Can you describe each step, I got a very big number in my calculation that wasn\

Question

Can you describe each step, I got a very big number in my calculation that wasn't correct.

BAND-MAID 11 Chapter 13 Gravity Y Plaskett's bi nary sys www.webassign.net/web/Student/Assignme Response /submit? pos 58ldep 1600346 Assignment scoring Your last submission is used for yourscore. 6. O 01 points I Previous Answers SerPSE9 13.P021.MI.FB My Notes Ask Your Teacher Plaskett's binary system consists of two stars that revolve in a circular orbit about a center of mass midway between them. This statement implies that the masses off the two stars are equal (see figure below Assume the orbital speed of each star is IV 210 km/s and the orbital period of each is 12.5 days. Find the mass M of each star. (For comparison, the mass of our sun is 1.99 x 30 kg.) 4796833.945 X If you know the orbital period and the speed of an object undergoing constant circular motion, how do you calculate the radius of the circle? solar masses CM Need Help? Read Master It Submit Answer Save Progress Practice Another Version View Previous Question Question 6 of 7 View Next Question Home My Assignments Extension Reques? WebAssignE 4.0 1007-2017 Achwanoed instructio Systems, in 455 PM 4 4/22/2017 Type here to search

Explanation / Answer

There is a single force acting on each body, that of gravity. Apply Newton's Second Law. The bodies are traveling in a

circular path, so their acceleration is centripetal.

Fg = ma; a = v^2 / r

Fg = mv^2/r

Evaluate the force of gravity using Newton's Law of Universal Gravitation. Note that the r in the formula is the

distance between the two bodies, not the radius of their orbit

Fg = Gm1m2 / r^2

Fg = GM^2 / (2r)^2

Combine the above equations.

GM^2 / 4r^2 = Mv^2 / r

M = 4v^2r / G

R is unknown, so we must reexpress it in terms of a variable we do know, T

vT = 2pi*r

M = 2v^3T / pi*G

R is unknown, so we must reexpress it in terms of a variable we do know, T

M = (2 x (210 x 10^3)^3 x 12.5 days x 86400 s/day) / (3.14 x 6.67 x 10^-11)

M = 9.55 x 10^31 kg

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