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
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