13.4. Gravitational potential
A subsection of Physics, 9702, through 13. Gravitational fields
Listing 10 of 30 questions
Define gravitational potential at a point. A satellite X, of mass M, orbits a planet at a constant distance 4R from the centre of the planet, as shown in . R 4R orbit of Y orbit of X planet satellite X, mass M satellite Y, mass 2M (not to scale) A second satellite Y, of mass 2M, orbits the planet with orbital radius R. The gravitational potential at X due to the planet is –Φ. The planet is a uniform sphere. Explain why the gravitational potential at X is negative. State an expression, in terms of Φ, for the gravitational potential at Y due to the planet. gravitational potential = Complete Table 1.1 by giving expressions, in terms of some or all of M, R and Φ, for the quantities indicated for each of the satellites X and Y. Table 1.1 satellite X satellite Y gravitational field strength at satellite due to planet gravitational potential energy of satellite
9702_s24_qp_41
THEORY
2024
Paper 4, Variant 1
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Define gravitational potential at a point. A satellite X, of mass M, orbits a planet at a constant distance 4R from the centre of the planet, as shown in . R 4R orbit of Y orbit of X planet satellite X, mass M satellite Y, mass 2M (not to scale) A second satellite Y, of mass 2M, orbits the planet with orbital radius R. The gravitational potential at X due to the planet is –Φ. The planet is a uniform sphere. Explain why the gravitational potential at X is negative. State an expression, in terms of Φ, for the gravitational potential at Y due to the planet. gravitational potential = Complete Table 1.1 by giving expressions, in terms of some or all of M, R and Φ, for the quantities indicated for each of the satellites X and Y. Table 1.1 satellite X satellite Y gravitational field strength at satellite due to planet gravitational potential energy of satellite
9702_s24_qp_43
THEORY
2024
Paper 4, Variant 3
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State what is meant by gravitational potential at a point. Suggest why, for small changes in height near the Earth’s surface, gravitational potential is approximately constant. The Moon may be considered to be a uniform sphere with a diameter of 3.5 × 103 km and a mass of 7.4 × 1022 kg. A meteor strikes the Moon and, during the collision, a rock is sent off from the surface of the Moon with an initial speed v. Assuming that the Moon is isolated in space, determine the minimum speed of the rock such that it does not return to the Moon’s surface. Explain your working. minimum speed = m s–1
9702_w18_qp_41
THEORY
2018
Paper 4, Variant 1
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State what is meant by gravitational potential at a point. Suggest why, for small changes in height near the Earth’s surface, gravitational potential is approximately constant. The Moon may be considered to be a uniform sphere with a diameter of 3.5 × 103 km and a mass of 7.4 × 1022 kg. A meteor strikes the Moon and, during the collision, a rock is sent off from the surface of the Moon with an initial speed v. Assuming that the Moon is isolated in space, determine the minimum speed of the rock such that it does not return to the Moon’s surface. Explain your working. minimum speed = m s–1
9702_w18_qp_43
THEORY
2018
Paper 4, Variant 3
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Define gravitational potential. The Earth E and the Moon M can both be considered as isolated point masses at their centres. The mass of the Earth is 5.98 × 1024 kg and the mass of the Moon is 7.35 × 1022 kg. The Earth and the Moon are separated by a distance of 3.84 × 108 m, as shown in . 3.84 × 108 m Earth E mass 5.98 × 1024 kg Moon M mass 7.35 × 1022 kg P x (not to scale) P is a point, on the line joining the centres of E and M, where the resultant gravitational field strength is zero. Point P is at a distance x from the centre of the Earth. Explain how it is possible for the gravitational field strength to be zero despite the presence of two large masses nearby. Show that x is approximately 3.5 × 108 m. Calculate the gravitational potential φ at point P. φ = J kg–1
9702_w21_qp_41
THEORY
2021
Paper 4, Variant 1
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State the relationship between gravitational potential and gravitational field strength. A moon of mass M and radius R orbits a planet of mass 3M and radius 2R. At a particular time, the distance between their centres is D, as shown in . D x P planet mass 3M radius 2R moon mass M radius R Point P is a point along the line between the centres of the planet and the moon, at a variable distance x from the centre of the planet. The variation with x of the gravitational potential φ at point P, for points between the planet and the moon, is shown in . φ 2R D – R x Explain why φ is negative throughout the entire range x = 2R to x = D – R. One of the features of is that φ is negative throughout. Describe two other features of . 1. 2. On , sketch the variation with x of the gravitational field strength g at point P between x = 2R and x = D – R. 2R x g D – R
9702_w21_qp_42
THEORY
2021
Paper 4, Variant 2
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Define gravitational potential. The Earth E and the Moon M can both be considered as isolated point masses at their centres. The mass of the Earth is 5.98 × 1024 kg and the mass of the Moon is 7.35 × 1022 kg. The Earth and the Moon are separated by a distance of 3.84 × 108 m, as shown in . 3.84 × 108 m Earth E mass 5.98 × 1024 kg Moon M mass 7.35 × 1022 kg P x (not to scale) P is a point, on the line joining the centres of E and M, where the resultant gravitational field strength is zero. Point P is at a distance x from the centre of the Earth. Explain how it is possible for the gravitational field strength to be zero despite the presence of two large masses nearby. Show that x is approximately 3.5 × 108 m. Calculate the gravitational potential φ at point P. φ = J kg–1
9702_w21_qp_43
THEORY
2021
Paper 4, Variant 3
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Define gravitational potential at a point. TESS is a satellite of mass 360 kg in a circular orbit about the Earth as shown in . Earth radius of Earth 6.4 × 106 m radius of orbit satellite TESS (not to scale) The radius of the Earth is 6.4 × 106 m and the mass of the Earth, considered to be a point mass at its centre, is 6.0 × 1024 kg. It takes TESS 13.7 days to orbit the Earth. Show that the radius of orbit of TESS is 2.4 × 108 m. 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 Use the information in to calculate the ratio: gravitational field strength on surface of Earth gravitational field strength at location of TESS in orbit . ratio =
9702_m20_qp_42
THEORY
2020
Paper 4, Variant 2
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State Newton’s law of gravitation. Planets have been observed orbiting a star in another solar system. Measurements are made of the orbital radius r and the time period T of each of these planets. The variation with R3 of T2 is shown in . 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4 2.6 0.2 0.4 0.6 R3 / 1034 m3 T2 / year2 0.8 1.0 1.2 0.1 0.3 0.5 0.7 0.9 1.1 The relationship between T and R is given by T2 = 4π2R3 GM where G is the gravitational constant and M is the mass of the star. Determine the mass M. M = kg A rock of mass m is also in orbit around the star in . The radius of the orbit is r. Explain why the gravitational potential energy of the rock is negative. Show that the kinetic energy Ek of the rock is given by Ek = GMm 2r . Use the expression in to derive an expression for the total energy of the rock.
9702_m21_qp_42
THEORY
2021
Paper 4, Variant 2
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Questions Discovered
30