An M-dwarf star of mass M_Q=.o8M_s, where M_s is suns mass. Assume Q is in an or

Question

An M-dwarf star of mass M_Q=.o8M_s, where M_s is suns mass. Assume Q is in an orbit with same semi major axis as Jupiter a =5.204Au a) what is the reduced mass of the Sun-Q system in terms of M_s b) How will Q's orbital period compare with jupiter's? Assume jupiters mass negligible An M-dwarf star of mass M_Q=.o8M_s, where M_s is suns mass. Assume Q is in an orbit with same semi major axis as Jupiter a =5.204Au a) what is the reduced mass of the Sun-Q system in terms of M_s b) How will Q's orbital period compare with jupiter's? Assume jupiters mass negligible a) what is the reduced mass of the Sun-Q system in terms of M_s b) How will Q's orbital period compare with jupiter's? Assume jupiters mass negligible

Explanation / Answer

a) reduced mass = M_Q*M_S/[M_Q+M_S]

                    = 0.08*1/1.08 M_s

                 = 0.0741 M_s

b) By kelpers third law, T^2/R^3 is constant.

(Tq/Tj)^2 = (aq/aj)^3

(Tq/Tj)^2 = 1^3 = 1

period of Q is equal to that of jupiter

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