For a satellite to orbit around the earth, which of the following must be true?

Options

A. It must be above the equator at some time
B. It cannot pass over the poles at any time
C. Its height above the surface cannot exceed `36000km`
D. Its period of rotation must be ` gt 2pi sqrt(R//g)`.

Answer

To determine the conditions necessary for a satellite to orbit around the Earth, we need to analyze the options provided in the question.

### Step-by-Step Solution:

1. **Understanding Satellite Orbits**:
A satellite orbits the Earth due to the gravitational force acting on it. For a stable orbit, the satellite must have a specific velocity that balances the gravitational pull.

2. **Option Analysis**:
- **Option 1**: "It must be above the equator at some time."
- This statement is **not necessarily true**. A satellite can have an orbit that is inclined to the equator, meaning it can pass over the poles and other latitudes. Therefore, this option is **incorrect**.

- **Option 2**: "It cannot pass over the poles at any time."
- This statement is **false**. Satellites can be placed in polar orbits, allowing them to pass directly over the poles. Thus, this option is **incorrect**.

- **Option 3**: "Its height above the surface cannot exceed 36,000 kilometers."
- This statement is also **false**. Satellites can be placed in orbits at various altitudes, including those much higher than 36,000 kilometers. Therefore, this option is **incorrect**.

- **Option 4**: "Its period of freewheel rotation must be greater than \(2\pi \sqrt{\frac{r}{g}}\)."
- The correct formula for the orbital period \(T\) of a satellite is \(T = 2\pi \sqrt{\frac{r^3}{GM}}\), where \(r\) is the distance from the center of the Earth. The statement implies a condition that is not universally true. The period must equal \(2\pi \sqrt{\frac{r^3}{GM}}\) for a stable orbit. Therefore, this option is **incorrect** as stated.

3. **Conclusion**:
After analyzing all the options, we find that none of the provided statements are universally true for a satellite to orbit the Earth. The correct conditions for a satellite's orbit are based on gravitational laws and orbital mechanics, which are not fully captured by the options given.

### Final Answer:
None of the options provided are true for a satellite to orbit around the Earth.