Download PH709-08-test-ans

PH709/08/TEST
UNIVERSITY OF KENT
SCHOOL OF PHYSICAL SCIENCES
EXOPLANETS
2008
Test: SMITH questions
1. The newly discovered planet transitting the F0V star CoRoT-Exo-4 is
named CoRoT-Exo-4b. It has an orbital period P = 9.2 days, an inclination
angle of 90o and an eccentricity of 0. The estimated mass and radius of
the star are 1.1 solar masses and 1.2 solar radii. The planet has a radius of
1.2 Jupiter radii.
(i)
(ii)
(iii)
(iv)
If the planet has the reported low mean density of 530 kg m-3,
calculate its mass in Jupiter masses (RJ = 7.1 × 107 m , MJ = 1.9 ×
1027 kg).
Estimate the maximum radial velocity of the star (G = 6.7 10-11
m3 kg-1 s-2, Msun = 2.0 × 1030 kg).
Determine how close the planet is to the star in AU (1 AU = 1.5 x
1011 m).
Estimate the change in magnitude during a transit (Rsun = 7.0 ×
108 m).
turn over
2
ANSWERS
(i) Mass = average density x volume = average density x (4/3)  R3
=
530 x 1.33 x3.14 x (1.2x 7.1 x 107)3 kg
=
530 x 1.33 x3.14 x (1.2x 7.1 x 107)3 / 1.9 x` 1027 Mj
=
0.7 Mj
[10 marks]
(ii) The planet orbital speed Vp is given by Vp2 = GM*/a
where a is
the star-planet distance.
The star is about one solar mass and the perioid is about 9/360 = 1/40 of
a year. Since in the solar system P2 = a3
in years and AU, a3 =
1/1600 approximately Hence a = 1/12 roughly
i.e. a = 0.08 AU roughly. So Vp2 = 6.7 x 10-11 x 2 x 1030 / (0.08 x 1.5 x
1011) = 1.4 x 1010 m2/s2
So Vp = 1.2 x 105 m/s .
V* = (Mp/M*) Vp = 0.7 x 0.001 x 1.2 x 105 m/s = 800 m/s approx.
[10 marks]
(iii) Rearrange
2
P =
2 3
4 a
G (mA + mB)
and take mB = 0 for the planet to yield a = 1.2 1010 m = 0.08 AU.
Mj
[10 marks]
(iv)
Relative change in flux change dF/F = (Rp/R*)2
= 0.01
[10 marks]
Magnitude change dM = -2.5 log ( 1 + dF/F) = 0.01
[10 marks]