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A satellite is to revolve round the eart...

A satellite is to revolve round the earth in as circle of radius 8000 km. With what speed should this satellite be projected into orbit? What will be the time period?
Take g at the surface `=9.8ms^-2` and radius of the earth =6400 km.

Text Solution

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Suose the speed of the stellite ils v. The accelerationof the satellite is `v^2/r`. Where is the radius of the orbit. The force on the satelite is `(GMm)/r^2` with usual symbols. Using Newton's second law,
`(GMm)/r^2=mv^2/r`
or, `v^2=(GM)/r=(gR^2)/r=((9.8ms^-2)(6400km)^2)/((8200 km))`
giving `v=7.08kms^-1`
The time period is `(2pir)/v=((2pi(8000km))/((7.08kms^-1)~~118minutes.`
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