Astronomy 362 Problem Set #1
Due Friday, January 24
at 12 noon
In the homework problems below, “C&O” refers to your textbook.
I have selected the
problems with the expectation that they will take up to 1 hour of hard thinking/calculating
each.
If you are taking longer than this, feel free to come by my office to hash out where
you are stuck.
Note on collaborating:
You may work together on this problem set, but all work
presented here must be your own.
You must clearly acknowledge any people you
collaborated with.
ASSUMED READING:
Please finish C&O Chapters 2 and 3 before Friday, January 24.
1.
[C&O 2.4 (tweaked)]
Derive
E
=
1
2
μ
v
2
−
GM
μ
r
(Eq. 2.25), the expression for the
total energy of a twobody system in terms of reduced mass from the expression
for total energy of a twobody system in general cartesian coordinates
E
=
1
2
m
1
!
v
1
2
+
1
2
m
2
!
v
2
2
−
Gm
1
m
2
!
r
2
−
!
r
1
.
HINT:
Write down expressions for
!
r
1
and
!
r
2
in terms of
!
r
and the masses
m
1
and
m
2
first.
Use those to find expressions for velocities
!
v
1
=
d
!
r
1
dt
and
!
v
2
=
d
!
r
2
dt
and go
from there.
You may assume constant masses.
2.
[C&O 2.7 (tweaked)]
Calculate the escape speed from the Solar System, starting
from Earth's orbit. This is the minimum speed spacecraft must reach to escape
directly from Earth to interstellar space (e.g. 
New Horizons
). You can assume
that the Sun constitutes all of the mass of the Solar System.
NOTE:
For full
credit, clearly explain your reasoning.
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 Spring '14
 Dr.JuanCabanela
 Solar System, low surface brightness

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