Physics-the Martian moon travels in a circular orbit of radius 9.4x10^6 m around Mars with a period of 7.6 hours Calculate the mass of mars?

Answer 1

T = 2π√[R³/GM]

7.6 hr x 3600 s/hr = 2π√[(9.4e6)³/6.673e-11•M]

√[(9.4e6)³/6.673e-11•M] = 4354.479

(9.4e6)³/6.673e-11•M = 1.896149e7

M = (9.4e6)³ / 1.896149e7 • 6.673e-11

  = 6.56e23 kg

published value: 6.42e23 kg

Satellite motion, circular

V = √(GM/R)

V = √(gR)

T = 2π√[R³/GM]

  T is period of satellite in sec

  V = velocity in m/s

  G = 6.673e-11 Nm²/kg²

  M is mass of central body in kg

  R is radius of orbit in m