Version 037/AACBB – quiz1121 – Demkov – (59910)
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001
10.0 points
Given:
k
=
4
π
2
G M
s
,
where
M
s
is the mass oF the Sun.
Suppose that the gravitational Force law
between two massive objects is
F
g
=
G m
1
m
2
r
2+
ǫ
,
where
ǫ
is a small number.
Which oF the Following would be the rela
tionship between the period
T
and radius
r
oF
a planet in circular orbit?
1.
T
2
=
k r
3
−
2
ǫ
2.
T
2
=
k r
3
3.
T
2
=
k r
3+2
ǫ
4.
T
2
=
k r
3+
ǫ
correct
5.
T
2
=
k r
3+2
/ǫ
6.
T
2
=
k r
2+3
ǫ
7.
T
2
=
k r
3
ǫ
8.
T
2
=
k r
2
−
3
ǫ
9.
T
2
=
k r
3
−
ǫ
10.
T
2
=
k r
3
/ǫ
Explanation:
Kepler’s third law changes From its normal
Form iF gravity is not quite an inverse square
law.
Let
M
p
be the mass oF a planet and
M
s
be
the mass oF the Sun.
r
will be the radius oF
the orbit.
M
p
v
2
r
=
G M
s
M
p
r
2+
ǫ
.
Since
v
=
2
π r
T
4
π
2
r
2
r T
2
=
G M
s
r
2+
ǫ
.
Kepler’s third law becomes
T
2
=
4
π
2
G M
s
r
3+
ǫ
,
where
4
π
2
G M
s
is a constant.
002
10.0 points
A rocket oF mass
m
is to be launched From
planet X, which has a mass
M
and a radius
R
.
What is the minimum speed that the
rocket must have For it to escape into space?
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 Spring '07
 Swinney
 mechanics, Mass, General Relativity, Gravitational constant, G Ms

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