Radius of orbit of satellite of earth is `R`. Its kinetic energy is proportional to

Options

A. `1/R`
B. `1/(sqrt(R))`
C. `R`
D. `1/(R^(3//2))`

Explanation

To determine how the kinetic energy of a satellite in orbit is related to the radius of its orbit (R), we can follow these steps:

### Step-by-Step Solution:

1. **Understand the orbital velocity of the satellite**:
The orbital velocity (v) of a satellite in a circular orbit around a planet (like Earth) is given by the formula:
\[ v = \sqrt{\frac{GM}{R}} \]
where \( G \) is the gravitational constant and \( M \) is the mass of the Earth.

2. **Write the expression for kinetic energy**:
The kinetic energy (KE) of the satellite can be expressed as:
\[ KE = \frac{1}{2} m v^2 \]
where \( m \) is the mass of the satellite.

3. **Substitute the expression for orbital velocity into the kinetic energy formula**:
By substituting \( v \) from step 1 into the kinetic energy formula, we get:
\[ KE = \frac{1}{2} m \left(\sqrt{\frac{GM}{R}}\right)^2 \]

4. **Simplify the expression**:
Squaring the velocity gives:
\[ KE = \frac{1}{2} m \frac{GM}{R} \]
This can be rewritten as:
\[ KE = \frac{GMm}{2R} \]

5. **Identify the proportionality**:
From the expression \( KE = \frac{GMm}{2R} \), we can see that the kinetic energy is inversely proportional to the radius \( R \). Therefore, if we consider the relationship in terms of proportionality, we can say:
\[ KE \propto \frac{1}{R} \]

### Conclusion:
The kinetic energy of the satellite is inversely proportional to the radius of its orbit \( R \).