Question

a satellite with a mass of 100kg fires it’s engines to increase velocity, thereby increasing the size of its orbit around the earth. as a result it moves from a circular orbit if radius 7.5x10^6 m to an orbit of radius 7.7x10^6 m. what is the approximate change in gravitational force from the earth as a result of this change in the satellites orbit?

Answer 1

The approximate change in gravitational force from Earth as a result of the change in radius of the satellite's orbit is -95.07N

What is the universal law of gravitation?

The universal law of gravitation states that the particle of matter in the universe attracts another particle with a force directly proportional to the product of their masses and inversely proportional to the square of the distance between them.

It is written thus;

F = G $M_1M_2$÷ $r^2$

Where

F = Gravitational force

G = Gravitational constant

$M_1$ and $M_2$ are the masses of the object

r = radius

How to calculate the gravitational force

Formula:

F = G $M_1M_2$÷ $r^2$

Given $M_1$ = 100kg

$M_2$ = 5.97 x$10^{24}$ kg

r = 7.5 x $10^6$ m

G =  6.67 x $10^{-11}$ N-m²/kg²

For the first orbit, substitute the values

F = 6.67 x $10^{-11}$× 150 ×  5.97 x $10^{24}$ ÷ (7.5 x$10^6$)$^2$

F = 5.95 × $10^{16}$ ÷ 56.25 × $10^{12}$=  105.77 N

For the second orbit of radius 7.7 x 10^6 m

F =  6.67 x $10^{-11}$ × 100 ×  5.97 x $10^{24}$ ÷ (7.7 x $10^6$)2

F = 5.95 × $10^{16}$÷ 59.25 × $10^{12}$ = 200. 84 N

The approximate change = 105. 77 - 200. 84 = -95.07N

Hence, the approximate change in gravitational force from Earth as a result of the change in radius of the satellite's orbit is -95.07N

Learn more about gravitational force here:

brainly.com/question/19050897

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