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The 1969 film “Journey to the far side of the sun” chronicles the mission of sev

ID: 1698160 • Letter: T

Question

The 1969 film “Journey to the far side of the sun” chronicles the mission of several astronauts to a parallel Earth, which orbits our sun always exactly on the other side from our Earth. Let’s imagine a simplified version of this solar system in which there are only three objects: a star of mass M = 5 x 1028 kg (a brown dwarf) and two planets, each with mass m = 2 x 1027 kg (about the mass of Jupiter), that are moving in perfectly circular orbits, each with the same radius of r = 8 x 1011 m (about the radius of Jupiter’s orbit), but always on opposite sides of the star. What would the period (in years) of the rotation of the planets be?

Explanation / Answer

1)use G*m/R^2=m*w^2*R  ( grav force = centripetal force )

   w=ang vel=2*pi/T          (T = period )

cancel,rearrange u got KeplerII.

T^2= [ 4 * pi^2 * R^3 ]/(G*M).

pi = 3.14 ; R = 6.38 * 10^3 km ; G = 6.67 * 10^-11 ; M = 6 * 10^24

by plugin these values in the above equation, we get approximately 80 years