JEE Main · 2019 · 12 Jan 2019 · Shift 1 · Gravitation

Just before impact the satellite is moving tangentially with the orbital speed $v$, while the meteorite of equal mass is falling radially inward with the same speed $v$. Since the collision is perfectly inelastic, momentum adds as vectors: the tangential momentum $mv$ and the radial momentum $mv$ combine on a body of mass $2m$, so the combined object moves off with speed $\frac{v}{\sqrt{2}}$ directed at $45^{\circ }$ to the radius. Compare this with what a circular orbit at radius $R$ demands. The speed has fallen below the circular value, so the body can no longer hold the circle of radius $R$; at the same time $\frac{v}{\sqrt{2}}$ falls well short of the escape speed, so it cannot fly off to infinity either. A bound orbit whose speed and direction no longer match a circle is an ellipse, so the combined body settles into an elliptical orbit about the earth.