using g?

Show Answer
sqrt(2gR).

NEET Exam-style Question 3

Orbital velocity formula?

Show Answer
sqrt(GM/r).

NEET Exam-style Question 4

Near Earth orbital velocity?

Show Answer
sqrt(gR).

NEET Exam-style Question 5

Relation between escape and orbital velocity?

Show Answer
ve=sqrt2 vo.

NEET Exam-style Question 6

Escape velocity depends on projectile mass?

Show Answer
No.

NEET Exam-style Question 7

Orbital radius for height h?

Show Answer
r=R+h.

NEET Exam-style Question 8

Gravity provides what in circular orbit?

Show Answer
Centripetal force.

NEET Exam-style Question 9

Time period formula?

Show Answer
T=2pi sqrt(r3/GM).

NEET Exam-style Question 10

Geostationary time period?

Show Answer
24 hours.

NEET Exam-style Question 11

Geostationary orbit plane?

Show Answer
Equatorial plane.

NEET Exam-style Question 12

Geostationary height approximately?

Show Answer
35,786 km above Earth.

NEET Exam-style Question 13

Geostationary radius approximately?

Show Answer
42,164 km from Earth's centre.

NEET Exam-style Question 14

Polar satellite passes over?

Show Answer
Poles.

NEET Exam-style Question 15

Polar satellite use?

Show Answer
Earth observation and remote sensing.

NEET Exam-style Question 16

Satellite kinetic energy?

Show Answer
GMm/(2r).

NEET Exam-style Question 17

Satellite potential energy?

Show Answer
-GMm/r.

NEET Exam-style Question 18

Satellite total energy?

Show Answer
-GMm/(2r).

NEET Exam-style Question 19

Binding energy?

Show Answer
GMm/(2r).

NEET Exam-style Question 20

Is satellite gravity zero?

Show Answer
No.

NEET Exam-style Question 21

Weightlessness in satellite due to?

Show Answer
Continuous free fall.

NEET Exam-style Question 22

If r doubles, orbital velocity becomes?

Show Answer
v/sqrt2.

NEET Exam-style Question 23

If r becomes 4r, orbital velocity?

Show Answer
v/2.

NEET Exam-style Question 24

If r doubles, escape velocity from that radius?

Show Answer
v/sqrt2.

NEET Exam-style Question 25

If r doubles, time period?

Show Answer
2sqrt2 times.

NEET Exam-style Question 26

If r becomes 4r, time period?

Show Answer
8 times.

NEET Exam-style Question 27

Satellite PE is how many times KE?

Show Answer
U=-2K.

NEET Exam-style Question 28

Total energy in terms of KE?

Show Answer
E=-K.

NEET Exam-style Question 29

Communication satellite commonly?

Show Answer
Geostationary.

NEET Exam-style Question 30

Weather satellite may be?

Show Answer
Polar or geostationary depending purpose.

NEET Exam-style Question 31

Satellite velocity direction?

Show Answer
Tangential.

NEET Exam-style Question 32

Satellite acceleration direction?

Show Answer
Towards Earth's centre.

NEET Exam-style Question 33

Minimum launch speed for escape called?

Show Answer
Escape velocity.

NEET Exam-style Question 34

Total energy at escape threshold?

Show Answer
Zero.

NEET Exam-style Question 35

If planet mass doubles, escape velocity?

Show Answer
sqrt2 times.

NEET Exam-style Question 36

If planet radius doubles, escape velocity?

Show Answer
1/sqrt2 times.

NEET Exam-style Question 37

If planet mass and radius double, escape velocity?

Show Answer
Unchanged.

NEET Exam-style Question 38

If planet mass and radius double, orbital velocity near surface?

Show Answer
Unchanged.

NEET Exam-style Question 39

For a low orbit, r is approximately?

Show Answer
R.

NEET Exam-style Question 40

For height h, common mistake?

Show Answer
Using h instead of R+h.

NEET Exam-style Question 41

Natural satellite of Earth?

Show Answer
Moon.

NEET Exam-style Question 42

Artificial satellite is?

Show Answer
Human-made orbiting object.

NEET Exam-style Question 43

Escape speed from orbit radius r?

Show Answer
sqrt(2GM/r).

NEET Exam-style Question 44

Orbital speed from radius r?

Show Answer
sqrt(GM/r).

NEET Exam-style Question 45

Which satellite appears fixed?

Show Answer
Geostationary satellite.

NEET Exam-style Question 46

Which satellite scans Earth strip by strip?

Show Answer
Polar satellite.

NEET Exam-style Question 47

Satellite total energy sign?

Show Answer
Negative.

NEET Exam-style Question 48

Binding energy sign?

Show Answer
Positive magnitude.

NEET Exam-style Question 49

Does escape speed depend on atmosphere?

Show Answer
Ideal formula ignores atmosphere.

NEET Exam-style Question 50

Most important radius rule?

Show Answer
Use distance from Earth's centre.

JEE Main Question Bank

JEE Main 1

Derive vo from force balance.

Show Answer
GMm/r2=mv2/r gives v=sqrt(GM/r).

JEE Main 2

Derive ve from energy.

Show Answer
1/2 mv2=GMm/R gives v=sqrt(2GM/R).

JEE Main 3

At same radius, ve/vo?

Show Answer
sqrt2.

JEE Main 4

If r=9R, vo compared to near surface?

Show Answer
v/3.

JEE Main 5

If r=9R, T compared to near-surface same M?

Show Answer
27 times.

JEE Main 6

Binding energy of circular satellite?

Show Answer
GMm/(2r).

JEE Main 7

Energy to shift satellite from r to 2r circular orbits?

Show Answer
E2-E1=-GMm/(4r)+GMm/(2r)=GMm/(4r).

JEE Main 8

Geostationary angular speed?

Show Answer
Same as Earth's rotation angular speed.

JEE Main 9

Can geostationary satellite be polar?

Show Answer
No, it must be equatorial.

JEE Main 10

Polar satellite time period generally?

Show Answer
Much less than 24 h for low Earth orbit.

JEE Main 11

If orbital velocity is v, kinetic energy?

Show Answer
K=1/2 mv2=GMm/(2r).

JEE Main 12

If U=-100 J, K for circular orbit?

Show Answer
K=50 J.

JEE Main 13

If U=-100 J, total energy?

Show Answer
E=-50 J.

JEE Main 14

If total energy is -80 J, binding energy?

Show Answer
80 J.

JEE Main 15

Escape speed from circular orbit in terms of orbital speed?

Show Answer
sqrt2 vo.

JEE Main 16

Speed increment to escape from circular orbit?

Show Answer
(sqrt2-1)vo.

JEE Main 17

Time period proportionality?

Show Answer
T proportional to r3/2.

JEE Main 18

v proportionality?

Show Answer
v proportional to r-1/2.

JEE Main 19

E proportionality?

Show Answer
E proportional to -1/r.

JEE Main 20

BE proportionality?

Show Answer
BE proportional to 1/r.

JEE Main 21

At h=R, orbital radius?

Show Answer
2R.

JEE Main 22

At h=R, orbital speed relative to surface orbit?

Show Answer
1/sqrt2 times.

JEE Main 23

At h=R, escape speed relative to surface escape?

Show Answer
1/sqrt2 times.

JEE Main 24

At h=R, time period ratio?

Show Answer
2sqrt2.

JEE Main 25

If T becomes 8T, r becomes?

Show Answer
4r.

JEE Main 26

If v becomes v/3, r becomes?

Show Answer
9r.

JEE Main 27

If BE halves, r becomes?

Show Answer
2r.

JEE Main 28

Which satellite is used for fixed TV dish?

Show Answer
Geostationary satellite.

JEE Main 29

Which satellite for global scanning?

Show Answer
Polar satellite.

JEE Main 30

Can satellite be at rest in orbit?

Show Answer
No, it needs tangential velocity.

JEE Main 31

Why mass cancels in orbital speed?

Show Answer
m appears in both gravitational and centripetal force.

JEE Main 32

Why mass cancels in escape speed?

Show Answer
m appears in both kinetic energy and potential energy.

JEE Main 33

For same density planets, surface escape speed proportional to?

Show Answer
R, because M proportional R3.

JEE Main 34

For same density planets, surface orbital speed proportional to?

Show Answer
R.

JEE Main 35

For same M and doubled R, surface ve?

Show Answer
v/sqrt2.

JEE Main 36

For same R and doubled M, surface ve?

Show Answer
sqrt2 v.

JEE Main 37

For same R and doubled M, T at same r?

Show Answer
T/sqrt2.

JEE Main 38

Satellite acceleration?

Show Answer
GM/r2 toward centre.

JEE Main 39

Satellite speed direction?

Show Answer
Tangent to orbit.

JEE Main 40

Force direction?

Show Answer
Toward Earth's centre.

JEE Main 41

What happens if speed below orbital speed?

Show Answer
Satellite moves to lower path or falls, depending conditions.

JEE Main 42

What if speed equals escape speed?

Show Answer
It just escapes with zero speed at infinity.

JEE Main 43

What if launch speed exceeds escape speed?

Show Answer
It escapes with positive speed at infinity.

JEE Main 44

Total energy for escape threshold?

Show Answer
Zero.

JEE Main 45

Total energy for bound circular orbit?

Show Answer
Negative.

JEE Main 46

GPS satellites are primarily for?

Show Answer
Navigation.

JEE Main 47

Remote sensing satellites commonly use?

Show Answer
Polar or near-polar orbits.

JEE Main 48

Geostationary satellite appears fixed because?

Show Answer
Same angular speed as Earth and equatorial orbit.

JEE Main 49

Satellite energy becomes less negative at larger r?

Show Answer
Yes, approaches zero.

JEE Main 50

Most common JEE radius error?

Show Answer
Using h instead of R+h.

JEE Advanced Question Bank

These focus on satellite energy, escape velocity, orbital velocity, geostationary orbit, energy and angular momentum.

JEE Advanced 1

Derive circular satellite total energy.

Show Answer
From v2=GM/r, K=GMm/(2r), U=-GMm/r, so E=-GMm/(2r).

JEE Advanced 2

Energy needed to escape from circular orbit.

Show Answer
Add GMm/(2r), equal to binding energy.

JEE Advanced 3

Boost speed from circular orbit to escape.

Show Answer
Delta v=(sqrt2-1)sqrt(GM/r).

JEE Advanced 4

Angular momentum of circular satellite?

Show Answer
L=mvr=m sqrt(GMr).

JEE Advanced 5

If radius quadruples, angular momentum changes?

Show Answer
L proportional sqrt(r), so doubles.

JEE Advanced 6

If radius quadruples, total energy?

Show Answer
E becomes E/4 in magnitude, less negative.

JEE Advanced 7

If kinetic energy is K, total energy?

Show Answer
E=-K.

JEE Advanced 8

If potential energy is U, total energy?

Show Answer
E=U/2.

JEE Advanced 9

If total energy is E, potential energy?

Show Answer
U=2E.

JEE Advanced 10

If total energy is E, kinetic energy?

Show Answer
K=-E.

JEE Advanced 11

Find geostationary radius expression.

Show Answer
Set T=24 h in T=2pi sqrt(r3/GM), giving r=(GMT2/4pi2)1/3.

JEE Advanced 12

Why geostationary orbit cannot be inclined?

Show Answer
Inclined orbit moves north-south in sky; it will not appear fixed.

JEE Advanced 13

Why polar satellites cover whole Earth over time?

Show Answer
They pass over poles while Earth rotates beneath them.

JEE Advanced 14

If satellite height small compared to R, approximate orbital speed?

Show Answer
v approx sqrt(gR) with small corrections.

JEE Advanced 15

Escape energy from surface using g?

Show Answer
GMm/R=mgR.

JEE Advanced 16

Escape velocity from surface using density rho and radius R?

Show Answer
M=(4/3)pi rho R3, so v=sqrt(8pi G rho R2/3).

JEE Advanced 17

Same density planet radius doubled, escape speed?

Show Answer
Doubles.

JEE Advanced 18

Same density planet radius doubled, orbital speed near surface?

Show Answer
Doubles.

JEE Advanced 19

Satellite in circular orbit has radial velocity?

Show Answer
Zero.

JEE Advanced 20

Satellite acceleration is perpendicular to velocity?

Show Answer
Yes, in circular orbit.

JEE Advanced 21

Work by gravity in one circular orbit?

Show Answer
Zero because force is radial and displacement tangential.

JEE Advanced 22

Change in kinetic energy over one circular orbit?

Show Answer
Zero.

JEE Advanced 23

If satellite moved to higher circular orbit, energy change sign?

Show Answer
Positive, energy becomes less negative.

JEE Advanced 24

If satellite moved to lower circular orbit, energy change sign?

Show Answer
Negative, energy decreases.

JEE Advanced 25

At what radius is orbital velocity half surface orbital velocity?

Show Answer
r=4R.

JEE Advanced 26

At what radius is escape speed half surface escape speed?

Show Answer
r=4R.

JEE Advanced 27

At what radius is time period 8 times surface orbit period?

Show Answer
r=4R.

JEE Advanced 28

If orbital radius is R+h and speed is given, find M.

Show Answer
From v2=GM/(R+h), M=v2(R+h)/G.

JEE Advanced 29

If T and r are known, find M.

Show Answer
M=4pi2r3/(GT2).

JEE Advanced 30

Satellite orbit gives planet mass how?

Show Answer
Use Kepler relation T2=4pi2r3/GM.

JEE Advanced 31

What happens to total energy if speed at circular orbit is raised to escape speed?

Show Answer
Total energy becomes zero.

JEE Advanced 32

If speed exceeds escape speed, total energy?

Show Answer
Positive.

JEE Advanced 33

If speed below escape but above circular at same radius?

Show Answer
Bound elliptical orbit in ideal two-body model.

JEE Advanced 34

Minimum energy to put mass into circular orbit from surface ignoring losses?

Show Answer
Compare final E=-GMm/(2R) with initial rest energy -GMm/R; add GMm/(2R).

JEE Advanced 35

Why real launch energy is higher?

Show Answer
Atmosphere, Earth rotation, engine inefficiency and trajectory losses.

JEE Advanced 36

Does satellite inside orbit feel gravity?

Show Answer
Yes, gravity supplies centripetal acceleration.

JEE Advanced 37

Why astronaut feels weightless?

Show Answer
Normal reaction is zero during free fall orbit.

JEE Advanced 38

What is satellite apparent weight?

Show Answer
Zero inside freely falling satellite cabin.

JEE Advanced 39

Can geostationary satellite be above Delhi latitude?

Show Answer
No, it must be above equator.

JEE Advanced 40

Polar satellite angular momentum direction changes relative to Earth?

Show Answer
Its orbital plane is near fixed inertially while Earth rotates beneath.

JEE Advanced 41

Energy graph E vs r for circular orbit shape?

Show Answer
Negative curve approaching zero as r increases.

JEE Advanced 42

Potential energy graph U vs r is compared to E?

Show Answer
U=2E for circular orbit.

JEE Advanced 43

Binding energy graph vs r?

Show Answer
Positive curve decreasing as 1/r.

JEE Advanced 44

Ratio K:|U|:|E|?

Show Answer
1:2:1.

JEE Advanced 45

If K=200 J, U and E?

Show Answer
U=-400 J, E=-200 J.

JEE Advanced 46

If BE=300 J, E?

Show Answer
E=-300 J.

JEE Advanced 47

If BE=300 J, U?

Show Answer
U=-600 J.

JEE Advanced 48

For launch from radius r, escape energy?

Show Answer
GMm/r.

JEE Advanced 49

For circular orbit at radius r, escape energy?

Show Answer
GMm/(2r).

JEE Advanced 50

Main advanced trap?

Show Answer
Using height h instead of orbital radius R+h and mixing escape energy from surface with binding energy from orbit.

IB / IGCSE / A-Level Questions

25 IB Questions

  1. Define escape velocity.
    Show Answer
    Minimum speed to escape gravitational field.
  2. Formula for escape velocity?
    Show Answer
    sqrt(2GM/R).
  3. Define orbital velocity.
    Show Answer
    Speed for circular orbit.
  4. Formula for orbital velocity?
    Show Answer
    sqrt(GM/r).
  5. Relation between speeds?
    Show Answer
    ve=sqrt2 vo.
  6. Time period formula?
    Show Answer
    2pi sqrt(r3/GM).
  7. What is geostationary?
    Show Answer
    24 h equatorial satellite appearing fixed.
  8. What is polar satellite?
    Show Answer
    Satellite passing over poles.
  9. Satellite KE?
    Show Answer
    GMm/(2r).
  10. Satellite PE?
    Show Answer
    -GMm/r.
  11. Total energy?
    Show Answer
    -GMm/(2r).
  12. Binding energy?
    Show Answer
    GMm/(2r).
  13. Why weightless?
    Show Answer
    Free fall.
  14. Is gravity zero?
    Show Answer
    No.
  15. Use r=R+h?
    Show Answer
    Yes for height h.
  16. Orbit force source?
    Show Answer
    Gravity.
  17. Velocity direction?
    Show Answer
    Tangent.
  18. Acceleration direction?
    Show Answer
    Radial inward.
  19. Communication satellite type?
    Show Answer
    Geostationary.
  20. Remote sensing type?
    Show Answer
    Polar.
  21. Escape total energy?
    Show Answer
    Zero at threshold.
  22. Bound orbit energy?
    Show Answer
    Negative.
  23. Mass dependence of escape speed?
    Show Answer
    Independent of projectile mass.
  24. Graph T vs r?
    Show Answer
    Increasing.
  25. Graph v vs r?
    Show Answer
    Decreasing.

25 IGCSE Questions

  1. What is a satellite?
    Show Answer
    Object orbiting a planet.
  2. Natural satellite of Earth?
    Show Answer
    Moon.
  3. Artificial satellite?
    Show Answer
    Human-made satellite.
  4. What keeps satellite in orbit?
    Show Answer
    Gravity.
  5. What is escape velocity?
    Show Answer
    Speed to escape gravity.
  6. What is orbit?
    Show Answer
    Path around a body.
  7. What is geostationary satellite?
    Show Answer
    Appears fixed above Earth.
  8. Time period?
    Show Answer
    24 hours.
  9. Use of geostationary?
    Show Answer
    Communication.
  10. Use of polar satellite?
    Show Answer
    Earth observation.
  11. Satellite velocity direction?
    Show Answer
    Tangent.
  12. Acceleration direction?
    Show Answer
    Towards centre.
  13. Does satellite fall?
    Show Answer
    It is continuously falling around Earth.
  14. Weightless means?
    Show Answer
    No support force.
  15. Gravity zero in satellite?
    Show Answer
    No.
  16. TV broadcasting satellite?
    Show Answer
    Geostationary.
  17. Weather satellite?
    Show Answer
    Weather monitoring satellite.
  18. GPS use?
    Show Answer
    Navigation.
  19. Orbit line in diagram should be?
    Show Answer
    Dark black in this page.
  20. Satellite object color here?
    Show Answer
    Red for visibility.
  21. Escape speed depends on mass?
    Show Answer
    No.
  22. Higher orbit speed is?
    Show Answer
    Lower.
  23. Higher orbit period is?
    Show Answer
    Longer.
  24. Polar passes over?
    Show Answer
    Poles.
  25. Common mistake?
    Show Answer
    Using height instead of orbital radius.

25 A-Level Questions

  1. Derive orbital speed.
    Show Answer
    Equate gravity to centripetal force.
  2. Derive escape speed.
    Show Answer
    Use energy conservation.
  3. Derive time period.
    Show Answer
    T=2pi r/v and v=sqrt(GM/r).
  4. Derive satellite energy.
    Show Answer
    K+U=-GMm/(2r).
  5. Binding energy?
    Show Answer
    GMm/(2r).
  6. Geostationary radius expression?
    Show Answer
    (GMT2/4pi2)1/3.
  7. Escape from orbit energy?
    Show Answer
    GMm/(2r).
  8. Escape from surface energy?
    Show Answer
    GMm/R.
  9. Angular momentum?
    Show Answer
    m sqrt(GMr).
  10. Speed boost to escape?
    Show Answer
    (sqrt2-1)vo.
  11. Why geostationary equatorial?
    Show Answer
    To remain above same point.
  12. Why polar useful?
    Show Answer
    Global coverage as Earth rotates.
  13. Energy sign in orbit?
    Show Answer
    Negative.
  14. Escape sign?
    Show Answer
    Total energy zero at threshold.
  15. r if T doubles?
    Show Answer
    r becomes 22/3r.
  16. r if v halves?
    Show Answer
    4r.
  17. r if BE halves?
    Show Answer
    2r.
  18. Same density escape scaling?
    Show Answer
    Proportional to R.
  19. Same mass radius scaling?
    Show Answer
    v proportional to 1/sqrt(R).
  20. Satellite force work in circular orbit?
    Show Answer
    Zero.
  21. Does speed change in circular orbit?
    Show Answer
    No, direction changes.
  22. Gravity as centripetal?
    Show Answer
    GMm/r2=mv2/r.
  23. Escape condition energy?
    Show Answer
    E at least zero.
  24. Bound orbit condition?
    Show Answer
    E negative.
  25. Advanced trap?
    Show Answer
    Mixing h and r.

Assertion Reason Questions

AR 1

Assertion: Escape velocity is independent of projectile mass. Reason: Mass cancels in energy equation.

Show Answer
Both true and reason explains assertion.

AR 2

Assertion: Orbital velocity is tangential. Reason: Centripetal acceleration is radial.

Show Answer
Both true and reason supports circular motion.

AR 3

Assertion: Satellite has zero gravity. Reason: Astronauts are weightless.

Show Answer
Assertion false; reason true in apparent-weight sense.

AR 4

Assertion: ve=sqrt2 vo. Reason: Escape energy is twice circular kinetic energy at same radius.

Show Answer
Both true and reason explains assertion.

AR 5

Assertion: Geostationary satellite has 24 h period. Reason: It matches Earth's rotation.

Show Answer
Both true and reason explains assertion.

AR 6

Assertion: Geostationary can be polar. Reason: Polar orbit passes over poles.

Show Answer
Assertion false; reason true.

AR 7

Assertion: Polar satellites are useful for Earth observation. Reason: Earth rotates below their orbital plane.

Show Answer
Both true and reason explains assertion.

AR 8

Assertion: Satellite total energy is negative. Reason: Circular satellite is bound.

Show Answer
Both true.

AR 9

Assertion: Binding energy is positive. Reason: It is energy required to escape.

Show Answer
Both true.

AR 10

Assertion: Use h in orbital speed formula. Reason: h is height above surface.

Show Answer
Assertion false; use r=R+h.

AR 11

Assertion: Higher orbit has lower speed. Reason: v is proportional to 1/sqrt(r).

Show Answer
Both true.

AR 12

Assertion: Higher orbit has longer period. Reason: T is proportional to r3/2.

Show Answer
Both true.

AR 13

Assertion: Work by gravity in circular orbit is zero. Reason: Force is perpendicular to displacement.

Show Answer
Both true and reason explains assertion.

AR 14

Assertion: Satellite PE equals -2K. Reason: Circular orbit obeys virial relation here.

Show Answer
Both true.

AR 15

Assertion: E=-K for circular satellite. Reason: E=K+U and U=-2K.

Show Answer
Both true and reason explains assertion.

AR 16

Assertion: Escape energy from orbit is GMm/r. Reason: Orbit total energy is -GMm/(2r).

Show Answer
Assertion false; from circular orbit it is GMm/(2r).

AR 17

Assertion: Escape energy from surface is GMm/R. Reason: Surface potential energy is -GMm/R.

Show Answer
Both true.

AR 18

Assertion: ve=sqrt(2gR). Reason: GM=gR2 at surface.

Show Answer
Both true.

AR 19

Assertion: GPS satellites are used for navigation. Reason: They send timing signals.

Show Answer
Both true.

AR 20

Assertion: Red objects improve visibility here. Reason: Low-contrast objects were hard to see.

Show Answer
Both true for this design.

AR 21

Assertion: Orbit lines should be black here. Reason: The design requires strong contrast.

Show Answer
Both true for this page.

AR 22

Assertion: Natural satellite example is Moon. Reason: Moon orbits Earth naturally.

Show Answer
Both true.

AR 23

Assertion: Artificial satellites are human-made. Reason: They are launched by rockets.

Show Answer
Both true.

AR 24

Assertion: Communication satellites are often geostationary. Reason: Fixed ground antennas can point at them.

Show Answer
Both true.

AR 25

Assertion: Remote sensing uses polar satellites. Reason: They can scan Earth over time.

Show Answer
Both true.

AR 26

Assertion: If r increases, binding energy decreases. Reason: BE=GMm/(2r).

Show Answer
Both true.

AR 27

Assertion: If r increases, total energy approaches zero. Reason: E=-GMm/(2r).

Show Answer
Both true.

AR 28

Assertion: Satellite speed is constant in circular orbit. Reason: Gravity does no work in circular orbit.

Show Answer
Both true and reason explains speed constancy.

AR 29

Assertion: Geostationary radius is about 42,164 km. Reason: It is measured from Earth's centre.

Show Answer
Both true.

AR 30

Assertion: Geostationary height is about 35,786 km. Reason: Height is measured above Earth's surface.

Show Answer
Both true.

Case Study Questions

Satellite Launch

Passage: A rocket launches a satellite near Earth and gives it tangential velocity.

  1. What speed is needed for circular orbit?
  2. What speed is needed for escape?
  3. What radius is used at height h?
Show Answer

Answers: sqrt(GM/r), sqrt(2GM/r), r=R+h. Explanation: Orbital and escape formulas use centre distance.

Geostationary Satellite

Passage: A satellite appears fixed above one point on Earth and is used for communication.

  1. What is its period?
  2. What is its orbit plane?
  3. Approximate height?
Show Answer

Answers: 24 h, equatorial, about 35,786 km. Explanation: Same angular speed as Earth is required.

Polar Satellite

Passage: A satellite passes over the north and south poles repeatedly.

  1. What is it called?
  2. One use?
  3. Is it geostationary?
Show Answer

Answers: Polar satellite, Earth observation/weather/remote sensing, no.

GPS Satellite

Passage: A navigation satellite sends timing signals to receivers on Earth.

  1. Main application?
  2. Why precise time?
  3. Which formula governs orbit period?
Show Answer

Answers: Navigation, distance from signal timing, T=2pi sqrt(r3/GM).

Escape Velocity

Passage: A body is launched from Earth's surface with just enough speed to reach infinity.

  1. Total energy at threshold?
  2. Formula for speed?
  3. Does projectile mass affect speed?
Show Answer

Answers: zero, sqrt(2GM/R), no. Explanation: Mass cancels in energy equation.

Satellite Energy

Passage: A satellite of mass m moves in a circular orbit of radius r.

  1. Write K.
  2. Write U.
  3. Write E.
Show Answer

Answers: GMm/(2r), -GMm/r, -GMm/(2r). Explanation: Circular orbit energy is negative.

Common Student Mistakes

Confusing Escape and Orbital Velocity

Escape speed is sqrt2 times orbital speed at the same radius.

Forgetting r = R + h

All satellite formulas use orbital radius from Earth's centre.

Using Height Instead of Radius

Do not put h directly in v=sqrt(GM/r) unless h is actually measured from the centre.

Wrong Energy Signs

Potential energy and total energy are negative for circular bound orbit; binding energy is positive.

Thinking Satellite Has Zero Gravity

Gravity is present and provides centripetal acceleration. Apparent weight can be zero.

Confusing Geostationary and Polar

Geostationary is equatorial and appears fixed. Polar passes over poles and scans Earth.

Forgetting ve = sqrt2 vo

This relation is only for the same orbital radius.

Searching for a Physics Tutor? If Escape Velocity, Orbital Velocity, Satellites or NEET/JEE gravitation numericals are not clear, contact Kumar Sir.

Phone: +91-9958461445 | Email: kumarsirphysics@gmail.com | Website: kumarphysicsclasses.com

WhatsApp Kumar SirVisit WebsiteEmail Kumar Sir
Scroll to Top