Answer:
In Newtonian mechanics, F = Gm1m2/r^2
Where F is the attractive force between 2 masses, m1 and m2, r is the distance between the centres of the masses and G is the universal gravitation constant, which is 6.674x10^-11 Nm^2/kg^2
IF, however, one mass is much greater than the other, we can write
g = GM/r^2 where M is the larger mass (and we call g “gravity”, or more properly “the acceleration due to gravity”; g has units of m/s^2)
In this case, if we neglect the mass of Sputnik (relative to that of earth) and note m1 = 5.98x10^24kg and r = 6.96x10^6, then
F = (6.674x10^-11)(5.98x10^24)/(6.96x10^6)^2 = 8.2389N
But F is actually centripetal acceleration, a = v^2/r
So 8.2389 = v^2 / 6.96x10^6
Then v = √(8.2389x6.96x10^6) = 7.5725x10^3m/s
The orbital velocity was 7,572.5m/s
Explanation: