Which of the following graphs represents the motion of the planet moving about the Sun. T is the periode of revolution and r is the average distance (from centre to centre) between the sun and the planet

Options

A.
B.
C.
D.

Explanation

To solve the question regarding which graph represents the motion of a planet moving around the Sun, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding Kepler's Third Law**:
According to Kepler's Third Law of planetary motion, the square of the period of revolution (T) of a planet is directly proportional to the cube of the average distance (r) from the Sun. This can be mathematically expressed as:
\[ T^2 \propto r^3 \]

2. **Formulating the Equation**:
From the proportionality, we can write:
\[ T^2 = k \cdot r^3 \]
where \( k \) is a constant.

3. **Identifying the Variables for Graphing**:
In this equation, if we want to graph \( T^2 \) against \( r^3 \), we can rearrange the equation to:
\[ T^2 = k \cdot (r^3) \]
This indicates that if we plot \( T^2 \) on the y-axis and \( r^3 \) on the x-axis, we should expect a straight line.

4. **Characteristics of the Graph**:
- The graph will have a positive slope since \( k \) is a positive constant.
- The y-intercept will be zero because when \( r = 0 \), \( T^2 \) must also be zero.

5. **Conclusion**:
Therefore, the correct graph representing the relationship between the period of revolution \( T \) and the average distance \( r \) will be a straight line passing through the origin (0,0) with a positive slope.

### Final Answer:
The correct option is the graph that shows a straight line with a positive slope and passes through the origin.

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