khounvivongsy (sk27799) – Homework 18 – Weathers – (17104)
1
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001
10.0 points
Halley’s comet moves about the Sun in an
elliptical orbit, with its closest approach to
the Sun being 0
.
714 AU and its greatest dis
tance being 32
.
2 AU (1 AU=the EarthSun
distance).
If the comet’s speed at closest approach is
31
.
3 km
/
s, what is its speed when it is farthest
from the Sun?
You may assume that its angular momen
tum about the Sun is conserved.
Correct answer: 0
.
694043 km
/
s.
Explanation:
Using conservation of angular momentum,
we have
L
apogee
=
L
perihelion
,
or
(
m r
a
2
)
ω
a
= (
m r
p
2
)
ω
p
,
thus
m r
a
2
v
a
r
a
=
m r
p
2
v
p
r
p
,
giving
r
a
v
a
=
r
p
v
p
,
or
v
a
=
r
p
r
a
v
p
=
(0
.
714 AU)
(32
.
2 AU)
(31
.
3 km
/
s)
=
0
.
694043 km
/
s
.
002
10.0 points
A distant star has a single planet circling it in
a circular orbit of radius 5
.
75
×
10
11
m. The
period of the planet’s motion about the star
is 781 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: 2
.
47024
×
10
31
kg.
Explanation:
Let :
G
= 6
.
67259
×
10

11
N
·
m
2
/
kg
2
,
R
B
= 5
.
75
×
10
11
m
,
and
T
B
= 781 day
.
T
B
= (781 day)
parenleftbigg
24 h
1 day
parenrightbigg
3600 s
1 h
= 6
.
74784
×
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
×
(5
.
75
×
10
11
m)
3
(6
.
74784
×
10
7
s)
2
=
2
.
47024
×
10
31
kg
.
003
10.0 points
Given:
G
= 6
.
67259
×
10

11
N m
2
/
kg
2
The acceleration of gravity on the surface of
a planet of radius
R
= 6850 km is 7
.
24 m
/
s
2
.
What is the period
T
of a satellite in circu
lar orbit
h
= 25345 km above the surface?
Correct answer: 62273
.
4 s.
Explanation:
Since the gravity on the surface of a planet
is given by
g
=
GM/R
2
, we can solve for the
mass of the planet:
M
=
gR
2
G
=
(7
.
24 m
/
s
2
)(6
.
85
×
10
6
m)
2
6
.
67259
×
10

11
N m
2
/
kg
2
= 5
.
09126
×
10
24
kg
.
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 Spring '09
 weathers
 mechanics, Mass, Potential Energy, Work, General Relativity, Correct Answer

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