A planet revolves round the sun in an elliptical orbit of semi minor and semi major axes `x` and `y` respectively. Then the time period of revolution is proportional to

Options

A. `(x+y)^(3/2)`
B. `(y-x)^(3/2)`
C. `x^(3/2)`
D. `y^(3/2)`

Explanation

To solve the problem of determining the proportionality of the time period of revolution of a planet in an elliptical orbit with semi-minor axis \( x \) and semi-major axis \( y \), we can follow these steps:

### Step-by-Step Solution:

1. **Understanding Kepler's Third Law**:
Kepler's Third Law states that the square of the time period \( T \) of a planet's orbit is directly proportional to the cube of the semi-major axis \( a \) of its orbit. Mathematically, this can be expressed as:
\[ T^2 \propto a^3 \]
In our case, the semi-major axis is given as \( y \).

2. **Identifying the Semi-Major Axis**:
In the context of the problem, we identify the semi-major axis \( a \) with the given value \( y \). Therefore, we can rewrite Kepler's Third Law specifically for our scenario:
\[ T^2 \propto y^3 \]

3. **Taking the Square Root**:
To find the time period \( T \), we take the square root of both sides of the equation:
\[ T \propto \sqrt{y^3} \]
This can also be expressed as:
\[ T \propto y^{3/2} \]

4. **Conclusion**:
Thus, the time period of revolution \( T \) is proportional to \( y^{3/2} \), where \( y \) is the semi-major axis of the elliptical orbit.

### Final Answer:
The time period of revolution is proportional to \( y^{3/2} \).