Two asteroids (heavenly bodies) of equal masses revolve diametricallly opposite to each other in a circle of radius 100 km. If mass of each astreroid is `10^(10)` kg, then what would their velocites be
(Take `G = 6.67 xx 10^(-11) N m^(2) kg^(-2)`).

Explanation

(i) (1) Take the mass of the asteroid = m
Take the distance between the asteroid as = d
The attraction between the asteroid is given by, `F = (Gm^(2))/(d^(2))`
(2) The orbital velocity of each asteroid would be = v then,`" "F = (mv^(2))/(r)`
Equate (1) and (2) `F = (Gm^(2))/(d^(2)) = (mv^(2))/(r)`
Obtain the value of 'v'.
(ii) `1.29 xx 10^(3) m s^(-1)`