Mars has a mass of about 6.39 x 10^23 kg, and its moon Phobos has a mass of about 9.8 x 10^15 kg.If the magnitude of the gravitational force between the two bodies is 4.94 x 10^15 N, how far apart...

Mars has a mass of about 6.39 x 10^23 kg, and its moon Phobos has a mass of about 9.8 x 10^15 kg.

If the magnitude of the gravitational force between the two bodies is 4.94 x 10^15 N, how far apart are Mars and Phobos? The value of the universal gravitational constant is 6.673 x 10^-11 N times m^2/kg^2. Answer in units of m.

Asked on by won

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neela's profile pic

neela | High School Teacher | (Level 3) Valedictorian

Posted on

By Newton's law of gravitation, the force ,F of attraction between  mars of mass M and its  satellite Phobos of mass m is given by:

F = G Mm/d^2 ...........(1), where G is the universal gravitational constant and d is distance between Mars and its satellite Phobos.

We can arrive at the value of d from (1). Or rewriting (1) to get d, we get:

d =  sqrt{GM/Mm/F} = sqrt{(6.673 x 10^-11 N)(6.39 x 10^23 kg)*(9.8 x 10^15 kg.)/(4.94*10^15 N)}

= 9.1973*10^6 meters.

astrosonuthird's profile pic

astrosonuthird | Student, Kindergarten | (Level 1) Valedictorian

Posted on

Follow Newton's law of gravitation.

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