Question

find the speed and orbit radius for an earth satellite with a perioud of 1 day (86400s)

so for to get speed, its v= sqrt (gm/r)

and to get orbit r its v=2pir/t -> r=t*v/2pi ???

answer is v=3.07 * 10^3 m/s r= 4.23 * 10^7 m

i dont get it., how the hell u get 3.07 for v ?????? wth?

Answer 1

r = [GmT^2/4pi^2]^1/3

putting the value

r = 4.2x10^7 m

V = sqrt(Gm/r)

here G = universal constant = 6.67 x 10^-11 Nm^2/kg^2

m = 5.974 x 10^24 kg

r = 4.23 x 10^7 m

put all value in v = sqrt(Gm/r)

v = sqrt(9419995.272 )

v = 3069.20 = 3.07x 10^3 m/s

Answer 2