Question

what formula should I use to answer a question such as the one below when my normal formula doesn't fit:
'The radius of the Earth is 6400km, the height of a geostationary satellite is 35000km above the earth's surface. What is the speed of the geostationary satellite?'

Answer 1

Answer on Question #69913 – Physics – Astronomy | Astrophysics

What formula should I use to answer a question such as the one below when my normal formula doesn't fit: 'The radius of the Earth is 6400km, the height of a geostationary satellite is 35000km above the earth's surface. What is the speed of the geostationary satellite?'

Solution: the equality between gravitational and centripetal force should be satisfied:

$$\frac {m v ^ {2}}{r} = \frac {G m M}{r ^ {2}},$$

where $r = R_{E} + R_{G}, R_{E} = 6400 \, \text{km}, R_{G} = 35000 \, \text{km}$.

Answer: right formula is the following:

$$v = \sqrt {\frac {G M}{R _ {E} + R _ {G}}}.$$

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