The force of gravity on an any object due to earth is given by the equation F =

ID: 3899111 • Letter: T

Question

The force of gravity on an any object due to earth is given

by the equation F = G(moM/?) where G is the gravitational

constant, M is the mass of the earth, mf> is the mass

of the object and r is the distance between the center of

mass of the earth and the center of mass of the object. If

a rocket weighs 3.6 x 106 N at the surface of the earth

what is the force on the rocket due to gravity when

the rocket has reached an altitude of 1.2 x 104 km?

(G = 6.67 X 10-11 Nm'/kg', radius of the earth = 6370 km,

mass of the earth = 5.98 x 1024 kg).

Solution: 430000

Can someone help me understand why this is the solution?

weight = mg = mass*gravitational acceleration

= 3.6*10^6 N = mass*9.81

mass= 366972.47 kg

when rovket reach to altitude of 1.2 x 104 km

at this height force will be

F = GM*m/r^2

= 6.67 X 10-11*5.98*10^24*366972.47/((6370+1.2*10^4)*10^3)^2

= 433752.70 N

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