Different points in the earth are at slightly different distance from the sun and hence experience different force due to gravitation. For a rigid body, we know that if various forces act at various points in it, the resultant motion is as if a net force acts on the `CM` (centre of mass) causing translation and a net torque at the `CM` causing rotation around an axis through the `CM`. for the earth-sun system (approximating the earth as a uniform density sphere).

Options

A. the torques is zero
B. the torque causes the earth to spin.
C. the rigid body result is not applicable since the earth is not even approximately a rigid body.
D. the torque causes the earth to move around the sun.

Explanation

To solve the problem regarding the gravitational force experienced by different points on Earth due to its varying distance from the Sun, we need to analyze the torque exerted by the Sun on the Earth. Here’s a step-by-step breakdown of the solution:

### Step 1: Understanding the System
The Earth orbits the Sun, and different points on the Earth are at slightly different distances from the Sun. This creates a variation in the gravitational force experienced by these points.

**Hint:** Consider how the distance from the Sun affects the gravitational force on different points of the Earth.

### Step 2: Concept of Torque
Torque (\( \tau \)) is defined as the product of the distance (\( r \)) from the pivot point (in this case, the center of mass of the Earth) to the point where the force is applied, and the force (\( F \)) applied, multiplied by the sine of the angle (\( \theta \)) between the force vector and the lever arm vector:
\[ \tau = r \cdot F \cdot \sin(\theta) \]

**Hint:** Remember that torque depends on both the distance from the pivot and the angle at which the force is applied.

### Step 3: Direction of Gravitational Force
In this scenario, the gravitational force exerted by the Sun on the Earth acts along the line connecting the Earth and the Sun. Therefore, the angle \( \theta \) between the line of action of the gravitational force and the radius vector from the center of mass of the Earth to the Sun is zero degrees.

**Hint:** Think about how the direction of the gravitational force affects the angle in the torque equation.

### Step 4: Calculating Torque
Since \( \theta = 0 \), we can substitute this into the torque equation:
\[ \tau = r \cdot F \cdot \sin(0) = r \cdot F \cdot 0 = 0 \]
Thus, the torque exerted by the Sun on the Earth is zero.

**Hint:** Recall that the sine of zero degrees is zero, which leads to the conclusion that the torque is zero.

### Step 5: Conclusion
Since the torque is zero, it implies that there is no rotational effect on the Earth due to the gravitational force from the Sun. The Earth moves in a translational motion around the Sun without any net torque causing it to spin.

**Final Answer:** The torque exerted by the Sun on the Earth is zero.

**Hint:** Reflect on how the absence of torque influences the rotational motion of the Earth.