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Chapter 8: Problem 10

Does the gravitational force of the Sun do work on a planet in a circular orbit? In an elliptical orbit? Explain.

Short Answer

Expert verified
No, the gravitational force of the Sun does not do any work on a planet whether in a circular orbit or an elliptical orbit. This is because the force of gravity is always directed towards the Sun (perpendicular to the direction of the planet's motion), hence the angle between the force and the displacement is 90 degrees; yielding zero work since cosine of 90 degrees is zero.

Step by step solution

01

Understanding the Concept

In a circular orbit, the force vector, which is the gravitational force, is always perpendicular to the motion of the planet. The force vector points to the center of the circle (that is towards the Sun), while the motion (displacement) is tangent to the circle, thus making an angle of 90 degrees between the two vectors.
02

Application of Work Formula

Entering these values in the formula for work which is Work = Force x Distance x CosAngle. Considering the angle is 90 degrees and the cosine of 90 degrees is 0; the work done would be 0.
03

Comparing with Elliptical Orbit

Similarly, in an elliptical orbit, at any given point, the force vector (gravity) is pointing towards the Sun, at one of the foci. Again, the tangential motion of the planet (displacement) establishes a perpendicular (90 degrees) relationship with the force vector. Hence as in the circular orbit, here also, the work done by gravitational force is 0.
04

Conclusion

In both the circular and elliptical orbits, gravitational force does no work on the planet.

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