Question

What is geostationery satelite . Calvulate it's height

Answer 1

Answer:

just complete your question first

Answer 2

Answer:

Height = 36,000 km

Explanation:

Heya friend,

Here we go :-

Geostationery satellite :-

It is a satellite which revolves around the earth in an equatorial plane with same angular speed and in same direction in which the earth rotates about it's own axis.

It is also called synchronous satellite because the relative velocity of such a satellite with respect to the earth is zero. It is called geostationery because it appears to be stationery to an observer on the earth.  

Height of the geostationery satellite above the earth's surface :-

We know,

T = $\frac{2\pi r }{v_{0} }$

where,

$v_{0}$ is orbital velocity = $\sqrt{\frac{GM}{r} }$

So,

T = $\frac{2\pi r}{\sqrt{\frac{GM}{r} } }$

By squaring both sides, we get,

$T^{2}  = \frac{4\pi r^{2} }{GM}  * r$

or,

$r^{3} = \frac{GMT^{2} }{4\pi ^{2} }$

So,

r = $(\frac{GMT^{2} }{4\pi^{2}  } )^{\frac{1}{3} }$

By putting the values like :-

G = 6.6 * $10^{-11}$

M = 6 * $10^{24}$

$T^{2} = (24)^{2} *  (60)^{2} * 3600$

$\pi  = 3.14$

We get,

r = 42,330 km

Now, we know,

r = R + h

and we know R (radius of earth) = 6400 km

So,

h = 42,330 - 6400

  = 35,930 km

  ≈ 36,000 km

Thanks !

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