UNIT G484 Module 2 4.2.
2 Gravitational Fields 1 Calculate the gravitational attraction force between : 11
PRACTICE QUESTIONS (5) (a) The Earth and the Moon.
1 (b) The proton and the electron in an atom of hydrogen, given
that :
Use the data shown Electron rest mass = 9.11 x 10-31 kg.
below to calculate the Proton rest mass = 1.67 x 10-27 kg.
orbital radius and hence Electron’s orbital radius = 10-10 m.
the height above the
Earth’s surface of a
geostationary satellite. 2 Using the data provided at the start at the start of the Homework
Questions, calculate :
(a) The Earth’s gravitational field strength at the Moon.
Mass of the Earth = 6.0 x 1024 kg. (b) The gravitational force exerted by the Earth on the
Mean radius of the Earth = 6400 km. Moon.
Rotational period of the Earth = 24 hours.
Universal gravitational constant, G = 6.67 x 10-11 N m2 kg-2. (c) The magnitude of the Moon’s acceleration towards the
Earth.
2 Use the Internet to find out about the history of some of the
GEOSTATIONARY artificial satellites. 3 (a) Sketch the pattern of field lines of the gravitational field
surrounding a uniform spherical mass.
HOMEWORK QUESTIONS (b) On the diagram you have drawn for (a) :
G = 6.67 x 10-11 N m2 kg-2. g = 9.81 N kg-1 (m s-2)
(i) Mark two points X and Y where the gravitational field
strength has the same magnitude but is in opposite
EARTH - mean radius = 6400 km; mass = 6.0 x 1024 kg.
directions.
MOON - mean radius = 1740 km; mass = 7.4 x 1022 kg.
mean distance from Earth = 3.8 x 108 m. (ii) Mark a point Z where the gravitational field strength is
0.25 x the gravitational field strength at X and in the
SUN - mean radius = 700 000 km; mass = 2.0 x 1030 kg.
same direction.
mean distance from Earth = 1.5 x 1011 m.
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UNIT G484 Module 2 4.2.2 Gravitational Fields 5 This question is about gravitational fields. You may assume that 12
all the mass of the Earth, or the Moon, can be considered as a point
4 A planet P of mass (m) orbits mass at its centre.
the Sun of mass (M) in a mass = M
circular orbit of radius (r), (a) It is possible to find the mass of a planet by measuring the
as shown in the diagram. mass = m
r gravitational field strength at the surface of the planet and
knowing its radius.
The speed of the planet in P
S
its orbit is (v). (i) Define gravitational field strength, g.
(a) On the diagram, draw an (ii) Write down an expression for g at the surface of a planet in
arrow to represent the terms of its mass M and radius R.
linear velocity of P.
Label the arrow V. (iii) Show that the mass of the Earth is 6.0 x 1024 kg, given
Draw a second arrow representing the direction of the force that the radius of the Earth = 6400 km.
acting on P. Label this arrow F.
(b) (i) Use the data below to show the value of g at the Moon’s
(b) (i) Write down an expression, in terms of r and v, for the surface is about 1.7 N kg-1.
magnitude of the centripetal acceleration on P.
(ii) Write down an expression, in terms of m, r and v, for the mass of Earth = 81 x mass of Moon.
magnitude of the force F acting on P. radius of Earth = 3.7 x radius of Moon.
(iii) Write down an expression, in terms of m, M, r and G, for the
magnitude of the gravitational force F exerted by the Sun (ii) Explain why a high jumper who can clear a 2m bar on Earth
on the planet. should be able to clear a 7m bar on the Moon. Assume that
the high jump on the Moon is inside a ‘space bubble’ where
(c) From observations of the motions of the planets around the Sun, Earth’s atmospheric conditions exist.
KEPLER found that the square of the period of revolution of a
planet around the Sun (T2), was proportional to r3. (iii) The distance between the centres of the Earth and the
Moon is 3.8 x 108 m. Assume that the Moon moves in a
(i) Write down an expression for T in terms of the speed (v) of circular orbit about the centre of the Earth. Estimate the
the planet and the radius (r) of its orbit. period of this orbit to the nearest day.
Mass of Earth = 6.0 x 1024 kg.
(ii) Use your answers to (b) (ii), (b) (iii) and (c) (i) to show that 1 day = 8.6 x 104 s.
KEPLER’S relation T 2 α r3 would be expected.
(OCR A2 Physics - Module 2824 - January 2003)
(OCR A2 Physics - Module 2824 - Specimen paper)
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UNIT G484 Module 2 4.2.2 Gravitational Fields (a) (i) Draw, on the diagram, arrows to represent the force 13
acting on each star.
6 (a) Define gravitational field strength, g.
(ii) Explain why the stars must be diametrically opposite to
(b) Explain why the acceleration due to gravity and the gravitational travel in the circular orbit.
field strength at the Earth’s surface have the same value.
(b) Newton’s law of gravitation applied to the situation shown in the
(c) A space probe, with its engines shut down, orbits Mars at a diagram, may be expressed as :
constant distance of 3500 km above the centre of the planet
and in a time of 110 minutes.
F = GM2
(i) Calculate the speed of the space probe. 4R2
(ii) Show that the mass of Mars is about 6 x 1023 kg. State what each of the symbols F, G, M and R represents.
(d) (i) Write down an algebraic expression for g at the surface
(c) (i) Show that the orbital period T of each star is related to
of a planet in terms of its mass M and radius R.
its speed v by :
v = 2πR/T
(ii) The acceleration due to gravity at the surface of Mars is
(ii) Show that the magnitude of the centripetal force required
3.7 m s-2. Calculate the radius of Mars in kilometres.
to keep each star moving in its circular path is :
(OCR A2 Physics - Module 2824 - June 2008) F = 4π2MR
T2
7 A binary star is a pair of stars
which move in circular orbits (iii) Use equations from (b) and (ii) above to show that the mass
around their common centre of of each star is given by :
mass. For stars of equal mass,
they move in the same circular M = 16π2 R3
orbit, shown by the dotted line GT2
in the diagram opposite.
(d) Binary stars separated by a distance of 1 x 1011 m have been
In this question, consider the observed with an orbital period of 100 days. Calculate the mass
stars to be point masses of each star. (1 day = 86 400 s).
situated at their centres at
opposite ends of a diameter of (OCR A2 Physics - Module 2824 - June 2004)
the orbit.
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