96
Escape velocity
The minimum initial velocity needed for an object (such as a rocket) to escape to infinity from the
surface of a massive body (such as a planet) is given by
v
esc
=
2
GM
R
where
G
= 6.67
×
10
-11
m
3
kg s
-2
is the constant of gravitation,
M
is the mass of the body and
R
is its
radius. Note that
v
esc
only depends on the properties (mass and radius) of the massive body (not the
escaping object). Also notice that for a given mass,
M
,
v
esc
is higher the more compact the body (smaller
R
).
Lets examine this by imagining we can compress the Sun into a smaller and smaller volume. The mass
of the Sun is M
~
= 1.99
×
10
30
kg. Calculate the escape speed in each of the following situations, and
compare it with the speed of light (c=3.0
×
10
8
m s
-1
).
(a)
The normal-size Sun, R
~
=6.95
×
10
5
km.
(b)
The Sun when it is about the size of the Earth, R=6.95
×
10
3
km (the
Sun will actually reach this size when it ends its life as a white
dwarf).

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