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 two-body system in terms of reduced mass from the expression
for total energy of a two-body 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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