Question

a. compute the acceleration due to gravity of a moon which is 5/6 the radius of the earth and twice as massive as the earth?

b. how high above the moon would you ha e to go to have an acceleration due to gravity equal to earth?

Answer 1

Acceleration due to gravity on earth = a1= [GM_{​​​​​e}​]/R_e²

G= gravitational constant

M_{​​​​​​e} = 5.972 x 10^-24 kg

R_{​​​​​e ^{= 6378.1 km}}

Putting all values and solving, we get

a1= 9.8 m/s^{​​​​​​2}

Acceleration due to gravity on moon= a2= [GM_{​​​​​o} ]/R_{​​​​​​o}^​2

Me= mass of earth

Mo= mass of moon

Re= radius of earth

Ro= radius of moon

Ro= (5/6)(Re)

Mo= (2)(Me)

Acceleration due to gravity on moon= [G(2M_e)] / [(5/6)(R_{​​​​​​e})]²

⁼ (2.88){ [GM_{​​​​​e}​]/R_{​​​​​​e}^​​2 }

= 2.88(9.8)

= 28.224 m/s^{​​​​​​2}

(b) let u have to reach height h to have the acceleration equal to earth on moon

This implies, [GM_{​​​​​e} ]/R_{​​​​​​e}^{​​​​​2} = [G(2M_e)] /[(5/6)R_{​​​​​​e} + h]²

solving we get, h= (0.58)R_{​​​​​​e}

R_{​​​​​​e} = 6378.1 km

This implies h= (0.58)(6378.1) = 3704.9121km