The gravitational force exerted by the Sun on the Moon is about twice as great as the gravitational force exerted by the earth on the Moon, but still Moon is not escaping from the gravitational influence of the earth. Mark the option which correctly explains the above system.

Options

A. Escape speed is independent of the direction in which it is projected.
B. The rotational effect of the earth plays a role in computation of escape speed, however small it may be.
C. A body thrown in the eastward direction has less escape speed.
D. None of the above

Explanation

To solve the question, we need to analyze the gravitational forces acting on the Moon by both the Earth and the Sun, and understand why the Moon remains gravitationally bound to the Earth despite the Sun exerting a greater force.

### Step-by-Step Solution:

1. **Understanding Gravitational Forces**:
- The gravitational force exerted by the Earth on the Moon (F_E) is less than the gravitational force exerted by the Sun on the Moon (F_S). According to the problem, F_S is about twice F_E.
- Mathematically, we can express this as:
\[ F_S = 2F_E \]

2. **Distance Consideration**:
- The gravitational force is inversely proportional to the square of the distance between the two bodies. The Moon is much closer to the Earth than it is to the Sun.
- Let \( r_1 \) be the distance from the Earth to the Moon and \( r_2 \) be the distance from the Sun to the Moon. Since the Moon is much closer to the Earth, we have:
\[ r_1 < r_2 \]

3. **Gravitational Influence**:
- Even though the Sun exerts a greater gravitational force on the Moon, the Moon does not escape the gravitational influence of the Earth because it is still bound by the Earth's gravitational pull.
- The gravitational force from the Earth is sufficient to keep the Moon in orbit, despite the stronger force from the Sun.

4. **Escape Velocity**:
- The concept of escape velocity is important here. The Moon would need to reach a certain speed to escape the gravitational pull of the Earth. The escape velocity depends on the mass of the Earth and the distance from the center of the Earth to the Moon.
- The escape speed is independent of the direction in which it is projected.

5. **Conclusion**:
- The Moon remains in orbit around the Earth due to the gravitational influence of the Earth, which is still significant despite the greater force from the Sun. The energy required to escape the Earth's gravitational influence is not met by the Moon's current velocity.

6. **Correct Option**:
- The options given in the question suggest various explanations. The correct explanation is that the Moon is not escaping the Earth's gravitational influence because the gravitational force from the Earth, although less than that from the Sun, is still sufficient to keep the Moon in orbit.

### Final Answer:
The correct option is **D: None of the above**.