Question

Calculate the force of gravity on a spacecraft 12800 km (2 earth radii) above the earth's surface if its mass is 1600 kg. n (toward the earth)

Answer 1

Since the spacecraft is two earth radii the surface of the earth, it is three earth radii above the center.

Given: Radius of the earth re = 6.38 x 10⁶ m  r = 1.91 x 10⁷ m

           Mass of the spacecraft Ms = 1600 Kg

           Mass of the earth Me = 5.98 x 10²⁴ Kg

           G = 6.67 X 10⁻¹¹ N.m²/Kg²

Formula: F = GMeMs/r²

           F = (6.67 X 10⁻¹¹ N.m²/Kg²)(5.98 x 10²⁴ Kg)(1,600 Kg)/(1.91 x 10⁷ m)²

           F = 6.38 X 10¹⁷ N/3.65 X 10¹⁴ m²

           F = 1,748.5 N

      

Answer 2

Force of gravity on a spacecraft is 1748.5 N.

Explanation:

Given :

Distance = 12800 km

Mass = 1600 kg

Calculation :

Formula Used -

$\rm F = \dfrac{GM_eM_s}{r^2}$   ------ (1)

Where,

Radius of earth - $\rm r = 1.91\times10^7\; m$

$\rm M_s = 1600kg$

$\rm M_e=5.98\times10^2^4\;kg\;\;\;\;(Mass \;of\;earth)$

$\rm G = 6.67 \times 10^-^1^1\;Nm^2/kg^2$

So from equation (1),

$\rm F= \dfrac{6.67\times10^-^1^1\times5.98\times10^2^4\times1600}{(1.91\times10^7)^2}$

$\rm F = 1748.5\;N$

Therefore, force of gravity on a spacecraft is 1748.5 N.

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