graviational field and orbits
DESCRIPTION
Past paper questionTRANSCRIPT
1
1. Which one of the following graphs best represents the variation of the kinetic energy, KE, and of the gravitational potential energy, GPE, of an orbiting satellite with its distance r from the centre of the Earth?
0
0
0
0
0
0
0
0
Energy
Energy
Energy
Energy
KE
KE
KE
KE
GPE
GPE
GPE
GPE
r
r
r
r
A.
C.
B.
D.
(1)
2. The rings of Saturn are made of rocky particles that orbit the planet. The period T of each particle depends on its distance r from the centre of Saturn. The period T is proportional to rn. Which one of the following is n equal to?
A. 1.0
B. 1.5
C. 2.0
D. 3.0 (1)
2
3. Which of the following expressions correctly relates the radius R of the circular orbit of a planet round a star to the period T of the orbit?
A. R3 ∝ T2
B. 31R
∝ T2
C. R2 ∝ T3
D. 21
R ∝ T3
(1)
4. The kinetic energy EK of a satellite in orbit varies with its distance r from the centre of a planet of radius R.
Which one of the following graphs best shows the variation of EK with r?
A.EK
00 r=R r
B.EK
00 r=R r
C.EK
00 r=R r
D.EK
00 r=R r
(1)
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5. Which one of the following correctly relates the radius R of the circular orbit of planets about the Sun to the period T of the orbit?
A. T ∝ R2
B. T ∝ R3
C. T2 ∝ R3
D. T3 ∝ R2 (1)
6. A satellite is in an orbit around the Earth. It is moved to a new orbit that is closer to the surface of the Earth. Which of the following correctly describes the changes in the gravitational potential energy and in the orbital speed of the satellite?
potential energy speed
A. increases increases
B. increases decreases
C. decreases increases
D. decreases decreases
(1)
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7. Two satellites X and Y are in orbit around the Earth. The orbital radius of satellite X is twice that of satellite Y.
Which of the following correctly gives the ratio
?Y of period orbitalX of period orbital
A. 22
B. 3 4
C. 22
1
D. 3 41
(1)
8. The escape speed from a planet is defined as the speed at which an object must leave the planet’s surface to
A. escape completely from the gravitational field of the planet.
B. enter a geostationary orbit about the planet.
C. escape from the atmosphere of the planet.
D. overcome the gravitational force of the planet. (1)
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9. A planet is in a circular orbit of radius r about a star. The period of the planet in its orbit is T. A second planet orbits the same star in a circular orbit of radius rS.
Which of the following is a correct expression for the period of the second planet in its orbit about the star?
A. 23
S Trr
B. Trr 2
3
S
C. 32
S Trr
D. 23
S Trr
(1)
10. Two satellites, X and Y, move in circular orbits about the Earth. The orbital period of satellite X is eight times that of satellite Y.
The ratio isY satellite of radius orbitalX satellite of radius orbital
A. 2.
B. 4.
C. 8.
D. 16. (1)
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11. Planets A and B orbit the same star. The orbital radius of planet B is four times that of planet A.
Which of the following is the magnitude of the ratio
Aplanet for period orbitalBplanet for period orbital
?
A. 4
B. 8
C. 16
D. 64 (1)
12. The escape speed of an object of mass m from a planet of mass M and radius r depends on the gravitational constant and
A. M and r.
B. m and r.
C. M only.
D. M, m, and r. (1)
13. A spacecraft orbits Earth. An astronaut inside the spacecraft feels “weightless” because
A. the gravitational field in the spacecraft is negligible.
B. the Earth exerts equal forces on the spacecraft and the astronaut.
C. the spacecraft and the astronaut have the same acceleration towards the Earth.
D. the spacecraft and the astronaut exert equal and opposite forces on each other. (1)
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14. Gravitational field strength at a point may be defined as
A. the force on a small mass placed at the point.
B. the force per unit mass on a small mass placed at the point.
C. the work done to move unit mass from infinity to the point.
D. the work done per unit mass to move a small mass from infinity to the point. (1)
15. The Earth is distance RM from the Moon and distance RS from the Sun. The ratio
Sun the todueEarth at thestrength field nalgravitatioMoon the todueEarth at thestrength field nalgravitatio
is proportional to which of the following?
A. 2
2M
SR
R
B. SR
RM
C. 2
2S
MR
R
D. M
S
RR
(1)
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16. Newton’s law of gravitation for the force F between two point objects of masses M and m, separated by a distance d may be written as
Fd2 ∝ Mm.
The expression may also be used for the force of attraction between the Sun and the Earth, although they are not point masses. This is because
A. the gravitational constant G is not involved in the expression.
B. the force between the Sun and the Earth is very large.
C. the separation of the Sun and the Earth is much greater than their radii.
D. the mass of the Earth is much less than the mass of the Sun. (1)
17. A powered spaceship is moving directly away from a planet as shown below.
planet Spaceship
P
At point P the motors of the spaceship are switched off but the spaceship remains under the influence of the planet. Which one of the following graphs best represents the variation with time t of the velocity v of the spaceship after it passes point P?
v v
v v
t t
t t
0 0
0 0
0 0
0 0
A. B.
C. D.
(1)
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18. The diagram below shows lines of electric equipotential. The change in potential on moving from one line to the next is always the same. At which point does the electric field strength have its greatest magnitude?
A
B
C
D
(1)
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19. Which one of the following graphs best shows the variation of the total energy E of a satellite orbiting the Earth with distance r from the centre of the Earth? (The radius of the Earth is R.)
B. E
r0
0
r = R
A. E
r0
0
r = R
D. E
r0
0
r = R
C. E
r0
0
r = R (1)
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20. Which one of the following statements correctly defines the gravitational potential at a point P in a gravitational field?
A. The work done per unit mass in moving a small mass from point P to infinity.
B. The work done per unit mass in moving a small mass from infinity to point P.
C. The work done in moving a small mass from infinity to point P.
D. The work done in moving a small mass from point P to infinity. (1)
21. The gravitational potential at point X due to the Earth is –7 kJ kg–1. At point Y, the gravitational potential is –3 kJ kg–1.
The change in gravitational potential energy of a mass of 4 kg when it is moved from point X to point Y is
A. 4 kJ.
B. 10 kJ.
C. 16 kJ.
D. 40 kJ. (1)
12
22. An isolated point object has mass M. A second small point object of mass m is placed a distance x from the larger mass.
Which one of the following is a correct expression for the gravitational potential energy of the mass m?
A. x
GM−
B. x
GMm−
C. 2xGM
−
D. 2xGMm
−
(1)
23. A rocket of mass m stands on the surface of planet Mars. Mars has mass M and radius R. The gravitational potential energy of the rocket due to Mars is
A. .RGM−
B. .RGM+
C. .R
GMm−
D. .R
GMm+
(1)
13
24. A point object of mass m is brought from infinity to the point P, a distance r from the centre of an isolated sphere of mass M.
r P
m
M
The work done by the gravitational force in bringing the point object from infinity to point P is
A. .r
MG
B. .r
MmG
C. .r
MG−
D. .r
MmG−
(1)
14
25. The gravitational potential at the surface of Earth is V. The radius of Mercury is about one third the radius of Earth. Earth and Mercury are spheres of the same density and the volume of a sphere is
.34 3rπ
The gravitational potential at the surface of Mercury is
A. .91V
B. .31V
C. 3 V.
D. 9 V. (1)
26. A satellite is in orbit about Earth. The satellite moves to an orbit closer to Earth. Which of the following correctly gives the change in the potential energy and the kinetic energy of the satellite?
change in potential energy change in kinetic energy
A. Decreases Increases
B. Decreases Decreases
C. Increases Increases
D. Increases Decreases
(1)
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27. The diagram below shows two planets X and Y of masses 2M and M respectively. The centres of the two planets are separated by a distance 2d. Point P is midway between planets X and Y. The mass of each planet may be assumed to be concentrated at its centre.
planet X planet Y
P
2d
The magnitude of the gravitational field strength at point P due to the two planets is
A. zero.
B. .2dGM
C. .22d
GM
D. .32d
GM
(1)
28. The magnitude of the gravitational field strength at the surface of a planet of radius R is 8.0 N kg–1. Which of the following is a correct expression for the gravitational potential at the surface of the planet?
A. R0.8
−
B. 20.8
R−
C. 0.8
R−
D. – 8.0R (1)
16
29. The diagram below shows some lines of equipotential in the region of an electric field.
X Y
Which graph best shows the magnitude E of the electric field strength along the line XY?
E
X Yposition
A. B.
C. D.E
X Yposition
E
X Yposition
E
X Yposition
(1)
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30. The centres of two isolated spherical stars each of mass M and radius R are separated by a distance d as shown in the diagram below.
X
M
R
M
R
d
The distance d is very large compared to R. Point X is mid-way between the stars. The gravitational potential at point X due to the two stars is
A. .4d
GM−
B. .2R
GM−
C. .d
GM−
D. zero. (1)
31. The gravitational potential at a point P above the surface of a planet is defined as the work done per unit mass in moving a small test mass
A. from point P to the surface of the planet.
B. from the surface of the planet to point P.
C. from point P to infinity.
D. from infinity to point P. (1)
18
32. A satellite is placed in a circular orbit about the Earth.
Which of the following correctly shows the change in the kinetic energy and in the gravitational potential energy of the satellite with increase in the orbital radius?
kinetic energy gravitational potential energy
A. increase decrease
B. increase increase
C. decrease decrease
D. decrease increase (1)
33. A satellite is in orbit about Earth. The satellite moves to an orbit closer to Earth. Which of the following correctly gives the change in the potential energy and the kinetic energy of the satellite?
change in potential energy change in kinetic energy
A. decreases increases
B. decreases decreases
C. increases increases
D. increases decreases
(1)
19
34. Which of the following diagrams best represents the gravitational equipotential surfaces due to two equal spherical masses?
(1)
35. A satellite of mass m and speed v orbits the Earth at a distance r from the centre of the Earth. The gravitational field strength due to the Earth at the satellite is equal to
A. rv .
B. r
v 2
.
C. r
mv .
D. r
mv 2
.
(1)
20
36. Planet X has radius R and mass M. Planet Y has radius 2R and mass 8M.
Which one of the following is the correct value of the ratio
? Yplanet of surfaceat strength field nalgravitatio Xplanet of surfaceat strength field nalgravitatio
A. 4
B. 2
C. 21
D. 41
(1)
37. In Newton’s universal law of gravitation the masses are assumed to be
A. extended masses.
B. masses of planets.
C. point masses.
D. spherical masses. (1)
21
38. The acceleration of free fall of an object of mass m at the surface of Mars is a. The gravitational field strength at the surface of Mars is
A. a.
B. ma.
C. .ma
D. .am
(1)
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39. Two isolated spheres of masses M and m are held a distance d apart, as shown below.
d
x
mM
Mass M is greater than mass m.
The gravitational field strength g is measured on a line between the two masses. Which graph best shows the variation with distance x from the larger sphere of the magnitude of the field strength g? The Earth’s gravitational field is to be ignored.
00
g
d x00
g
d x
00
g
d x00
g
d x
A. B.
C. D.
(1)
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40. The mass of Mars is approximately 0.1 times the mass of Earth and its diameter is approximately 0.5 times that of Earth.
What is the approximate gravitational field strength on the surface of Mars?
A. 2N kg–1
B. 4N kg–1
C. 25N kg–1
D. 50N kg–1 (1)
41. This question is about gravitation.
A binary star consists of two stars that each follow circular orbits about a fixed point P as shown below.
star mass P star massM1 M2
R1 R2
The stars have the same orbital period T. Each star may be considered to act as a point mass with its mass concentrated at its centre. The stars, of masses M1 and M2, orbit at distances R1 and R2 respectively from point P.
(a) State the name of the force that provides the centripetal force for the motion of the stars.
................................................................................................................................... (1)
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(b) By considering the force acting on one of the stars, deduce that the orbital period T is given by the expression
( ) .4 2211
2
22 RRR
GMT +
π=
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(c) The star of mass M1 is closer to the point P than the star of mass M2. Using the answer in (b), state and explain which star has the larger mass.
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(Total 6 marks)
42. This question is about the energy of orbiting satellites.
(a) Define the term gravitational potential at a point in a gravitational field.
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(b) A satellite is in orbit about Earth at a distance R from the centre of Earth. The Earth may be regarded as a point mass situated at its centre.
Deduce that the kinetic energy of the satellite is numerically equal to half the potential energy of the satellite.
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(c) The distance between the centre of the Moon and the centre of Earth is about 4.0 × 108 m. The Moon may also be regarded as a point mass situated at its centre. The orbital period of the Moon about the Earth is 2.4 × 106 s.
(i) Calculate the orbital speed of the Moon.
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(ii) Use your answer in (b) and (c)(i) to calculate a value for the gravitational potential due to Earth at a distance of 4.0 × 108 m from its centre.
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(Total 9 marks)
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43. This question is about gravitation.
A space probe is launched from the equator in the direction of the north pole of the Earth. During the launch, the energy E given to the space probe of mass m is
E =e
34RGMm
where G is the Gravitational constant and M and Re are, respectively, the mass and radius of the Earth. Work done in overcoming frictional forces is not to be considered.
(a) (i) Explain what is meant by escape speed.
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(ii) Deduce that the space probe will not be able to travel into deep space.
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The space probe is launched into a circular polar orbit of radius R.
(b) Derive expressions, in terms of G, M, Re, m and R, for
(i) the change in gravitational potential energy of the space probe as a result of travelling from the Earth’s surface to its orbit.
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(ii) the kinetic energy of the space probe when in its orbit.
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(c) Using your answers in (b) and the total energy supplied to the space probe as given in (a), determine the height of the orbit above the Earth’s surface.
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A space probe in a low orbit round the Earth will experience friction due to the Earth’s atmosphere.
(d) (i) Describe how friction with the air reduces the energy of the space probe.
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(ii) Suggest why the rate of loss of energy of the space probe depends on the density of the air and also the speed of the space probe.
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(iii) State what will happen to the height of the space probe above the Earth’s surface and to its speed as air resistance gradually reduces the total energy of the space probe.
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(Total 18 marks)
44. This question is about atomic and nuclear structure and fundamental forces.
In a nuclear model of the atom, most of the atom is regarded as empty space. A tiny nucleus is surrounded by a number of electrons.
(a) Outline one piece of experimental evidence that supports this nuclear model of the atom.
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(b) Explain why the protons in a nucleus do not fly apart from each other.
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(c) In total, there are approximately 1029 electrons in the atoms making up a person. Estimate the electrostatic force of repulsion between two people standing 100 m apart as a result of these electrons.
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(d) Estimate the gravitational force of attraction between two people standing 100 m apart.
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(e) Explain why two people standing 100 m apart would not feel either of the forces that you have calculated in parts (c) and (d).
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(Total 13 marks)
30
45. This question is about a spacecraft.
A spacecraft above Earth’s atmosphere is moving away from the Earth. The diagram below shows two positions of the spacecraft. Position A and position B are well above Earth’s atmosphere.
Earth A B
At position A, the rocket engine is switched off and the spacecraft begins coasting freely. At position A, the speed of the spacecraft is 5.37 × 103 m s–1 and at position B, 5.10 × 103 m s–1. The time to travel from position A to position B is 6.00 × 102 s.
(a) (i) Explain why the speed is changing between positions A and B.
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(ii) Calculate the average acceleration of the spacecraft between positions A and B.
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(iii) Estimate the average gravitational field strength between positions A and B. Explain your working.
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(b) The diagram below shows the variation with distance from Earth of the kinetic energy Ek of the spacecraft. The radius of Earth is R.
energy Ek
R0
0 distance
On the diagram above, draw the variation with distance from the surface of Earth of the gravitational potential energy Ep of the spacecraft.
(2) (Total 8 marks)
46. This question is about gravitational fields.
(a) Define gravitational field strength.
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(b) The gravitational field strength at the surface of Jupiter is 25 N kg–1 and the radius of Jupiter is 7.1 × 107 m.
(i) Derive an expression for the gravitational field strength at the surface of a planet in terms of its mass M, its radius R and the gravitational constant G.
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(ii) Use your expression in (b)(i) above to estimate the mass of Jupiter.
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(Total 6 marks)
47. This question is about satellite motion.
A satellite of mass m orbits a planet of mass M and radius R as shown below. (The diagram is not to scale.)
planet mass M
R
x
satellite mass m
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The radius of the circular orbit of the satellite is x. The planet may be assumed to behave as a point mass with its mass concentrated at its centre.
(a) Deduce that the linear speed v of the satellite in its orbit is given by the expression
v = x
GM ,
where G is the gravitational constant.
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(b) (i) Derive expressions, in terms of m, G, M and x, for the kinetic energy of the satellite and for the gravitational potential energy of the satellite.
Kinetic energy:
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Gravitational potential energy:
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(ii) Deduce an expression for the total energy of the satellite.
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The satellite is moved into an orbit closer to the planet where there is friction with the planet’s atmosphere.
(c) (i) State the effect of these frictional forces on the total energy of the satellite.
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(ii) Apply your equation in (b)(ii) to deduce that, as a result of this friction, the radius of the orbit will change continuously.
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(iii) Describe the effect of this change in orbital radius on the speed of the satellite.
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(iv) The frictional forces will change as the orbit of the satellite changes. Suggest and explain the effect on the motion of the satellite of these changing frictional forces.
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(Total 13 marks)
48. Fields and potential
Electric fields and potential
(a) Define electric potential.
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An isolated metal sphere of radius 50.0 cm has a positive charge. The electric potential at the surface of the sphere is 6.0 V.
50.0 cmmetal sphere
(b) (i) On the diagram above, draw a line to represent an equipotential surface outside the sphere.
(1)
(ii) On the axes below, draw a sketch graph to show how the potential V outside the sphere varies with distance r from the surface of the sphere.
V / V
6
4
2
0 0.0 0.5 1.0 1.5 r / m
(4)
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(iii) Explain how the graph drawn in (b) (ii) can be used to determine the magnitude of the electric field strength at the surface of the sphere.
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(c) On the diagram below draw lines to represent the electric field outside the sphere.
50.0 cmmetal sphere
(2)
Gravitational fields and potential
(d) Derive an expression for the gravitational field strength as a function of distance away from a point mass M.
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(e) The radius of the Earth is 6400 km and the gravitational field strength at its surface is 9.8 N kg–1. Calculate a value for the mass of the Earth.
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(f) On the diagram below draw lines to represent the gravitational field outside the Earth.
(2)
(g) A satellite that orbits the Earth is in the gravitational field of the Earth. Discuss why an astronaut inside the satellite feels weightless.
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(h) The gravitational potential outside the Earth and the electric potential outside the sphere both vary with distance. Compare these variations.
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(Total 23 marks)
49. This question is about the gravitational field associated with a neutron star.
(a) Define gravitational field strength.
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(b) Neutron stars are very dense stars of small radius. They are formed as part of the evolutionary process of stars that are much more massive than the Sun.
A particular neutron star has radius R of 1.6 × 104 m. The gravitational field strength at its surface is g0. The escape speed ve from the surface of the star is 3.6 × 107 m s–1.
(i) The gravitational potential V at the surface of the star is equal to – g0R. Deduce, explaining your reasoning, that the escape speed from the surface of the star is given by the expression
.2 0Rgve =
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(ii) Calculate gravitational field strength at the surface of the neutron star.
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(c) The period T of rotation of the neutron star is 0.02 s. Use your answer to (b)(ii) to deduce that matter is not lost from the surface of the star as a result of its high speed of rotation.
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(Total 10 marks)
40
50. Kepler’s third law.
(a) Kepler’s third law states that the period T of the orbit of a planet about the Sun is related to the average orbital radius R of the planet by the relationship
T2 = KR3
where K is a constant.
(i) Suggest why the law specifies the average orbital radius.
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(ii) State the name of the force that causes the acceleration of the planets orbiting the Sun.
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(iii) State an expression for the magnitude F of the force in (ii) in terms of the mass MS, of the Sun, the mass m of the planet, the radius R of the orbit and the universal gravitational constant G.
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(iv) Hence deduce, explaining your working, that the constant K is given by the expression
.4
S
2
GMK π=
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(b) Ganymede is one of the moons of Jupiter and the following data are available.
Average orbital radius of Ganymede = 1.1 × 109 m
Orbital period of Ganymede = 6.2 × 105 s
Universal gravitational constant G = 6.7 × 10−11 N m2 kg−2
(i) Deduce that the gravitational field strength of Jupiter at the surface of Ganymede is approximately 0.1 N kg−1.
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(ii) Estimate the mass of Jupiter.
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(Total 12 marks)
42
51. Gravitation
The diagram below illustrates the planet Saturn.
Saturn
2.72 10 8m
A ring
Saturn has several rings, each of which consists of many small particles that orbit the planet. Saturn may be considered to be a sphere with its mass M concentrated at its centre.
(a) Deduce that, for a particle in one ring moving in a circular orbit of radius R, the linear speed v of the particle in its orbit is given by the expression
GM = Rv2.
Explain your reasoning.
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(b) One ring, the A ring, has an outer diameter of 2.72 × 108 m. The mass of Saturn is 5.69 × 1026 kg. A particle orbits on the outer edge of this ring. Determine the time for the particle to complete one orbit of Saturn.
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(c) Another particle of mass m is orbiting at a distance r from the centre of Saturn.
(i) State a formula, in terms of G, M, m and r for the gravitational potential energy EP of the particle.
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(ii) The gravitational potential energy of this particle decreases. Suggest and explain the change, if any, in the linear speed of the particle.
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(d) Explain the concept of escape speed.
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(e) A planet has radius R and the acceleration of free fall at its surface is g. The planet may be considered to be a sphere with its mass concentrated at its centre.
Deduce that the escape speed ves is given by the expression
( ).2es gRv =
Explain your working and state one assumption that is made in the derivation.
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(f) Calculate the escape speed for a spherical planet of radius 1.7 × 103 km having an acceleration of free fall at its surface of 1.6 m s–2.
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(g) The mean kinetic energy EK, in joule, of helium-4 atoms at thermodynamic temperature T is given by the expression
EK = 2.1 × 10–23 T.
Determine the surface temperature of the planet such that helium-4 atoms on the surface of the planet have the escape speed calculated in (f).
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(h) Suggest one reason why, at temperatures below that calculated in (g), helium will escape from the planet.
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(Total 19 marks)
52. Motion of a satellite
(a) Define gravitational potential.
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(b) A satellite of mass m is in a circular orbit around the Earth at height R from the Earth’s surface. The mass of the Earth may be considered to be a point mass concentrated at the Earth’s centre. The Earth has mass M and radius R.
orbit
satellite mass m
R R
Earth mass M
(i) Deduce that the kinetic energy EK of the satellite when in orbit of height R is
.4K R
GMmE =
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(ii) The kinetic energy of the satellite in this orbit is 1.5 × 1010 J. Calculate the total energy of the satellite.
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(iii) Explain how your answer to (b)(ii) indicates that the satellite will not escape the Earth’s gravitational field and state the minimum amount of energy that must be provided to this satellite so that it does escape.
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(Total 11 marks)
53. This question is about gravitation.
(a) State Newton’s universal law of gravitation.
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(b) The average distance of Earth from the Sun is 1.5 × 1011 m. The gravitational field strength due to the Sun at the Earth is 6.0×10–3N kg–1.
Estimate the mass of the Sun.
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(c) Deduce that the orbital period T of a planet about the Sun is given by the expression
T2 = KR3
where R is the radius of the orbit and K is a constant.
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(Total 11 marks)
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54. This question is about gravitational potential.
(a) Define gravitational potential at a point.
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(b) A meteorite moves towards the Moon from a long distance away.
(i) On the axes below, sketch a graph to show the variation with distance from the centre of the Moon of the gravitational potential of the meteorite as it approaches the Moon. The radius of the Moon is r.
gravitationalpotential
+ve
–ve
r0
distance from centre of Moon
(2)
(ii) The radius r of the Moon is 1.7 × 106 m and its mass is 7.3 × 1022 kg.
Estimate the impact speed with which the meteorite hits the surface of the Moon.
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(iii) Suggest one factor that will make the impact speed greater than your estimate.
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(c) A similar meteorite moves towards the Earth from a long distance away.
Suggest how the total energy of the meteorite varies with distance when the meteorite is
(i) outside the Earth’s atmosphere;
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(ii) inside the Earth’s atmosphere.
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(Total 10 marks)
55. This question is about gravitation.
A spherical planet has radius R and mass M. A satellite of mass m orbits the planet with constant linear speed v at a height h above the planet’s surface, as shown below (not to scale).
planet mass Mv
R h
satellite mass m
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(a) Outline why
(i) although the satellite is moving at constant speed, it is not in equilibrium.
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(ii) an object in the satellite appears to be weightless.
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(b) For the satellite in its orbit,
(i) state an expression, in terms of M, m, R and h, for its potential energy.
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(ii) derive an expression, using the same terms as in (b)(i), for its kinetic energy.
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(c) The total energy of the satellite is reduced. Use your expressions in (b) to outline what change, if any, occurs in the radius of the orbit and the speed of the satellite.
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(d) The force of friction between the satellite and the atmospheric air increases as the speed of the satellite increases. By reference to your answer in (c), suggest why small satellites will “burn up” as they re-enter the Earth’s atmosphere.
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(Total 17 marks)