Download A201 – Solutions #5

A201 – Solutions #5
1.
[Hint: use SI units throughout; wikipedia is a good source for planetary data.] [10 marks]
(a) Compute the blackbody temperature of Io. Quote your answer in degrees Kelvin.
Look up the albedo of Io on the internet, and quote your source (it should be close to 0.6).
Solution: The appropriate equation from the notes is
TIo = TSun [ (1 – α)1/2 RSun / 2D ] 1/2
where α is the albedo of Io and D is the orbital radius of Jupiter (which is the average orbital
radius of Io from the Sun). Inserting the appropriate numbers for Io and the Sun you will find
the blackbody temperature of Io is ~45 K.
(b) Given the blackbody temperature you derived for Io, how do you explain Io as a molten,
volcanic planet?
Solution: Wikipedia quotes the surface temperature as ranging from 90 to 130 K, which is not
too far off from our calculation. However, we know that Io undergoes volcanic eruptions with
lava flowing on its surface – rock flows at temperatures over 700 K. Thus, something else is
heating Io, which we believe is tidal heating due to the slightly eccentric orbit of Io around
Jupiter (again, wikipedia to the rescue, eccentricity of the orbit of Io = 0.0041).
2. Short answer questions. Each question is worth 5 marks. Answers to each question should be
no more than 150 words.
(a) How do we explain the observation that Jovian planets have many more moons than
Terrestrial planets?
Solution: Jovian planets have many more moons than terrestrial planets because they are more
massive. Jovian planets create many moons “in-situ" by accreting a disk of planetesimals during
the creation of the Solar System and by subsequent gravitational capture of asteroids at later
times.
(b) Why do we believe that Europa has a salty liquid water ocean?
Solution: Spectroscopy and imaging of the surface of Europa indicates that it is composed of
water ice. Galileo magnetic measurement of Europa indicate the presence of a magnetic field
induced by Jupiter, best modelled as a salty ocean (because the salt increases the conductivity
and thus the susceptibility to the magnetic field).
(c) Broadly speaking, what types of extra solar planets have been detected to date?
Solution: Extra-solar planets detected by Doppler velocity shifts are typically massive (Jupitersized or larger) and have small orbital radii (compared to the orbit of Jupiter). Meanwhile, the
Kepler mission uses transits and they are finding exoplanets of all sizes and orbital radii.
3. Arrange the following types of planetary systems in order of decreasing detectability using
current techniques. a) Earth-sized planets in Earth-sized orbits, b) Jupiter-sized planets in
Jupiter-sized orbits, c) Earth-sized planets in Jupiter-sized orbits, d) Jupiter-sized planets in
Earth-sized orbits. Justify the order of each entry.
[10 marks]
Solution: One way to order these is d), b), a), c). If we had only the Doppler velocity shifts
methods, then Jupiter mass planets are easier to find, and smaller orbits show up as larger
wavelength shifts.
The results are similar for transits in the Kepler data since Jupiter mass
planets are also physically larger and cause deeper magnitude changes during a transit –
similarly if they have small orbits, then they are more likely to be caught during a transit by the
Kepler data. Because the Kepler mission is so sensitive to micro changes in magnitudes, you
might order these as d), a), b), c) though – that is, switching a) and b) – if you argue that
exoplanets in small orbits are easier to find and confirm with repeat measurements.