you have been hired as a consultan for the new star trek tv series to make sure

Question

you have been hired as a consultan for the new star trek tv series to make sure that any science on the show is correct. in this episode, the crew of the enterprise discovers an abandoned space station in deep space far from any stars. this station is obviously the work of an advanced race and consists of four 4x10^20 kg asteroids configured si that each is at the corner of a square with 150 km sides. according to the tricorder, the station has been abandoned ffor at least two centuries. you know that such a configuration is unstable and worry whether there would be observable motion of the asteroids after two hundred years so you calculate the acceleration of one of the asteroids in the proposed configuration. make sure you give both the magnitude and direction of the acceleration

note: far away from earth, we cant use a constant gravitational force Fg=mg insted, we need to use a more general expression: Fg= (Gm1m2)/r^2, where m1 and m2 are the objects masses, r is the distance between them, and G is a constant, G= 6.674x10^-11 N.m^2/kg^2

Explanation / Answer

force on 1 asteroid by other

F = 2*Gm1m2/r^2 + Gm1m2/2r^2

F = Gm1m2/r^2( 2 + 1/2)

m1 = m2

F = 5G*m^2/2r^2

F = 1.186 x 10^21 N

F = ma

a = F/m

a = 2.96 m/s^2

direction = 45 degree

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