A binary system is composed of two identical stars orbiting each other with some period To. a) Now imagine scaling all lengths (separation between the stars and the radius of the stars) by a factor k, but keeping the density of the stars the same. By what factor does the period change? b) Now instead of scaling the lengths, scale the density by k (i.e. p → kx p). By what factor does the period change?

A binary system is composed of two identical stars orbiting each other with some period To. a) Now imagine scaling all lengths (separation between the stars and the radius of the stars) by a factor k, but keeping the density of the stars the same. By what factor does the period change? b) Now instead of scaling the lengths, scale the density by k (i.e. p → kx p). By what factor does the period change?