For a satellite orbiting very close to earth's surface, total energy is

Options

A. zero
B. `(GMm)/(R)`
C. `-(GMm)/(R)`
D. `-(GMm)/(2R)`

Explanation

To find the total energy of a satellite orbiting very close to the Earth's surface, we can follow these steps:

### Step-by-step Solution:

1. **Understand the Total Energy Formula**:
The total energy (E) of a satellite in orbit is given by the formula:
\[ E = -\frac{GMm}{2r} \]
where:
- \( G \) is the universal gravitational constant,
- \( M \) is the mass of the Earth,
- \( m \) is the mass of the satellite,
- \( r \) is the distance from the center of the Earth to the satellite.

2. **Identify the Distance (r)**:
Since the satellite is orbiting very close to the Earth's surface, we can approximate \( r \) as the radius of the Earth (\( R \)):
\[ r = R \]

3. **Substitute r in the Total Energy Formula**:
Now, substituting \( r \) with \( R \) in the total energy formula:
\[ E = -\frac{GMm}{2R} \]

4. **Conclusion**:
Therefore, the total energy of a satellite orbiting very close to the Earth's surface is:
\[ E = -\frac{GMm}{2R} \]
This indicates that the total energy is negative, which is typical for bound systems like satellites in orbit.