h7s - Solutions for Homework # 7 1. In 1959, Kopal...

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Solutions for Homework # 7 1. In 1959, Kopal determined that the Roche lobe radius R R with nearly the same volume as the Roche lobe surrounding the star m which is orbiting the star M is R R = 0 . 46 D m M + m 1 / 3 . D is the distance between the stars and they are assumed to be in a circular orbit. The Roche lobe is the volume defined by the potential surface that defines the Roche limit, i.e., the potential surface that passes through the inner Lagrangian point. The Ja- cobi radius r J , which is the distance from the center of m to the inner Lagrangian point when m << M , is r J = D m 3 M + m 1 / 3 . Which, r J or R R , is larger, and why? When m << M , r R /R J = 0 . 46 3 1 / 3 = 0 . 66 so r J is big- ger. This is because R R is the radius that would result if the volume of the Roche lobe was spherical. An ellipsoid with the x, y semi-major axes of r J has a z semi-major axis r z , and its volume satisfies r 2 J r z = R 3 R . Since r z < r J , we have r J > R R ....
View Full Document

Page1 / 2

h7s - Solutions for Homework # 7 1. In 1959, Kopal...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online