Explain how it is possible for the gravitational force to cause the satellite to accelerate while its speed remains constant.

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Jocelyn Higgins
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1 YEAR 12 PHYSICS: GRAVITATION PAST EXAM QUESTIONS Name: QUESTION 1 (1995 EXAM) (a) State Newton s Universal Law of Gravitation in words (b) A satellite of mass (m) moves in orbit of a planet with mass (M). The satellite, m, is smaller in mass than the planet, M. Assume that the satellite moves around the planet in a circular orbit with a radius, R with a constant speed, v. (i) Explain how it is possible for the gravitational force to cause the satellite to accelerate while its speed remains constant.

2 (ii) If T is the period of the satellite in its orbit around the planet, show that the radius of the 3 orbit of the satellite is r = Gm 2T 2 given that T 2 = 4π2 r 3 4π 2 Gm 2 (iii) Calculate the moon s orbital radius given that its period of rotation is approximately 27 days and 7 hours ( x 10 6 s)

3 QUESTION 2 (1996 EXAM) Whilst orbiting the Earth, the space shuttle Endeavour had a velocity of 7.8 x 10 3 ms -1 (a) Calculate the radius of its circular orbit (b) Two isolated masses M and m are separated by a distance, r. The mass M is twice the mass of the smaller body, m. On the diagram above, draw vector arrows to illustrate the gravitational force (F) on each mass

4 QUESTION 3 (1999 EXAM) The uniform circular motion of a space vehicle in a circular orbit round a planet is caused by the gravitational force between the planet and the vehicle. (a) Calculate the magnitude and direction of the gravitational force on a space vehicle of mass m= 1.00 x 10 3 kg at a distance r of 1.65 x 10 7 m from the centre of a planet of mass M= 2.00x kg given the Universal Gravitation law (F = Gm 1m 2 r 2 ). (b) Show that the speed v of the space vehicle is given by the formula v = Gm 2 r (c) Using the relationship for the speed of the space vehicle given in part (ii) and an expression for the period T, showing that (T 2 = 4π2 r 3 Gm 2 )

5 QUESTION 4 (2000 EXAM) (a) Calculate the magnitude of the gravitational force F on mass m = 20.0 kg, positioned at 1.00 x 10 6 m above the Earth's surface. The mass of the Earth ME = 5.98 x kg and the radius of the Earth RE = 6.38 x 10 6 m. (b) A space vehicle of mass m is moving at a constant speed v in a circular orbit of radius r round the Earth. (i) Derive an expression for v in terms of the radius r and the mass of the Earth ME. (ii) Explain why the space vehicle does not need to use rocket engines to maintain its uniform circular motion. Ignore air resistance.

QUESTION 5 (2001 EXAM) (a) State, in words, Newton's law of universal gravitation. (b) Two masses exert a force of magnitude F on each other when placed a distance d apart.

6 QUESTION 5 (2001 EXAM) (a) State, in words, Newton's law of universal gravitation. (b) Two masses exert a force of magnitude F on each other when placed a distance d apart. State the magnitude of the force, in terms of F, if the distance d between the masses is doubled. (1 mark) (c) Explain why the gravitational forces between two particles of different mass, M and m, as shown below, are consistent with Newton's third law.

7 (c) Using Newton's second law and law of universal gravitation, derive the expression (g = Gm 2 r2 ) for the gravitational acceleration at the Moon's surface. (M is the mass of the Moon, r the radius of the Moon.) (d) Calculate the value of the acceleration due to gravity at the Moon's surface. (The mass of the Moon M = 7.35 x kg and the radius of the Moon r = 1.74 x 10 6 m.) (e) The orbit of a geostationary satellite round the Earth is shown in the diagram below: (i) Explain why this satellite must orbit in the same direction as the Earth rotates. (1 mark)

8 (ii) Explain why the orbit of this satellite must be equatorial. (f) Explain why low-altitude polar orbits are used for surveillance satellites. (g) A space vehicle is moving at constant speed in a circular orbit A round a planet, as shown in the diagram below: Draw and label vectors on the diagram to represent the velocity v and acceleration a of the space vehicle at position P.

9 QUESTION 6 (2002 EXAM) (a) Calculate the magnitude of the gravitational acceleration g at the Earth's surface, using Newton's second law and the law of universal gravitation. The mass of the Earth M is 5.98 x kg and the radius of the Earth R is 6.38 x 10 6 m. (b) A satellite orbits the Earth with constant speed in a circle whose radius is twice the radius of the Earth, as shown in the diagram below. The mass of the Earth is M= 5.98 x kg and its mean radius is R = 6.38 x 10 6 m. (i) Show that the speed at which the satellite is moving is approximately 6 x 10 3 ms -1.

10 (ii) Calculate the period of the satellite. (iii) Explain why the satellite travels with uniform circular motion in a fixed orbit.

11 QUESTION 7 (2003 EXAM) (a) Show that the speed v of a satellite moving in an orbit of radius r round a planet of mass M is given by, (v = GM r ), where G is the gravitational constant. (b) Explain the advantage of launching a low-altitude equatorial-orbit satellite in a west-to-east direction.

12 QUESTION 8 (2004 EXAM) Two satellites, A and B, orbit the Earth, as shown in the diagram below. Both satellites are in circular orbits. The radius of satellite B is greater than the radius of satellite A. (a) On the diagram above, draw and label vectors to represent the acceleration of satellite A and satellite B. (b) Satellite A orbits at a radius of x 10 7 m. Satellite B orbits at a radius of x 10 7 m and at a speed of 3072 ms -1. (i) Show that the speed v of a satellite moving in an orbit of radius r round a planet of mass M is given by, (v = GM r ), where G is the gravitational constant.

13 (ii) Hence show that the mass of the Earth is approximately 5.98 x kg. (iii) Calculate the orbital speed of satellite A. (iv) Calculate the orbital period of satellite B. (v) Geostationary satellites move in an equatorial orbit in the same direction as the Earth's rotation. Explain why geostationary satellites have orbits of relatively large radius.

14 (vi) Two satellites of equal mass orbit the Earth. One satellite has a radius of rx and the other has a radius of r2x (double the radius of rx). Calculate the ratio Fx : F2x of the gravitational forces acting on the satellites. QUESTION 9 (2005 EXAM) Astronaut A is on the surface of a moon of radius r. Astronaut B is at a distance of 3r from the centre of the moon, as shown in the diagram below: Astronaut A and astronaut B have identical masses. The magnitude of the gravitational force between the moon and astronaut A is 195 N. (a) Calculate, using proportionality, the magnitude of the gravitational force between the moon and astronaut B.

15 (b) A satellite is in a circular polar orbit around the Earth at an altitude of 8.54 x 10 5 m. The mass of the Earth is 5.97 x kg and its mean radius is 6.38 x 10 6 m. (i) Calculate the orbital speed of the satellite. (ii) State two reasons why low-altitude polar orbits are used in meteorology and surveillance.

16 QUESTION 10 (2006 EXAM) Some satellites have geostationary orbits and some satellites have polar orbits (a) State two differences between geostationary orbits and polar orbits. (b) Derive the formula (T 2 = 4π2 r 3 ) given the formulas v = 2πr and Gm 2 T v2 = Gm 2 r (c) Rearrange this formula to show that the period of satellite motion is given by the formula 3 r = Gm 2T 2 4π 2

17 (d) Hence determine the altitude of a satellite in a geostationary orbit around the Earth. The mass of the Earth is M = 5.97 x kg and its radius is R = 6.4 x 10 6 m. (4 marks) QUESTION 11 (2007 EXAM) The binary star system known as Sirius is shown, at one point in time, in the diagram below. The mass of Sirius A, measured using data obtained from the Hubble Space Telescope in 2005, is much larger than that of its partner star, Sirius B. (a) On the diagram above, draw vectors to show the gravitational force acting on each of these stars at this point in time. (b) Explain why Newton's law of universal gravitation is consistent with Newton's third law of motion.

(c) The polar-orbiting satellite NOAA-N was launched in May 2005, as shown in the photograph below: The satellite is now moving in a circular orbit above the Earth's surface at an altitude of 870 km.

18 (c) The polar-orbiting satellite NOAA-N was launched in May 2005, as shown in the photograph below: The satellite is now moving in a circular orbit above the Earth's surface at an altitude of 870 km. The mass of the Earth is 5.97 x kg and its mean radius is 6.38 x 10 6 m. (i) Show that the orbital speed of the satellite is 7.41 x10 3 ms -1 (ii) Calculate the magnitude of the acceleration due to gravity at the satellite's altitude. (iii) Explain why the centre of the circular orbit of any Earth satellite must coincide with the centre of the Earth.

19 QUESTION 12 (2008 EXAM) A satellite of mass m moves in a circular orbit of radius r about a planet of mass M, as shown in the diagram below. (a) Using Newton's law of universal gravitation and Newton's second law of motion, show that the period T of the satellite is given by (T 2 = 4π2 r 3 Gm 2 ) (5 marks) (b) Two identical satellites X and Y, with orbital radii 16r and r respectively, move in circular orbits about the Earth, as shown in the diagram below. (i) Using proportionality, calculate the ratio Tx : Ty of the satellites' orbital periods.

20 (ii) Satellite X is a geostationary satellite moving in the Earth's equatorial plane. Explain why this satellite must move in a particular orbit of relatively large radius. QUESTION 13 (2009 EXAM) The centripetal acceleration of the Earth in its orbit around the Sun has a magnitude of ms 2. This acceleration is caused by the gravitational force that the Sun exerts on the Earth. The mass of the Earth is kg and the mean radius of the Earth s orbit around the Sun is m. (a) Show that the magnitude of the gravitational force that the Sun exerts on the Earth is N. (b) Hence determine the mass of the Sun.

21 (c) Two satellites are moving in circular orbits around the Earth, Orbit A and Orbit B, as shown in the diagram below. The radius of Orbit B is double the radius of Orbit A. Speed of satellite in orbit A (i) Calculate the ratio Speed of satellite in orbit B (ii) Explain why the centripetal acceleration of a satellite in an orbit of constant radius is independent of the mass of the satellite.

22 (d) The diagram below shows two circular paths around the Earth. Path 1 is not a possible satellite orbit. Path 2 is a low-altitude polar orbit. (i) Explain why Path 1 is not a possible satellite orbit. (ii) State one reason why satellites in low-altitude polar orbits are often used for surveillance, and explain your answer.

23 (e) The Iridium satellite network consists of sixty-six communication satellites orbiting the Earth at a radius of m, with a speed of ms 1. On 10 February 2009 the Iridium 33 satellite collided with the Russian Cosmos 2251 satellite above Siberia. The damaged Iridium 33 satellite was replaced in the network by a spare satellite that was orbiting at a lower radius. Calculate the time that a satellite in the Iridium network takes to complete one orbit of the Earth. Give your answer to the correct number of significant figures. QUESTION 14 (2010 EXAM) (a) Explain why a geostationary satellite must orbit in a west-to-east direction. (b) Explain one advantage of launching equatorial-orbit satellites in a west-to-east direction.

24 The diagram below shows two isolated, spherically symmetric objects. The mass of Object A is much larger than the mass of Object B. On the diagram above, draw vectors to show the gravitational forces that these objects exert on each other. QUESTION 15 (2012 EXAM) In November 2012 parts of the world will experience a total solar eclipse. During such an eclipse the Earth, the Moon, and the Sun are in a straight line. The Moon is between the Earth and the Sun. In this alignment the distance between the Earth and the Moon is 3.85 x 10 8 m, and the distance between the Moon and the Sun is 1.50 x m. The mass of the Earth is 5.97 x kg. The mass of the Moon is 7.35 x kg. The mass of the Sun is 1.99 x kg. force on the moon due to earth Determine the magnitude of the ratio force on moon due to sun (4 marks)

The Quick Bird satellite is used to create images of the Earth. One such image is shown below left. The satellite orbits at an altitude of 482 km, and has a mass of 9.5 x 10 2 kg.

25 The Quick Bird satellite is used to create images of the Earth. One such image is shown below left. The satellite orbits at an altitude of 482 km, and has a mass of 9.5 x 10 2 kg. The International Space Station (shown in the image below right) orbits at an altitude of 390 km, and has a mass of 4.2 x 10 5 kg. (a) State whether the QuickBird satellite orbits the Earth at a faster or slower speed than the International Space Station. Give a reason for your answer. (b) State any effect that the different masses of the satellites will have on their speeds. Give a reason for your answer. (c) State one advantage of the QuickBird satellite's low-altitude orbit. (1 mark)

PHYSICS 12 NAME: Gravitation

PHYSICS 12 NAME: Gravitation NAME: Gravitation 1. The gravitational force of attraction between the Sun and an asteroid travelling in an orbit of radius 4.14x10 11 m is 4.62 x 10 17 N. What is the mass of the asteroid? 2. A certain