A-LevelPhysicsGravitational fields9702/42 · Feb/Mar 2020 · Q110 Marks

Answer all the questions in the spaces provided. (a) Define gravitational potential at a point. (b) TESS is a satellite of mass 360kg in a circular orbit about the Earth as shown in Fig. 1.1. [Figure 1.1] The radius of the Earth is 6.4 × 10⁶m and the mass of the Earth, considered to be a point mass at its centre, is 6.0 × 10²⁴ kg.

(a)Define gravitational potential at a point.[2]
(b)(i)It takes TESS 13.7 days to orbit the Earth. Show that the radius of orbit of TESS is 2.4 × 10⁸ m.[3]
(b)(ii)Calculate the change in gravitational potential energy between TESS in orbit and TESS on a launch pad on the surface of the Earth. change in gravitational potential energy = ................................................................ J [3][3]
(b)(iii)Use the information in (b)(i) to calculate the ratio: gravitational field strength on surface of Earth gravitational field strength at location of TESS in orbit ratio = ........................................................................ [2][2]

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Mark scheme

Marking points from the official mark scheme (Feb/Mar 2020). The mark or mark type is shown in brackets.

[1] work done per unit mass
[1] work done moving mass from infinity (to the point)
[1] gravitational force provides centripetal force
[1] mv² / r = GMm/r² and v = 2πr / T OR mrω² = GMm/r² and ω = 2π / T OR r³ = GMT² / 4π²
[1] r³ = 6.67 × 10⁻¹¹ × 6.0 × 10²⁴ × (13.7 × 24 × 3600)² / 4 π² so r = 2.4 × 10⁸ m
[1] (Ep = −) GMm/r
[1] work done = GMm / r₁ – GMm / r₂
[1] = 6.67 × 10⁻¹¹ × 360 × 6.0 × 10²⁴ (1/6.4 × 10⁶ – 1 / 2.4 × 10⁸) = 2.2 × 10¹⁰ J
[1] g = GM / r²
[1] ratio = r_TESS² / r_earth² = (2.4 × 10⁸/6.4 × 10⁶)² = 1400

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