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Answer to Question #21907 in Mechanics | Relativity for Lizbeth

Question #21907
Mars has a Mass of about 6.4*10^23kg, & it's moon Phobos has a mass of about 9.6*10^15kg. If the magnitude of the gravitational force between the two bodies is 4.6*10^15N, at what speed does Phobos orbit Mars?
Expert's answer
let us find distance between Mars and Phobos

we know that
F=G*m1*m2/r^2
then
r = sqrt(G*m1*m2/F) = 9 438 643 m = 9438.6 km
now we can find speed.
v^2/r=a
where a is centrifugal acceleration.
a=F/m2
where m2 is mass of Phobos. Hence the speed is
v=sqrt(r*a) = sqrt(r*F/m2 ) = 2 126.66 m/s = 2.1 km/s

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