The minimum and maximum distances of a satellite from the center of the Earth are 2R and 4R respectively, where R is the radius of Earth and M is the mass of Earth. The radius of curvature at the point of minimum distance is
Step 1: Formula used
By conservation of angular momentum,
Minimum distance of satellite from the center of earth
Maximum distance of satellite from the center of earth
Mass of the satellite
Velocity of satellite at minimum distance
Velocity of satellite at maximum distance
Step 2: Use conservation of energy and substitute the values
By conservation of energy
Total energy = Kinetic energy + Potential energy
Substitute in , we get
Step 3: Find the radius of curvature
If r is the radius of curvature at the minimum distance,
The radius of curvature at the point of minimum distance is .