Dance of a star: Part II - (Problem 4-6)

by Mee Wong-u-railertkun, David Vartanyan, John Pharo

Credit: ESO

We present the solution to problems from the worksheet "Planet Host Stars Wobble But They Don't Fall Down" (which could be found here.) The outline of this worksheet is as following. First, we are going to see how a planet affects the movement of a star. From that knowledge, we can observe this "weird" characteristic of a star to find exoplanets. In this post, we present solution to question four to six.

(4) We want to write the maximum velocity amplitude, K, in terms of solar masses, years and Jupiter masses. First, from the equation derived from "Dance of a star: Part I", we can write K as,

Thus, we can write in term of Jupiter mass, year, and solar mass by using the fact that Jupiter mass is around 2e27 kg, one year is around pi times 10^7 seconds, and solar mass is 2e30 kg.

Hence,

(5) Now, we want to see the radial velocity of a Jupiter-analog with a Solar-analog. Period of a Jupiter is approximately 12 years. Thus,

(6) What if we changes to an Earth-mass planet with one-year orbit around a G star. Our sun is a good example for G star. Earth mass is around 1/1000 of Jupiter mass. Thus,