Which of the following Kepler's laws is also known as harmonic law?

Options

A. A. First law
B. B. Second law
C. C. Third law
D. D. None of these

Explanation

To determine which of Kepler's laws is also known as the harmonic law, we can follow these steps:

### Step-by-Step Solution:

1. **Understand Kepler's Laws**:
Kepler formulated three laws of planetary motion. We need to identify which of these is referred to as the harmonic law.

2. **Identify the Laws**:
- **First Law**: The orbit of a planet is an ellipse with the Sun at one of the foci.
- **Second Law**: A line segment joining a planet and the Sun sweeps out equal areas during equal intervals of time.
- **Third Law**: The square of the period of any planet is proportional to the cube of the semi-major axis of its orbit.

3. **Focus on the Third Law**:
The third law can be mathematically expressed as:
\[ T^2 \propto R^3 \]
where \( T \) is the orbital period and \( R \) is the semi-major axis of the orbit. This relationship indicates that the square of the time period of a planet's orbit is directly proportional to the cube of the average distance from the Sun.

4. **Recognize the Term 'Harmonic Law'**:
The term "harmonic law" refers specifically to this relationship in Kepler's third law, which applies to all planets in the solar system.

5. **Choose the Correct Option**:
Based on the understanding that the third law relates to the harmonic law, we conclude that the correct answer is:
- **Option C: 3rd law**.

### Final Answer:
The Kepler's law that is also known as the harmonic law is **Option C: 3rd law**.

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