Assertion: The total energy of a satellite is negative.
Reason: Gravitational potential energy of an object is negative.

Options

A. If both assertion and reason are true and reason is the correct explanation of assertion
B. If both assertion and reason are truebut reason is not the correct explanation of assertion
C. If assertion is true but reason is false
D. If both assertion and reason are false.

Explanation

To solve the question regarding the assertion and reason about the total energy of a satellite and gravitational potential energy, we can follow these steps:

### Step 1: Understand the Concept of Gravitational Potential Energy
Gravitational potential energy (U) of an object in a gravitational field is given by the formula:
\[ U = -\frac{G M m}{r} \]
where:
- \( G \) is the 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.

### Step 2: Analyze the Sign of Potential Energy
From the formula, we can see that gravitational potential energy is negative because the value of \( U \) is negative when \( r \) is positive. This indicates that work must be done against the gravitational field to bring the satellite from its position to infinity (where potential energy is defined to be zero).

### Step 3: Determine Kinetic Energy of the Satellite
The kinetic energy (K) of the satellite in orbit is given by:
\[ K = \frac{1}{2} m v^2 \]
For a satellite in a stable orbit, the gravitational force provides the necessary centripetal force. Thus, we can equate the gravitational force to the centripetal force:
\[ \frac{G M m}{r^2} = \frac{m v^2}{r} \]
From this, we can derive the expression for kinetic energy:
\[ v^2 = \frac{G M}{r} \]
Substituting this into the kinetic energy formula gives:
\[ K = \frac{1}{2} m \left(\frac{G M}{r}\right) = \frac{G M m}{2r} \]

### Step 4: Calculate Total Energy of the Satellite
The total energy (E) of the satellite is the sum of its kinetic and potential energies:
\[ E = K + U \]
Substituting the expressions for \( K \) and \( U \):
\[ E = \frac{G M m}{2r} - \frac{G M m}{r} \]
\[ E = \frac{G M m}{2r} - \frac{2G M m}{2r} \]
\[ E = -\frac{G M m}{2r} \]

### Step 5: Conclusion on Total Energy
The total energy \( E \) is negative, which confirms the assertion that the total energy of a satellite is negative.

### Step 6: Verify the Reason
The reason states that the gravitational potential energy of an object is negative, which we have confirmed through our calculations.

### Final Answer
Both the assertion and the reason are true, and the reason correctly explains the assertion.