BR Physics Example 2.5b

[Fing Fang Foom]

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At which point in its orbit is Magellan moving the fastest?

There is a picture that goes along with this question so I cannot post it. Therefore, I think only someone with the book can help me.

The solution states that: Magellan will increase its speed and acceleration as it approaches Venus. Its maximum speed occurs at the instant it is closest to Venus, because once past that point, the acceleration will oppose its velocity.

Point C is the closest point of the satellite to Venus. I answered the question using the law of gravitation. Point C, being the closest point to Venus, will experience the greatest gravitational force. Using the net force, F=ma, I know that acceleration is directly proportional to the acceleration. So the point along the orbit that experiences the greatest force will also experience the greatest acceleration.

However, I do not understand the answer explanation and I was wanting to know if my thought process is correct. A similar thought process was used to answer question 2.5a, which asks where the acceleration and the force would be the smallest on the satellite. This would be where the distance is the greatest between the two masses and because the net force is directly proportional to acceleration they both would be at a minimum at this point.

I just want to know if my thinking is correct on this problem and perhaps if someone could explain their answer solution in the absence of a picture that would be great. Thanks.

 

[bullsfan1986]

At which point in its orbit is Magellan moving the fastest?

There is a picture that goes along with this question so I cannot post it. Therefore, I think only someone with the book can help me.

The solution states that: Magellan will increase its speed and acceleration as it approaches Venus. Its maximum speed occurs at the instant it is closest to Venus, because once past that point, the acceleration will oppose its velocity.

Point C is the closest point of the satellite to Venus. I answered the question using the law of gravitation. Point C, being the closest point to Venus, will experience the greatest gravitational force. Using the net force, F=ma, I know that acceleration is directly proportional to the acceleration. So the point along the orbit that experiences the greatest force will also experience the greatest acceleration.

However, I do not understand the answer explanation and I was wanting to know if my thought process is correct. A similar thought process was used to answer question 2.5a, which asks where the acceleration and the force would be the smallest on the satellite. This would be where the distance is the greatest between the two masses and because the net force is directly proportional to acceleration they both would be at a minimum at this point.

I just want to know if my thinking is correct on this problem and perhaps if someone could explain their answer solution in the absence of a picture that would be great. Thanks.

You can use a more general equation for a problem like this. Just calculate for centripetal force F=mv^2/r so when you're closer to an object you're orbiting, your radius decreases and thus your force increases. Because force is proportional to acceleration, yes, as the force increases (while keeping mass constant) the acceleration will also be increasing. Ie. I think your thought process is correct. Did that answer your question?