Question

a comet passes by a planet with a speed v0 such that the comet travels in a straight line at the instant shown in the figure. The comet's tangetial acceleration, centripetal acceleration, and force due to gravity from the planet at this location are provided in the table. Astronomers observe that the comet continues to travel in a nearly straight line, even though calculations show that the gravitational force exerted by the planet should cause the comet to move in a cicular orbit. Why does the comet not travel in a cicular path around the planet after the instant shown in the figure?

Answer 1

If the comet has a very high initial tangential speed (v0), it might have enough kinetic energy to escape the circular orbit and continue on a straight path.

In other words, the comet may have sufficient velocity to overcome the gravitational pull of the planet and not be captured into a circular orbit.

The centripetal acceleration required for circular motion is provided by the gravitational force in this scenario. If the centripetal force is insufficient, the comet won't follow a circular path. This could be due to a combination of low gravitational force and high tangential speed.

If the gravitational force is not directed towards the center of the planet, it may not provide the required centripetal force for circular motion. This could be the result of an asymmetrical gravitational field or other external forces acting on the comet.