PH709
UNIVERSITY OF KENT
SCHOOL OF PHYSICAL SCIENCES
EXOPLANETS
Assignment 1 (Smith)
1. State the physical property which differentiates planets from brown dwarfs and
the estimated critical mass which separates them.
2. By analysing the superposition of frequencies and amplitudes in the radial
velocity data for the star 55 Cancri A, the first three exoplanets in the system
were deduced. The star was found to have the following observed
parameters: 55 Cancri b corresponds to Vobs = 71.8 m s-1, and P = 14.6 days,
55 Cancri c corresponds to Vobs = 10.0 m s-1, and P = 43.9 days and 55
Cancri d corresponds to Vobs = 47.2 m s-1, and P = 5218 days. Assuming the
orbits are coplanar and circular, determine (i) which planet is furthest from the
star, (ii) which planet has the lowest mass and (iii) which planet has the
highest mass.
3.
Assignment 2
1. The planet transitting a mildly metal-poor G0V star is named CoRoTExo_1b. It has a period P = 1.5 days. The estimated mass and radius of
the star are 0.95 solar masses and 1.11 solar radii. The planet has a radius
of 1.49 Jupiter radii. If the planet has the reported particularly low
mean density of 0.38 g cm-3, calculate its mass and, hence, the maximum
radial velocity (of the star) that was measured.
Assignment 3
1. The planet transitting the yellowish-white F0V dwarf main-sequence star
CoRoT-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)
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 ×
turn over
2
(ii)
(iii)
(iv)
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) due to the orbiting planet.
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)
Assignment 4 : SMITH
1. State the technique through which the majority of the population of extrasolar
planets have so far been detected. State why this is an indirect method.
Sketch diagrams to show how the eccentricity of the exoplanet orbit is
determined. Describe the location relative to the star of exoplanets detected
by this method with (i) low eccentricity and (ii) high eccentricity.
Assignment 5 : SMITH
1. Suppose that two exoplanets are observed to transit the same star. They are
both in circular orbits with an inclination of 90 degrees. One produces periodic
dips with a period of 4 days and the other produces periodic dips with a period
of 108 days. The decrease in luminosity caused by both exoplanets is 1%.
Determine (i) how much further away the outer planet is from the central star
and (ii) how much larger the outer exoplanet is than the inner planet.
Assuming they have the same density, calculate which exoplanet will cause (i)
the highest variation in radial velocity and (ii) the largest wobble in location of
the central star.
Assignment 6 : SMITH
1. Describe how planetesimals form and grow from protoplanetary discs in the coreaccretion model. Explain why observed exoplanets are unlikely to have formed from
protostellar accretion discs or from debris discs.
Assignment 7
Describe the observed distribution of eccentricities of exoplanet orbits as presently
derived from known exoplanetary systems. Explain how the eccentricity distribution
is observed to depend on thesemi-major axis of the exoplanet
3
Explain the physical property that the parameter [Fe/H] is used to indicate and why
its measurement is providing support for the core accretion hypothesis for planet
formation
Assignment 8
A rocky planet of radius 0.001 R orbits a main-sequence G star of radius 1.0 R
and mass 1.0 M at an orbital radius of a = 0.2 AU.
(a) Photometric properties: calculate the orbital period in days, the (approximate)
transit duration in hours, and the depth (fractional change in flux) of an observed
transit in one of these systems if the inclination is i = 90°.
(b) Spectroscopic properties: determine the amplitude of the radial velocity oscillation
of the star in this system if the planet has a mass of 10 -6 M .
(c) Astrometric properties: determine the amplitude of the stellar motion in the plane
of the sky in arcseconds if the star is a distance of 10 parsecs from the Earth.
turn over