February 26, 2017

Homework Help: Astronomy (algebra-based physics)

Posted by Mark on Wednesday, March 4, 2009 at 4:19am.

Extrasolar planets

There are currently 340 known extrasolar planets, i.e., planets around other suns. Most of them we infer only by their gravitational pull on their host stars, and a handful appear to dim the light of their host star as they transit in front of the star. In November of last year, however, astronomers announced the detection of a planet which not only was not only resolved but whose orbital motion was also confirmed by direct imaging. In other words, in two pictures made by Hubble Space Telescope, the planet was observed to have shifted position.

This Jupiter-like planet is called Fomalhaut b, orbiting a star Fomalhaut, which is 25 light years from Earth. The host star has a mass of 2.1 M and its radius is 1.8 R. Its surface temperature is 8700 K. The planet orbits with the semimajor axis of 115 AU around the star, has small eccentricity, and the plane of the orbit is in the plane of the sky (in other words we are seeing the orbit face-on).

a) Determine the angular separation between the star and the planet, in arc seconds.

b) Determine the period of the planet, in years. Hubble imaged the system in 2004 and 2006. What is the distance that the planet traveled between the images, in AU? (Hint: if you are reaching for your lecture notes to find the formula for the velocity of
the planet, you are doing it the hard way.)

c) What is the angular separation between the position of the planet in 2004 and 2006, in arc seconds? Can the Hubble telescope, with the angular resolution of 0.04 arc seconds, detect this motion?

d) What is the equilibrium temperature on Fomalhaut b? You can ignore the effects of albedo and greenhouse effect. Can liquid water exist on Fomalhaut b?

e) At what distance from the star Fomalhaut would the planet have the same equilibrium temperature as on Earth? Again, ignore albedo and greenhouse effects.


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