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Question 1
This question is about Newton's law of gravitation.. |
a) | State Newton's law of gravitation.
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b) | Calculate the gravitational force on the Earth due to the Sun.
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c) | By considering the forces acting on the Earth as it orbits the Sun, show that the orbital time period T is related to the orbital radius r as shown below T2 ∝ r3
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Question 2
a) | State what is represented by gravitational field lines.
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b) | The diagram below shows the field lines close to the surface of a planet. Describe where the gravitational field strength is strongest and give a possible reason for the variation in field strength.
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c) | The diagram below shows the equipotentials that surround the planet. Explain what is meant by a gravitational equipotential.
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d) | The table below shows the gravitational potentials at points X, Y, and Z around the planet. Explain why the gravitational potentials are all negative.
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e) | A satellite of mass 1,800 kg is in orbit at point Y. Calculate the work done on the satellite in moving it from point Y to point Z.
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Question 3
The international space station orbits the Earth at a height h above the Earth's surface. The Earth has a mass M and a radius R. |
a) | Derive an expression for the angular velocity of the international space station in terms of M, h and R.
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b) | The international space station orbits the Earth every 92 minutes. The radius of the Earth is 6.37 x 106 m. The Earth's mass is 5.97 x 1024 kg. Calculate the height above the Earth's surface that the ISS orbits.
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c) | Calculate the gravitational potential of the ISS at this altitude.
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d) | Another satellite is in a higher circular orbit. Describe how the linear speed of this satellite compares with the linear speed of the ISS.
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Question 4
Earth has a mass of 5.97 x 1024 kg and a radius of 6.37 x 106 m. |
a) | Calculate the gravitational potential at the Earth's surface.
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b) | Explain why the gravitational potential is negative at the Earth's surface.
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c) | Derive an expression for the escape velocity of a mass on the Earth's surface.
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d) | Calculate the minimum velocity for an object on the Earth's surface to escape the Earth's gravitational field.
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Question 5
A geostationary satellite is in orbit above the Earth's surface. |
a) | State the conditions for the orbit of the satellite to appear geostationary.
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b) | State the position of the satellite above the Earth's surface.
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c) | Calculate orbital radius of a geostationary satellite. The mass of the Earth is 5.97 x 1024 kg.
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d) | The gravitational field strength at the Earth's surface is 9.81 m s-2. Calculate the gravitational field strength experienced by the geostationary satellite.
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Question 6
A planet has a mass of 6 x 1024 kg and a radius of 7 x 106 m. |
a) | Calculate the force of gravitational attraction between the planet and a 2,000 kg satellite that is orbiting 1,000 km above the planet's surface.
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b) | Calculate the gravitational potential at the surface of the planet.
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c) | Calculate the work done on the satellite in moving it from the surface of the planet to its orbit 1,000 km above the surface.
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Question 7
This question is about the gravitational field of a planet. |
a) | State what is meant by gravitational field strength.
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b) | A planet has a mass of 6.23 x 1024 kg. The gravitational potential at a distance of h above the surface is - 55.78 x 106 J kg-1. The gravitational field strength at 2h above the surface is 5.82 N kg-1. Calculate the radius of the planet.
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c) | The diagram below shows the equipotential lines surrounding the planet. A 400 kg mass is located at P. State how much work is done in moving the mass from P to Q.
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d) | The gravitational potential at P is -831 x 106 J kg-1. The gravitational potential at R is -693 x 106 J kg-1. Calculate the work done on the 400 kg mass when it is moved from position P to R.
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Question 8
A moon is in orbit around a planet. The moon has a radius of 1,800 km and the planet has a diameter of 6,750 km. The distance from the surface of the planet to the surface of the moon is 400,000 km. |
a) | The moon has a mass of 7.35 x 1022 kg and the planet has a mass of 6.03 x 1024 kg. Calculate the force of attraction between the moon and the planet.
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b) | At point X, between the planet and the moon, the gravitational field strength is zero. Calculate the distance from the centre of the planet to point X.
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Question 9
A satellite is in orbit around the Earth. |
a) | State Newton's law of gravitation.
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b) | The satellite is a geostationary satellite. State the conditions of a satellite's orbit for it to be considered geostationary.
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c) | Calculate the height above the Earth's surface for the orbit of a geostationary satellite. The radius of the Earth is 6.37 x 106 m. The mass of the Earth is 5.97 x 1024 kg. The mass of the satellite is 1,500 kg.
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Question 10
A moon of mass m is in a circular orbit around a planet of mass M. The mass of the moon is much less than the planet. |
a) | By considering the forces acting on the moon, show that the time period of orbit is related to the orbital radius as shown below T2 ∝ r3
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b) | The table below gives data for two of the moons of Jupiter. Calculate the orbital time period for Europa.
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c) | The graph below shows how the gravitational potential V varies with vertical distance from the surface of Jupiter. State what the gradient of the graph represents.
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