A satellite is moving around the earth with speed v in a circular orbit of radius r. If the orbit radius is decreased by 1 %, the speed of the satellite will

Question

A satellite is moving around the earth with speed v in a circular orbit of radius r. If the orbit radius is decreased by 1 %, the speed of the satellite will (A) increase by 1% (B) increase by 0.5% (C) decrease by 1% (D) decrease by 0.5%

Tardigrade Admin · Accepted Answer

Orbital speed v=√(GM/R) By power law of error (Δ v/v)=-(1/2)(Δ R/R) So, 1 % decrease in orbital radius will result is 0.5 % increase of the speed of the satellite.

Q. A satellite is moving around the earth with speed v in a circular orbit of radius $r$ . If the orbit radius is decreased by $1%$ , the speed of the satellite will

increase by 1%

increase by 0.5%

decrease by 1%

decrease by 0.5%

Orbital speed $v = \frac{GM}{R}$
By power law of error $\frac{Δ v}{v} = - \frac{1}{2} \frac{Δ R}{R}$
So, $1%$ decrease in orbital radius will result is $0.5%$ increase of the speed of the satellite.

Q. A satellite is moving around the earth with speed v in a circular orbit of radius r. If the orbit radius is decreased by 1%, the speed of the satellite will