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The earth revolves round the sun in an e...

The earth revolves round the sun in an elliptical orbit. Its speed

A

goes on decreasing continuously

B

greatest when it is closest to the sun

C

greatest when it is farthest from the sun

D

constant at all the points on the orbit

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The correct Answer is:
To solve the problem regarding the speed of the Earth as it revolves around the Sun in an elliptical orbit, we can follow these steps: ### Step-by-Step Solution: 1. **Understanding the Orbit**: The Earth revolves around the Sun in an elliptical orbit. An ellipse has two foci, and one of them is occupied by the Sun. 2. **Forces Acting on the Earth**: The only force acting on the Earth is the gravitational attraction exerted by the Sun. This force is directed towards the Sun. 3. **Torque Consideration**: Since the gravitational force acts along the line connecting the Earth and the Sun, there is no torque about the Sun. This means that the angular momentum of the Earth is conserved. 4. **Angular Momentum Conservation**: The angular momentum (L) of the Earth can be expressed as: \[ L = m \cdot v \cdot r \] where \( m \) is the mass of the Earth, \( v \) is the velocity of the Earth, and \( r \) is the distance from the Earth to the Sun. 5. **Constant Angular Momentum**: Since angular momentum is conserved, we can say that: \[ m \cdot v \cdot r = \text{constant} \] This implies that as \( r \) changes, \( v \) must change in such a way that the product \( v \cdot r \) remains constant. 6. **Analyzing the Relationship**: When the Earth is closest to the Sun (at perihelion), the distance \( r \) is at its minimum. Since \( m \) is constant, for the product \( m \cdot v \cdot r \) to remain constant, if \( r \) decreases, \( v \) must increase. Conversely, when the Earth is farthest from the Sun (at aphelion), \( r \) is at its maximum, and thus \( v \) must decrease. 7. **Conclusion**: Therefore, the speed of the Earth is greatest when it is closest to the Sun and least when it is farthest from the Sun. This leads us to conclude that the speed of the Earth varies inversely with the distance from the Sun. ### Final Answer: The speed of the Earth is greatest when it is closest to the Sun and decreases as it moves away from the Sun. ---
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