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Density of a Hot Jupiter
Last Thursday (February 1) in class, Professor Bailyn discussed a “Hot Jupiter” that
is aligned in just the right way such that the planet periodically passes in front of the
star (i.e. “transits”). We have observed another nearby sunlike star that also transits.
In order to determine the composition of the star, you set out to measure the density.
Since we know that density (
ρ
) = mass (
M
) / volume (
V
), we need to measure the mass
and volume
of the planet
in order to get the density
of the planet
.
v
=
2
πa
P
a
3
=
P
2
M
1 AU = 1
.
5
×
10
11
m
v
*
M
*
=
v
p
M
p
V
=
4
3
πR
3
1
M
±
= 2
×
10
30
kg
ρ
=
M
V
A
=
πR
2
1 year = 3
×
10
7
s
Step 1: Mass
From Doppler measurements, it’s been found that the re±ex velocity of the star (due
to the planet) is 85 m/s and that the period of the planet’s orbit is 3.5 days (= 10

2
yrs).
•
What is the semimajor axis (
a
) of the planet’s orbit?
a
3
=
P
2
M
= (10

2
)
2
*
1
= 10

4
a
= (100
×
10

6
)
1
/
3
a
= 5
×
10

2
A.U. = 7
.
5
×
10
9
m
•
What is the velocity of the planet in its orbit?
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This note was uploaded on 02/06/2012 for the course BENG 100 taught by Professor Marksaltzman during the Spring '08 term at Yale.
 Spring '08
 MarkSaltzman

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