Question

A Geostationary satellite has an 8kW RF transmission pointed at the earth. How much force does that induce on the spacecraft? (N)

Answer 1

The force induced on the aircraft is 2.60 N

Solution:

As per the question:

Power transmitted,
`P_(t) = 8 kW = 8000 W`

Now, the force, F is given by:

`P_(t) = Force(F)* velocity(v) = Fv` (1)

where

v = velocity

Now,

For a geo-stationary satellite, the centripetal force,
`F_(c)` is provided by the gravitational force,
`F_(G)`:

`F_(c) = F_(G)`

Thus from the above, velocity comes out to be:

`v = \sqrt{(GM_(e))/(R)}`

`v = \sqrt{(6.67* 10^(- 11)* 5.979* 10^(24))/(42166* 10^(3))} = 3075.36 m/ s`

where

R =
`R_(e) + H`

R =
`\sqrt{GM_(e)((T)/(2\pi))^(2)}`

where

G = Gravitational constant

T = Time period of rotation of Earth

R is calculated as 42166 km

Now, from eqn (1):

`8000 = F* 3075.36`

F = 2.60 N