A-LevelPhysicsGravitational fields9702/42 · Feb/Mar 2019 · Q112 Marks

Define gravitational potential at a point.

(a)(i)Define gravitational potential at a point.[2]
(a)(ii)Use your answer in (i) to explain why the gravitational potential near an isolated mass is always negative.[3]
(b)(i)A spherical planet has mass 6.00 × 10²⁴ kg and radius 6.40 x 10⁶ m. The planet may be assumed to be isolated in space with its mass concentrated at its centre. A satellite of mass 340kg is in a circular orbit about the planet at a height 9.00 × 10⁵m above its surface. For the satellite: show that its orbital speed is 7.4 × 10³ms⁻¹[2]
(b)(ii)calculate its gravitational potential energy.[3]
(c)Rockets on the satellite are fired for a short time. The satellite's orbit is now closer to the surface of the planet. State and explain the change, if any, in the kinetic energy of the satellite.[2]

Mark scheme

Marking points from the official mark scheme (Feb/Mar 2019). The mark or mark type is shown in brackets.

[B1] work done per unit mass
[B1] idea of work done moving mass from infinity (to the point)
[B1] (gravitational) force is attractive
[B1] (gravitational) potential at infinity is zero
[B1] decrease in potential energy as masses approach or displacement and force in opposite directions
[C1] Either mv² / R = GMm/R² Or v = √( GM/R) V² = (6.67 x 10⁻¹¹ × 6.00 × 10²⁴) / (7.30 × 10⁶)
[A1] giving v = 7.4 × 10³ m s⁻¹
[C1] Vp = − GMm/R
[C1] = − (6.67 x 10⁻¹¹ × 6.00 × 10²⁴ × 340) / (7.30 × 10⁶)
[A1] Vp = − 1.9 × 10¹⁰ J
[M1] v² ∝ 1/r, (r smaller) so v greater
[A1] and Ek greater

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