Name: _____________

Quiz: Gravitational Fields

Q1). This diagram shows the variation of the Earth’s gravitational field strength
with distance from its centre.

-
Figure 17.17

a) Determine the gravitational field strength at a height equal to 2R above the

Earth’s surface, where R is the radius of the Earth. [1].

g 98 Nkg Nkg
+
= =
2 45.

or 2 5
.

b) A satellite is put into an orbit at this height. State the centripetal acceleration
of the satellite. [1]

ac 2 45 or 25
g ms
=
.

=
.

c) Calculate the speed at which the satellite must travel to remain in this orbit. [2]
Fa = Fc
x
=m 9 =
v =

v = 7980ms

Q2) Calculate the potential energy of a spacecraft of mass 250 kg when it is

20 000 km from the planet Mars.
(Mass of Mars = 6.4 × 10^23 kg, radius of Mars = 3.4× 10^6 m.) [3]
Up 67x10" x 6 4x102 x
-GM 56x1083
= 6 250 4 .
-
.
.
.

(3 4x103 0x107)
. + 2 .

-4 .

6 x1089
.
 Q3) The Earth orbits the Sun with a period of 1 year at an orbital radius of 1.50
× 10^11 m. Calculate:
a) the orbital speed of the Earth [3]

t = 365x24x3600 R =
= 2a1 .
50 X10"
t
v =
2x1 . 50x10" 365x24X3600
S = 2Ar U =
29885 8 .

v = S/t = 29900 ms or 3 .
0x10" mst
b) the centripetal acceleration of the Earth [2]
ac
9 5 95x10" ms-r
.

=
=

c) the Sun’s gravitational field strength at the Earth. [2]

95x10 0x103
g = ac = 5
Nkga 6 .
.

Q4) The planet Mars has a mass of 6.4 × 10^23 kg and a diameter of 6790 km.
i) Calculate the acceleration due to gravity at the planet’s surface. [3]

x =

x
~ =
=
g
%
V = 3 395X10.
m

3 7 ms
g
.

M= 4x10"
6
kg
.
.

?
g =

ii) Calculate the gravitational potential at the surface of the planet. [3]
=
- 6 67
XXGo
.

-
1 .
26x107 -xgt
Q5) a) State Newton’s law of gravitation. [2]
Force between two point masses is
directly proportional to the

product of their masses and is

inversely proportional to the
square
their separation-
of
b) The planet Jupiter and one of
its moons, Io, may be considered
to be uniform spheres that are
isolated in space. Jupiter has
radius R and mean density ρ. Io
has mass m and is in a circular
orbit about Jupiter with radius nR,
as illustrated in Figure.
The time for Io to complete one orbit of Jupiter is T. Show that the time T is
related to the mean density ρ of Jupiter by the expression

where G is the gravitational constant. [4]

↑Ge M =

FG + Fa

Gampurco T9 =

3
GM = 23 z

G(XAR" =

uR][]2
c) (i)The radius R of Jupiter is 7.15 × 10^4 km and the distance between the
centres of Jupiter and Io is 4.32 × 10^5 km. The period T of the orbit of Io is
42.5 hours. Calculate the mean density ρ of Jupiter. [3]

=
R 15 X107
= 7
- in
1
NR = 4 .
32x103 m

08
=
e = 3 x (6 042)3
.

7 .
15 X107

n = 6 042 .
6 .
67x10" (42 .
5 x3600)"
T = 42 5x3600 .
C = 1 .
33x103 kgm Ay .

(ii) The Earth has a mean density of 5.5 × 10^3 kg m^−3. It is said to be a
planet made of rock. By reference to your answer in i, comment on the
possible composition of Jupiter. [1]
Jupiter is
likely to be a
gas/liquid at
high pressure.