Question

The mass of the Hubble Space Telescope is 11600 kg, determine the weight of the
telescope (i) when it was resting on the earth and (ii) as it is in its orbit 598 km above the
earth’s surface [hint: the earth’s radius = 6.38 x 106m].

Answer 1

Answer on question #53465, Physics / Mechanics — Kinematics — Dynamics

Question The mass of the Hubble Space Telescope is $11600\mathrm{~{}kg}$, determine the weight of the telescope (i) when it was resting on the earth and (ii) as it is in its orbit $598\mathrm{~{}km}$ above the earths surface [hint: the earths radius $=6.38\cdot 10^{6}\mathrm{~{}m}$].

Solution (i) On the Earth the weight will be

$$F = \frac {G M _ {e a r t h} m _ {h u b b l e}}{r _ {e a r t h} ^ {2}} = g m _ {h u b b l e} = 9. 8 1 \cdot 1 1 6 0 0 = 1 1 3 7 9 6 N$$

(ii) When it orbiting, its weight is equal to zero, as there is no reaction force. However, we can find gravitational force in this case

$$F = \frac {G M _ {e a r t h} m _ {h u b b l e}}{(r _ {o r b i t} + r _ {e a r t h}) ^ {2}} = \frac {6 . 6 7 \cdot 1 0 ^ {- 1 1} \cdot 5 . 9 7 \cdot 1 0 ^ {2 4} \cdot 1 1 6 0 0}{((6 . 3 8 + 0 . 5 9 8) \cdot 1 0 ^ {6}) ^ {2}} \approx 9 5 1 2 7. 5 N$$