The torque on a planet about the centre of sun is

Options

A. Zero
B. Negative
C. Positive
D. Depend on mass of planet

Answer

To find the torque on a planet about the center of the Sun, we can follow these steps:

### Step 1: Understand the Definition of Torque
Torque (τ) is defined as the cross product of the position vector (r) and the force vector (F). Mathematically, it is given by:
\[ \tau = \mathbf{r} \times \mathbf{F} \]
This can also be expressed in terms of the magnitudes of the vectors and the angle (θ) between them:
\[ \tau = rF \sin(\theta) \]

### Step 2: Identify the Position and Force Vectors
- The position vector (r) points from the center of the Sun to the planet.
- The gravitational force (F) acting on the planet due to the Sun is directed towards the center of the Sun.

### Step 3: Determine the Angle Between the Vectors
Since the force vector (F) is directed towards the Sun, and the position vector (r) points away from the Sun, the angle (θ) between these two vectors is 180 degrees.

### Step 4: Calculate the Sine of the Angle
Using the sine function:
\[ \sin(180^\circ) = 0 \]

### Step 5: Substitute into the Torque Formula
Substituting the values into the torque formula:
\[ \tau = rF \sin(180^\circ) = rF \cdot 0 = 0 \]

### Conclusion
The torque on a planet about the center of the Sun is zero.

### Final Answer
\[ \text{The torque on a planet about the center of the Sun is } 0. \]

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