lai (yl8859) – HW20 – Ross – (15200)
1
This
printout
should
have
7
questions.
Multiplechoice questions may continue on
the next column or page – find all choices
before answering.
001
10.0 points
A distant star has a single planet circling it in
a circular orbit of radius 7
.
11
×
10
11
m. The
period of the planet’s motion about the star
is 703 days.
What
is
the
mass
of
the
star?
The
value of the universal gravitational constant
is 6
.
67259
×
10

11
N
·
m
2
/
kg
2
.
Correct answer: 5
.
76416
×
10
31
kg.
Explanation:
Let :
G
= 6
.
67259
×
10

11
N
·
m
2
/
kg
2
,
R
B
= 7
.
11
×
10
11
m
,
and
T
B
= 703 day
.
T
B
= (703 day)
parenleftbigg
24 h
1 day
parenrightbigg
3600 s
1 h
= 6
.
07392
×
10
7
s
.
According to Newton’s explanation of Ke
pler’s third law
R
3
B
T
2
B
=
G M
s
4
π
2
=
const.
The mass of the star is thus
M
s
=
4
π
2
G
R
3
B
T
2
B
=
4
π
2
6
.
67259
×
10

11
N
·
m
2
/
kg
2
×
(7
.
11
×
10
11
m)
3
(6
.
07392
×
10
7
s)
2
=
5
.
76416
×
10
31
kg
.
002
10.0 points
An object is dropped from rest from a height
6
.
9
×
10
6
m above the surface of the earth.
If there is no air resistance, what is its speed
when it strikes the earth?
The acceleration
of gravity is 9
.
81 m
/
s
2
and the radius of the
Earth is 6
.
37
×
10
6
m.
Correct answer: 8
.
06136 km
/
s.
Explanation:
Let :
h
= 6
.
9
×
10
6
m
,
g
= 9
.
81 m
/
s
2
,
and
r
= 6
.
37
×
10
6
m
.
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 Winter '08
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 mechanics, Potential Energy, General Relativity, Standard gravity

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