Two-Star System: Calculating Inertia & Angular Momentum

[dreit]

Homework Statement

Given: Two stars A and B, are in circular orbits of radii r_a and r_b, respectively, about their common center of mass at point P. Each star has the same period of revolution T.

Determine expressions for A)the moment of inertia of the two-star system about its center of mass and B)the angular momentum of the system about the center of mass.

Homework Equations

A)? I need help on the conceptual reasoning of this

B) p=mv

The Attempt at a Solution

I don't have one because this has me very lost...

 

[dreit]

Another equation that may be useful is (Gm1m2/r^2). For the part b, i was also thinking that since the orbiting path is a circle that the angular momentum would be consistent throughout so could u just use like the centripetal force formula with a few modifications?

 

[Delphi51]

You can consider the stars to be point masses for the moment of inertia calculation, so it will be your simplest formula for moment of inertia.

You also need a basic formula for angular momentum.

The formulas can be found in Wikipedia if you don't have them handy already.

 

[dreit]

L= r*mv right? Cause the page says with respect to a point, which in this problem is p

 

[Delphi51]

Yes. And angular momentum adds, so
total L = (L of star 1) + (L of star 2).