Answer:
acceleration due to gravity at 16197 km above the ground = 2.76[tex]\frac{m}{s^{2}}[/tex]
Explanation:
force of gravity two bodies [tex]\frac{GMm}{r^{2}}[/tex]
where G is the gravitational constant, M is the mass of earth, m the mass of other body, and r the distance of separation.
when the body is on the surface of earth acceleration due to gravity will be
[tex]\frac{GM}{r^{2}}[/tex] = g
when the body is at a height h above the surface of the ground acceleration due to gravity will be [tex]\frac{GM}{(r+h)^{2}}[/tex]
[tex]\frac{GM}{(r+h)^{2}}[/tex] = [tex]\frac{GM}{r^{2}(1+\frac{h}{r})}[/tex]
[tex]\frac{GM}{r^{2}(1+\frac{h}{r})}[/tex] = [tex]\frac{g}{1+\frac{h}{r}}[/tex]
we know that g = 9.8[tex]\frac{m}{s^{2}}[/tex]
therefore acceleration due to gravity = [tex]\frac{9.8}{1+\frac{16197}{6378}}[/tex]
acceleration due to gravity = [tex]\frac{9.8}{1+\frac{16197}{6378}}[/tex]
=2.76 [tex]\frac{m}{s^{2}}[/tex]
