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Homework 2
University Astronomy
4/1/10
1
University Astronomy 1017301
Homework Assignment 2
Instructor:
Dr Andrew Robinson
Due Date:
9 am Friday, 9 April 2009.
To tackle some of the following problems you will need to do some research, using either the
textbook or other resources, to find various pieces astronomical data and the values of certain
physical constants. For calculations,
show all your workings in order to receive full credit
.
1.
It is believed that, were it not for Jupiter’s strong gravity, a 5
th
terrestrial planet would
probably have formed out of the material now occupying the asteroid belt between
Mars and Jupiter. Let us suppose that somehow, such a planet did form at this
location. Let’s call it
Phoenix
. Astronomers have accumulated some basic data on
Phoenix.
It is a terrestrialtype planet, with an albedo and rotation period about the
same as those of Mars but has a radius 1.5
×
that of Earth. It has a nearly circular orbit
and is 3 AU from the sun. It also has a small moon, which has a circular orbit around
Phoenix
with a radius of 2.83
×
10
5
km and a period of 10 d. Calculate or deduce the
following properties of Phoenix.
a.
The length of a year on
Phoenix
(in Earth days).
b.
Its orbital speed.
c.
Its mass.
Length of year = period of orbit around sun. Since we know the radius of
Phoenix’s orbit, we can find the period from Kepler’s 3
rd
law:
P
=
2
"
a
3 2
GM
!
(see Lecture 5). With a=3 AU
≈
4.5x10
11
m and M
=2x10
30
kg
(mass of sun), P
≈
1900 d
≈
5.2 y
Mass: Phoenix has a moon, whose orbital period and radius we know. We
again apply Kepler’s 3
rd
law, but this time it is the moon orbiting Phoenix,
so the relevant mass (M
ph
) is that of Phoenix:
P
=
2
a
3 2
GM
Ph
. Solving for M
ph
, with the orbital period and radius given for
the moon, we find M
ph
≈
1.79x10
25
kg
≈
3xEarth’s mass.
Phoenix has a nearly circular orbit, so knowing the radius and period, the
mean orbital speed is v
orb
= 2
π
a/P
≈
17.2 km s
1
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University Astronomy
4/1/10
2
d.
Its escape speed.
e.
Its average surface temperature.
f.
Given the escape speed and surface temperature, what is the likely composition of
Phoenix’s atmosphere? (Refer to the graph in Lecture 8.)
2.
Tidal evolution. As discussed in Lecture 6, frictional coupling causes a misalignment
between Earth’s tidal bulges and the EarthMoon direction. The resulting torque (off
center force) slows Earth’s rotation and hence decreases its angular momentum.
Assuming that angular momentum is conserved in the EarthMoon system (not a bad
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This note was uploaded on 05/11/2010 for the course AST 1017.301 taught by Professor Drandrewrobinson during the Spring '10 term at RIT.
 Spring '10
 DrAndrewRobinson
 Astronomy

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