The solution must include the following parts: given or known, find, basic or ba
ID: 1529028 • Letter: T
Question
The solution must include the following parts: given or known, find, basic or basic relations), the symbolic or symbolic solution, and the numerical or numerical solution. All work, units, and conversions to standard units must be shown and must be correct. Two stars M_1 and M_2 of equal mass make up a binary star system. They move in a circular orbit that has its center at the midpoint of the line that separates them. If M_1 = M_2 = 5.45 sm (solar mass), and the orbital period of each star is 1.95 days, find their orbital speed. (The mass of the sun is 1.99 times 10^30 kg)Explanation / Answer
Both Stars are moving in the circular orbits, with required Centripital force provided by the gravitational force from the opposite star.
That gives the basic relation
GM2/ (2R)2 = MV2/R
where G is gravitational constant 6.6 x 10-11 , M is mass of both stars, R is radius of circular path of each Star and V is their orbital speed.
Hence GM/4R = V2
R = GM/4V2 ...1
Time period of rotation T = 2 pi R /V
Taking value of R from 1st equation we get
T = 2 pi (GM/4V2) /V = pi G M/ 2 V3
V = (pi G M / 2 T)1/3
V = ( pi x 6.67 x 10-11 x 5.45 x 1.99 x 1030 / 2 x 1.95 x 24 x 3600 )1/3
= 2.25 x105 m/s
T = 4 pi R3/2 / (GM)1/2