For a particle projected in a transverse direction from a height `h` above earth's surface, find te minimum initial velocity so that it just grazes the surface of earth such that path of this particle would be an ellipse with centre of earth as the farther focus, point of projection as the apogee and a diametrically opposite point on earth's surface as perigee.

Explanation

To solve the problem of finding the minimum initial velocity required for a particle projected from a height \( h \) above the Earth's surface such that it grazes the Earth's surface in an elliptical path, we will follow these steps:

### Step 1: Understand the Geometry of the Problem
The particle is projected from a height \( h \) and will follow an elliptical path. The point of projection is the apogee (highest point) of the ellipse, and the point on the Earth's surface directly opposite the point of projection is the perigee (lowest point).

### Step 2: Define the Relevant Variables
Let:
- \( R \) = radius of the Earth
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