## Project for ASTR7741

*Fall Semester, 2007*

**
Separation as a Function of Time During Binary Mass-Transfer
**

**Part I:** Conservative System of Point Masses
First, consider two point mass objects, M_{1} and M_{2},
in circular orbit about one another. Derive an expression for their total
(orbital) angular momentum J_{orb} in terms of their mass ratio "q",
total mass "M", and separation "a". Plot "a" versus "q" for fixed "M"
and "J_{orb}".
What is the gravitational wave strain "h_{norm}" as a function of "q"?

**Part II:** Finite-Sized stars with Spin

Now, consider that each of the two stars has a radius R_{1} and
R_{2}, and that both stars are rotating synchronously with their
orbital motion. Write an expression for the system's total angular
momentum "J_{tot}" that includes the spin angular momentum of
each star, in addition to the orbital angular momentum. Plot "a" versus
"q" assuming the stars remain tidally locked (and conserve "M" and
"J_{tot}") during the mass-transfer
event. Finally, what is the gravitational wave strain "h_{norm}"
as a function of "q" under this condition?