An artifical satellitee of mass `100 kg` is in a circular orbit at `500 km` above the Earth's surface. Take redius of Earth as `6.5 xx 10^(6) m`.(a) Find the acceleration due to gravity at any point along the satellite path (b) What is the centripetal acceleration o fthe satellite?

Explanation

Here, `h = 500 km = 0.5 xx 10^(6) m`,
`R = 6.5 xx 10^(6) m`.
`r = R + h = 6.5 xx 10^(6) + 0.5 xx 10^(6)`
`= 7.0 xx 10^(6) m`.
(a) Now, `g' = g ((R)/(R + h))^(2)`
`= 9.8 ((6.5 xx 10^(6))/(7.0 xx 10^(6)))^(2)= 8.45 ms^(-2)`
(b) Centripetal force on the satellite,
`F = m upsilon^(2)//r`
`:.` centreipetel acceleration,
`a = (F)/(m) = (upsilon^(2))/(r ) = ((sqrt(gR^(2)//r))^(2))/(r)`
`= (g R^(2))/(r^(2)) = g.(R^(2))/((R + h)^(2)) = 8.45 ms^(-2)`