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 the earth . Find
(a) its minimum and maximum speeds,
(b) radius of curvature at the point of minimum distance.

Explanation

To solve the problem, we will follow these steps:

### Step 1: Understanding the Problem
We have a satellite orbiting the Earth with minimum and maximum distances from the center of the Earth given as \(2R\) and \(4R\) respectively, where \(R\) is the radius of the Earth. We need to find the minimum and maximum speeds of the satellite and the radius of curvature at the point of minimum distance.

### Step 2: Conservation of Angular Momentum
The angular momentum of the satellite is conserved. The angular momentum \(L\) can be expressed as:
\[
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