- #1

ChrisBaker8

- 24

- 0

## Homework Statement

The solar-like star HD209458 with a mass of 1.14 solar masses exhibits radial velocity variations with a period of 3.52 days and an amplitude of 84m/s. What is the mass of its companion and what type of object is it?

## Homework Equations

M/m = r/R = v/V

[M,R,V = star, m,r,v = companion]

## The Attempt at a Solution

I've just worked this out myself so if it's off please tell me, but I have to assume the star and planet (or body) are both moving in circular orbits, and the are on opposite sides of the centre of mass, and rotating around it in their orbits (stars one much smaller) with equal periods, as shown in this clip:

http://en.wikipedia.org/wiki/File:Planet_reflex_200.gif

from Wikipedia (Radial Velocity).

Now, I'm assuming the data given means that (in the above animation, assuming the viewer is to the left of the centre of mass at infinity) the star will be moving 42m/s faster towards the observer (or 42m/s slower away from the observer, to be more accurate) at the bottom of the orbit, and 42m/s faster away from the observer at the top of the orbit.

The orbit of both takes 3.52 days. So if I know the star is traveling (forgetting the whole system is moving) at 42m/s around the circle, and I know the period, I can calculate the circumference and therefore radius of the stars orbit. But from there I don't know. The companion could be close and large, or far away and small. I'm not sure how I can work this out.