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Klio2033 [76]
3 years ago
11

What is the distance of the spaceship from the earth

Physics
1 answer:
PIT_PIT [208]3 years ago
6 0

Gravitational force on spaceship is given by equation

F = \frac{Gm_1m_2}{r^2}

here m_1, m_2 = masses of two objects

r = distance between their centers

now it is given that gravitation force due to earth is two times the force of gravitation due to moon

F_{earth} =2 F_{moon}

\frac{GM_e m}{r^2} =2 \frac{GM_m m}{(d-r)^2}

\frac{M_e}{r^2} =2 \frac{M_m }{(d-r)^2}

M_e (d -r)^2 =2 M_m r^2

(\sqrt{2\frac{M_m}{M_e}} + 1)r = d

given that

M_m = 7.35 * 10^{22} kg

M_e = 5.98 * 10^{24} kg

d = 384000 km

now from above equation

(\sqrt{2\frac{7.35* 10^{22}}{5.98*10^{24}}} + 1)r = 384000 km

r = 269875.5 km

<u>so the distance from earth will be 269875.5 km</u>

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