Compute the speeds of the star

[leonne]

Homework Statement

Compute the speeds (in km s^-1) of S0-2 and S0-16 at pericenter and apocenter.
star S0-2: period P = 15:8 yr, semimajor axis a = 1025 AU, and
eccentricity e = 0:880;

Homework Equations

Vp=((1+e)u)/(1-e)a))^1/2 va=((1-e)u)/(1+e)a))^1/2

u=(m1m2)/m1+m2

The Attempt at a Solution

I found this formula to calc the velocity of the 2 but I was never given a mass for the star. This is a 3 part problem and the other two asked to find mass of black hole and then Compute the pericenter and apocenter distances of the star. Do i use a diffrent formula? or I have to find the mass of the star? Thinking maybe to find mass of the star to use P^2=(4pie^2 a^3)/G(m1+m2) m1 ill make it the mass of the black hole and solve for m2, is that right?

Note the problem asks to do this for two stars idk if this changes anything in the formula but both stars orbit the black hole.
thxs

 

[mark726]

Thank you for your post. It seems like you are on the right track in terms of using the correct formula to calculate the velocities of the stars at pericenter and apocenter. However, you are correct in noting that you will need to know the mass of the stars in order to use these formulas. In this case, you can use the formula you mentioned (P^2=(4pie^2 a^3)/G(m1+m2)) to solve for the mass of the stars. As you mentioned, you can use the known mass of the black hole and solve for the mass of the stars. Once you have the mass of the stars, you can plug them into the velocity formulas and calculate the speeds at pericenter and apocenter for both stars. Remember to use the correct units (AU for distance and years for period) in order to get the final answer in km/s.

I hope this helps. Good luck with your calculations!