Binding energy of moon and earth is :-

Options

A. `(GM_(e)M_(m))/r_(em)`
B. `(GM_(e)M_(m))/(2r_(em))`
C. `-(GM_(e)M_(m))/r_(em)`
D. `-(GM_(e)M_(m))/(2r_(em))`

Answer

To find the binding energy of the Moon-Earth system, we can follow these steps:

### Step 1: Understand Binding Energy
Binding energy is the energy required to separate a system into its individual components. In the case of the Earth-Moon system, it is the energy that binds the Moon to the Earth.

### Step 2: Calculate Potential Energy
The gravitational potential energy (U) between two masses (in this case, the Earth and the Moon) is given by the formula:
\[ U = -\frac{G \cdot M_E \cdot M_M}{R_{EM}} \]
where:
- \( G \) is the universal gravitational constant,
- \( M_E \) is the mass of the Earth,
- \( M_M \) is the mass of the Moon,
- \( R_{EM} \) is the distance between the centers of the Earth and the Moon.

### Step 3: Total Energy of the System
The total energy (E) of the system is the sum of the kinetic energy and potential energy. However, for the purpose of binding energy, we can focus on the potential energy, as the kinetic energy is not directly needed for this calculation. The total energy can be expressed as:
\[ E = U + K \]
For a bound system, we can consider the total energy to be:
\[ E = -\frac{G \cdot M_E \cdot M_M}{2R_{EM}} \]
This is because the kinetic energy is related to the potential energy in a bound system.

### Step 4: Binding Energy Calculation
The binding energy (BE) is defined as the negative of the total energy:
\[ BE = -E = \frac{G \cdot M_E \cdot M_M}{2R_{EM}} \]

### Step 5: Conclusion
Thus, the binding energy of the Moon and Earth is given by:
\[ BE = \frac{G \cdot M_E \cdot M_M}{2R_{EM}} \]

### Final Answer
The binding energy of the Moon and Earth is:
\[ \text{Binding Energy} = \frac{G \cdot M_E \cdot M_M}{2R_{EM}} \]

---