Astronomy 10, Fall 2008
Homework 4  40 points total
Due in the boxes in the basement of Campbell Hall by
5pm Tuesday, September 30
. Be sure to
include your name, SID, Section Number, and GSI name on your homework, and staple it together.
1.
Inside the Giant
(12 points)
In this question we will crudely estimate the radius of Jupiter’s inner, rocky core. We suppose
that Jupiter’s total mass,
M
J
, consists of its rocky core mass,
M
c
, and the mass of the gas,
M
g
.
Throughout this question
do not plug in numbers
until you get to part (e).
(a) Let the radius of Jupiter’s rocky core be
r
c
, and the density of the core
ρ
c
. What is the mass,
M
c
, of Jupiter’s core in terms of
ρ
c
and
r
c
? (2 points)
(b) What is the volume of the shell of gas that extends beyond Jupiter’s core? Assume that this
shell begins at the radius of the core,
r
c
, and ends at the full radius of Jupiter,
R
J
. (2 points)
(c) Let us call the density of the gas
ρ
g
. What is the mass,
M
g
, of all of Jupiter’s gas in terms of
ρ
g
and your answer to part (b)? (1 point)
(d) Use your answers in part (a) and (c) to express the total mass of Jupiter,
M
J
, in terms of
ρ
g
,
ρ
c
,
R
J
, and
r
c
. (1 point)
(e) You can now substitute in numbers and solve for
r
c
, the radius of Jupiter’s rocky core. The
total mass of Jupiter is
M
J
= 2
×
10
30
g and its radius is
R
J
= 7
×
10
9
cm. Take the density
of the gas to be 1 g/cm
3
, and the density of the rock to be 10 g/cm
3
. Find
r
c
itself, and also
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 Fall '06
 NORM
 Astronomy, Solar System, Planet, Pluto, Comet

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