Gravitational Field and Force Questions

Data: Mmoon = 7.3 x 1022 kg Rmoon = 1737 km G = 6.67 x 10-11 Nm2 kg-2

1. Distinguish between weight and mass. Calculate the weight of a 1000kg buggy on the
surface of the moon and at a distance of 100km above its surface.

2. Calculate the gravitational force between two adjacent protons, 10-15 m apart, each of mass
1.67 x 10-27 kg.

3. Calculate the gravitational field strength on the surface of the moon. The find the ratio of
the gravitational field strength at its surface to the gravitational field strength 100 km above
its surface.

4. Show that 1 N kg-1 is equivalent to 1 m s-2, using F=ma. Use a similar method to show that
the acceleration experienced in freefall in a gravitational field is always equal to 𝑔, the
gravitational field strength.
 Past Paper Questions
Q1. Exoplanets are planets orbiting stars other than our own Sun. Most exoplanets
discovered so far are giant planets similar to the planet Jupiter. The exoplanet Kepler-7b has
a mass about 0.43 times the mass of Jupiter, and a radius about 1.6 times the radius of
Jupiter.
Take the gravitational field strength at the surface of Kepler-7b to be gK, and the gravitational
field strength at the surface of Jupiter to be gJ.

The ratio is
A 0.17
B 0.27
C 0.69
D 1.1 (Total for question = 1 mark)

Q2. The gravitational field strength at the surface of the Earth is 9.8 N kg−1. A satellite is
orbiting at a height above the ground equal to the radius of the Earth.

The gravitational field strength, in N kg−1, at this height is

A 0.0
B 2.5
C 4.9
D 9.8 (Total for Question = 1 mark)

Q3. Select the graph that shows correctly the relationship between the gravitational force F
between two masses and their separation r.

A
B
C
D
(Total for question = 1 mark)

Q4. A small satellite has a weight of 1200 N at the Earth's surface. It is launched into a
circular orbit with radius equal to twice the radius of the Earth. The weight of the satellite in
this orbit is
A 0N
B 300 N
C 600 N
D 1200 N
(Total for question = 1 marks)
Q5.

Q6. Mars is our nearest neighbour in the solar system. In August 2003 the distance between
Mars and the Earth was the closest in recorded history at 5.6 × 1010 m.
mass of Mars = 6.4 × 1023 kg
mass of Earth = 6.0 × 1024 kg
Calculate the gravitational force between Mars and the Earth when they were at this
distance.
(2)
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Gravitational force = ...........................................................

(Total for question = 2 marks)

Q7.

In 2014 the Rosetta spacecraft reached the comet Churyumov-Gerasimenko.

Rosetta went into orbit around the comet.
The following table gives some data for the comet.

The comet is irregular in shape but can be modelled as a spherical object.

(a) Show that a sphere with this mass and density has a radius of about 1700 m.
(3)
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(b) Calculate the gravitational field strength at the surface of the comet.
(2)
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Gravitational field strength = ...........................................................

(c) A probe was sent from the Rosetta spacecraft to land on the comet.
The probe bounced off the surface of the comet and took 1 hour and 50 minutes to return to
the surface again.
Calculate the height above the surface of the comet that the probe would have reached.
Assume that the acceleration of the probe is constant with the magnitude calculated in
(b).
(2)
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Height = ...........................................................

(d) Explain, using gravitational field theory, how the actual height reached would compare
with the value calculated in part (c).
You may assume there are no resistive forces such as air resistance.
(3)
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(Total for question = 10 marks)

Q8.
The planet Venus may be considered to be a sphere of uniform density
5.24 × 103 kg m−3.
The gravitational field strength at the surface of Venus is 8.87 N kg−1.

(a) (i) Show that the gravitational field strength gs at the surface of a planet
is related to the the density ρ and the radius R of the planet by the
expression

where G is the gravitational constant.

(2)

(ii) Calculate the radius of Venus.

Give your answer to an appropriate number of significant figures.

radius = ____________________ m
(3)
(b) At a certain time, the positions of Earth and Venus are aligned so that the
distance between them is a minimum.
Sketch a graph on the axes below to show how the magnitude of the
gravitational field strength g varies with distance along the shortest straight
line between their surfaces.
Consider only the contributions to the field produced by Earth and Venus.
Mark values on the vertical axis of your graph.

(3)
(Total 8 marks)
 Gravitational Field and Force Questions - ANSWERS

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𝐺𝑀
𝑟
𝑔 (𝑟 + ℎ) (1737 + 100)
𝑅𝑎𝑡𝑖𝑜 = = 𝐺𝑀 = = = 1.12
𝑔 (𝑟 + ℎ) 𝑟 1737

Resultant force on a body in freefall = 𝑚𝑔

Newton s second law: Resultant force = 𝑚𝑎

∴ for a body in freefall, 𝑚𝑔 = 𝑚𝑎, so the acceleration is eaual to the gravtational field strength
Q1. A
Q2. B
Q3. D
Q4. B
Q5. B

Q6.

Q7.
Q8.

(a) (i) M= π R3 ρ ✔

combined with gs = (gives gs = πGRρ) ✔

Do not allow r instead of R in final answer but
condone in early stages of working.
Evidence of combination, eg cancelling R2 required
for second mark.
2

(ii) ✔

gives R = 6.06 × 106 (m) ✔

answer to 3SF ✔
SF mark is independent but may only be awarded
after some working is presented.
3

(b) line starts at 9.81 and ends at 8.87 ✔

correct shape curve which falls and rises ✔
falls to zeo value near centre of and to right of centre of distance
scale ✔
[Minimum of graph in 3rd point to be >0.5 and <0.75 SE-SV distance]

For 3rd mark accept flatter curve than the above in

central region.
3
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