Answer:
g = 4.7 × [tex]10^{-16}[/tex] m/[tex]s^{2}[/tex]
Explanation:
Given that the mass of the satellite = 700 kg, and 10,000 m above the earth;s surface.
From Newton's second law,
F = mg ............... 1
From Newton's gravitation law,
F = [tex]\frac{GMm}{r^{2} }[/tex] .................. 2
Where: F is the force, G is the gravitational constant, M is the mass of the first body, m is the mass of the second body, g is the gravitational force and r is the distance between the centers of the two bodies.
Equate 1 and 2 to have,
mg = [tex]\frac{GMm}{r^{2} }[/tex]
⇒ g = [tex]\frac{GM}{r^{2} }[/tex]
But; G = 6.67 × [tex]10^{-11}[/tex] N [tex]m^{2} Kg^{-2}[/tex], M = 700 Kg, r = 10000 m
Thus,
g = [tex]\frac{6.67*10^{-11*700} }{10000^{2} }[/tex]
= [tex]\frac{4.669*10^{-8} }{1*10^{8} }[/tex]
= 4.669 × [tex]10^{-16}[/tex] m/[tex]s^{2}[/tex]
The force of gravity on the satellite is 4.7 × [tex]10^{-16}[/tex] m/[tex]s^{2}[/tex].
