Question

The minimum and maximum distances of a satellite from the centre of the Earth are 2R and 4R respectively, where R is the radius of Earth and M is the Earth.Find radius of curvature at the point of the minimum distance.

Answer 1

$V_1=\sqrt{\frac{2GM}{3R}};V_2=\sqrt{\frac{GM}{6R}}$

If $r$ is the radius of curvature at point $A$

$\frac{{mv}_1^2}{r}=\frac{GMm}{{\left(2R\right)}^2}\Rightarrow r=\frac{4V_1^2{R}^2}{GM}=\frac{8R}{3}$