Question

a satellite is orbiting a planet a distance r from its center and another satellite is orbiting at a distance 3r from its center. what is the relation between the accelerations due to gravity for each case?

Answer 1

Answer:

The relation between acceleration due to gravity for both cases $g_{1} = 9g_{2}$

Explanation:

What is acceleration due to gravity ?

Any object's acceleration when it is only being affected by gravity.

According to the given information

Acceleration due to gravity could be found by  $\frac{GM}{r^{2} }$

Distance between satellite orbiting planet from center = r

Acceleration due to gravity for this case $g_{1}$ = $\frac{GM}{r^{2} }$

Distance between satellite orbiting planet from center = 3r

Acceleration due to gravity for this case $g_{2}$ = $\frac{GM}{(3r)^{2} }$

relation between the acceleration due gravity in each case

$\frac{g_{1} }{g_{2} } =\frac{(3r)^{2} }{r^{2} }$

$\frac{g_{1} }{g_{2} } =\frac{9r^{2} }{r^{2} }$

$\frac{g_{1} }{g_{2} }$ = 9

$g_{1} = 9g_{2}$

The relation between acceleration due to gravity for both cases $g_{1} = 9g_{2}$

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