Gravitational potential energy

Dear Student

Gravitation at a distance r    g=  GM_e / r²  ----------------------(1)

Where G is Universal gravitational constant,M_e earth mass.

PE of a mass m at a distance r from the earth = mgr =m (GM_e / r²) r =mGM_e / r

Given that  mGM_e / r =100GM_e / 10⁷ =4.8 x 10⁹ joule  ==>  GM_e=4.8X10^{4  m3}/s²  ------(2)

Gravitation at a distance 10 ⁹m   g=  GM_e / 10¹⁸         [    from eqn(1) ]   ----------------(3)

Weight of the rocket at  10 ⁹m  = mg= 100GM_e / 10¹⁸      =100X  4.8 x 10⁴   /10¹⁸  =4.8X10^-12  N.

weight of the rocket in newton at a distance        10 ⁹m =4.8X10^-12  N.

Regards

Topperlearning

 

Get GM_e from equation (3)  ==>  mg=  100  X