Suppose a new planet is discovered between Uranus and Neptune. Its time period would be

Options

A. less than that of Neptune.
B. more than that of Neptune.
C. equal to that of Neptune or Uranus
D. less than that of Uranus.

Answer

To determine the time period of a newly discovered planet located between Uranus and Neptune, we can use Kepler's Third Law of Planetary Motion, which states that the square of the orbital period (T) of a planet is directly proportional to the cube of the semi-major axis (a) of its orbit around the Sun. This can be expressed mathematically as:

\[ T^2 \propto a^3 \]

### Step-by-Step Solution:

1. **Identify the Positions of Uranus and Neptune**:
- Uranus is the seventh planet from the Sun, while Neptune is the eighth. A new planet discovered between them would be positioned at a distance greater than Uranus but less than Neptune.

2. **Understand the Relationship Between Distance and Time Period**:
- According to Kepler's Third Law, the time period of a planet is related to its distance from the Sun. The further a planet is from the Sun, the longer its orbital period.

3. **Determine the Time Period of the New Planet**:
- Since the new planet is located between Uranus and Neptune, its distance from the Sun will be greater than that of Uranus but less than that of Neptune. Therefore, we can conclude:
- Time period of the new planet < Time period of Neptune
- Time period of the new planet > Time period of Uranus

4. **Conclude the Time Period Range**:
- Thus, the time period of the new planet will be less than that of Neptune and greater than that of Uranus.

5. **Select the Correct Answer**:
- Based on the analysis, the correct answer is that the time period of the new planet is less than that of Neptune and greater than that of Uranus.

### Final Answer:
The time period of the new planet is less than that of Neptune and greater than that of Uranus.