Question

In 3–5 sentences, explain how the shape of planetary orbits affects their orbital velocity. Include the proper law of planetary motion as part of your answer.

Answer 1

There is no torque exerted on the planet by the gravitational field of the sun.Therefore its angular momentum about the sun remains constant.
m r^2 omega = constant
r omega is the speed
so radius * speed = constant

Answer 2

The shape of planetary orbits affects their orbital velocity because according to Kepler's second law of planetary motion, planets sweep out equal areas in equal times. This means that when a planet is closer to the sun in its elliptical orbit, it moves faster to cover the same area in the same amount of time. Conversely, when a planet is further from the sun, it moves slower. Therefore, the shape of the orbit directly influences the orbital velocity of the planet.

Answer 3

I apologize for the incorrect response. You are correct that in the absence of any external torques, the angular momentum of a planet remains constant. In a circular orbit, this implies that the product of the radius and orbital velocity (not speed) remains constant. Therefore, for planets with circular orbits, as the radius increases, the orbital velocity decreases, maintaining the constant angular momentum. The shape of the orbit does not affect the orbital velocity in this case.