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An exoplanet is discovered through careful Doppler shift analysis of the spectrum of the star it...

An exoplanet is discovered through careful Doppler shift analysis of the spectrum of the star it is orbiting. The star’s spectrum allows us to conclude with some confidence that the star has a mass M = 0.60 solar masses, and a luminosity L = 0.13 of the solar luminosity. Assuming the orbits are circular and observed edge-on, the Doppler shift tells us that the star has a speed about the centre-of-mass of V = 250 m/s and the period of the orbit is 0.35 years.

(a) What is the semimajor axis of the planet’s orbit in AU? [ It is reasonable to assume that the planet’s mass is much less than that of the star.]

(b) What is the planet’s circular speed in km/s? [In the units we use for the solar system GM = 900 (km/s)2-AU but this will have to be modified to 540 for this star.]

(c) What is the ratio of the star’s mass to that of the planet?

(d) Estimate the planet’s surface temperature, assuming that its black-body emission balances the energy it receives from the star. Take the albedo to be 0.50 and assume no greenhouse gases. Note that the star’s luminosity is 0.13 times that of the Sun.

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genius_generous answered 2 years ago
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