Acceleration due to gravity on earth = a1= [GMe]/Re2
G= gravitational constant
Me = 5.972 x 10-24 kg
Re = 6378.1 km
Putting all values and solving, we get
a1= 9.8 m/s2
Acceleration due to gravity on moon= a2= [GMo ]/Ro2
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(2Me)] / [(5/6)(Re)]2
= (2.88){ [GMe]/Re2 }
= 2.88(9.8)
= 28.224 m/s2
(b) let u have to reach height h to have the acceleration equal to earth on moon
This implies, [GMe ]/Re2 = [G(2Me)] /[(5/6)Re + h]2
solving we get, h= (0.58)Re
Re = 6378.1 km
This implies h= (0.58)(6378.1) = 3704.9121km
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