Amplitude of spectroscopic signal

[kvan]

Homework Statement

What is the amplitude of the spectroscopic signal if the inclination is 45 degrees?
Mass star = 1 mass of sun = 1.9891 x 10^30kg
Mass Planet = 10 mass Earth = 5.9736 x 10^25kg
Orbital period = 1 year

Homework Equations

I'm not sure about even what equation to use.

The Attempt at a Solution

I calculated the velocity of both masses, with velocity of the planet equalling 29.7km/s and the velocity of the star being 0.891km/s.

 

[mark726]

I then used the equation for amplitude of a spectroscopic signal, A = vplanet/vstar, and plugged in the values to get an amplitude of 33.3. However, I'm not sure if this is correct or if there is another equation I should be using. Can anyone confirm if this is the correct approach?

Your approach is close, but there are a few issues.

First, the equation for amplitude of a spectroscopic signal, A = vplanet/vstar, is not quite correct. The correct equation is A = vplanet*sin(i)/vstar, where i is the inclination angle. This accounts for the fact that the velocity of the planet is not directly towards or away from us, but rather at an angle.

Second, you have calculated the velocities using the masses and orbital period, but these are not the only factors that determine the velocities. You also need to know the orbital radius of the planet and the star.

To calculate the orbital radius, you can use Kepler's third law, which relates the orbital period, the orbital radius, and the masses of the two bodies. So, you can use this equation to calculate the orbital radius of the planet and the star, and then plug these values into your equation for amplitude.

Finally, just a minor point, but the units for velocity should be m/s, not km/s.

So, to summarize, the correct approach would be to use Kepler's third law to calculate the orbital radius of the planet and the star, then use the equation A = vplanet*sin(i)/vstar to calculate the amplitude of the spectroscopic signal.