Question 1Multiple choice · 1 markA* challenge
A planet has the same density as the Earth but 4 times its radius.
What is escape speed from the planetescape speed from the Earth?
- A 2.0
- B 4.0
- C 8.0
- D 16
Show answer
Answer: B
Free D.1 Gravitational fields questions for IB Physics (SL & HL), part of D Fields. Each question has the answer and the marking points an examiner would look for.
Generate a full D.1 Gravitational Fields worksheet →All D Fields questionsA planet has the same density as the Earth but 4 times its radius.
What is escape speed from the planetescape speed from the Earth?
Answer: B
A probe of mass 2000 kg is to be placed in a circular orbit 300 km above the surface of a planet of mass 6.42 × 1023 kg and radius 6.05 × 106 m.
Define gravitational potential at a point.
Calculate the escape speed from the surface of the planet.
Show that the total energy of a satellite in a circular orbit of radius r is −GMm2r.
Calculate the minimum energy needed to place the probe in this orbit from rest on the surface, ignoring the planet’s rotation.
Atmospheric drag acts on the probe. Explain why its speed increases as it spirals inwards.
| Part | Answer and marking points | Marks |
|---|---|---|
| (a) | work per unit mass from infinity the work done per unit mass ✓ in bringing a small mass from infinity to that point ✓ | 2 |
| (b) | 3760 m s−1 v = √2GMR ✓ 3760 m s−1 ✓ | 2 |
| (c) | derivation KE = ½mv2 = GMm2r using v2 = GM/r ✓ PE = −GMmr ✓ total = −GMm2r ✓ | 3 |
| (d) | 7.41 × 109 J Eorbit = −6.74 × 109 J ✓ Esurface = −GMmR = −1.42 × 1010 J ✓ difference = 7.41 × 109 J ✓ | 3 |
| (e) | total energy falls, KE rises drag reduces total energy, so r decreases ✓ KE = GMm/2r increases as r decreases (PE falls by twice as much) ✓ | 2 |
The Earth (mass 5.97 × 1024 kg) and the Moon (mass 7.35 × 1022 kg) are 3.84 × 108 m apart.
Define gravitational field strength.
Determine the distance from the centre of the Earth at which the resultant gravitational field strength is zero.
Explain why a spacecraft travelling to the Moon needs no further energy input beyond this point.
| Part | Answer and marking points | Marks |
|---|---|---|
| (a) | force per unit mass force per unit mass on a small test mass ✓ | 1 |
| (b) | 3.5 × 108 m GME/x2 = GMM/(d − x)2 ✓ x/(d − x) = √81.2 = 9.01 ✓ x = 3.46 × 108 m ✓ | 3 |
| (c) | field towards Moon beyond this point the resultant field points towards the Moon ✓ so the spacecraft is pulled towards the Moon and gains kinetic energy ✓ | 2 |
A satellite orbits the Earth at a height of 400 km. Earth mass = 5.97 × 1024 kg, radius = 6.37 × 106 m.
Calculate the gravitational field strength at this height.
Calculate the orbital speed.
Explain why astronauts in the satellite appear weightless.
| Part | Answer and marking points | Marks |
|---|---|---|
| (a) | 8.7 N kg−1 g = GM/r2 ✓ 8.7 N kg−1 ✓ | 2 |
| (b) | 7.7 km s−1 v = √(GM/r) ✓ 7.67 × 103 m s−1 ✓ | 2 |
| (c) | free fall together astronaut and satellite are both in free fall ✓ with the same acceleration, so no contact force ✓ | 2 |
A spacecraft of mass 800 kg moves from the surface of the Earth (mass 5.97 × 1024 kg, radius 6.37 × 106 m) into a circular orbit of radius 3R.
Calculate the gravitational potential at the surface.
Determine the gravitational field strength at a distance 3R from the centre.
Calculate the change in gravitational potential energy of the spacecraft.
Determine the orbital speed and the total energy of the spacecraft in orbit.
| Part | Answer and marking points | Marks |
|---|---|---|
| (a) | −6.3 × 107 J kg−1 V = −GM/R = −6.3 × 107 J kg−1 ✓ | 1 |
| (b) | 1.1 N kg−1 g = GM/r2 ✓ = 1.1 N kg−1 ✓ | 2 |
| (c) | 3.3 × 1010 J ΔEp = mΔV ✓ = 3.3 × 1010 J ✓ | 2 |
| (d) | 4600 m s−1; −8.3 × 109 J v = √(GM/r) ✓ = 4600 m s−1 ✓ ET = −GMm/2r = −8.3 × 109 J ✓ | 3 |
A satellite of mass 1200 kg orbits the Earth at a height of 400 km above the surface. Mass of the Earth = 5.97 × 1024 kg; radius of the Earth = 6.37 × 106 m.
Show that the orbital speed is v = √GMr.
Calculate the orbital speed and the period of the satellite.
Calculate the gravitational field strength at the height of the orbit.
An astronaut in the satellite feels “weightless”. Explain why, given that the field strength is not zero.
A geostationary satellite has a period of 23.9 hours. Calculate its orbital radius.
| Part | Answer and marking points | Marks |
|---|---|---|
| (a) | gravity provides centripetal force GMmr2 = mv2r ✓ hence v = √GMr ✓ | 2 |
| (b) | 7670 m s−1; 92.4 min r = 6.77 × 106 m ✓ v = 7670 m s−1 ✓ T = 2πrv = 5546 s (92.4 min) ✓ | 3 |
| (c) | 8.69 N kg−1 g = GMr2 ✓ 8.69 N kg−1 ✓ | 2 |
| (d) | free fall both the astronaut and the satellite are in free fall with the same acceleration ✓ so there is no contact (normal) force on the astronaut ✓ | 2 |
| (e) | 4.21 × 107 m T2 = 4π2r3GM ✓ r = 4.21 × 107 m ✓ | 2 |
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