# 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

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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