28) We are told that Pluto has an elliptical orbit about the Sun. This question is asking us to find the true statement. The best way to do this is to go through and eliminate the false choices.
Choice A: This choice talks about the direction fo the gravitational force. Gravitational force between two objects will always point towards the center of the object. For example, the gravitational force exerted on us by Earth pulls us towards the center of Earth.
Here's another way to think of it. As shown in the sketch above, an object traveling in an elliptical path is always turning. This means that the force of gravity cannot point in the direction of the velocity. If it did, the object would simply travel in a straight line. We can definitely eliminate choice A.
Choice B: This choice states that the gravitational force is greatest at the farthest point in the orbit. Let's first look at the universal gravitational formula.
For this question, we can assume the mass of the planets to be approximately constant. The equation above shows the inverse relationship between the distance squared and the gravitational force. Since they are related inversely, the gravitational force decreases as the masses move further apart. Likewise, the gravitational force increases when the masses get closer. Thus, the force will be lowest at the furthest point in the orbit, so we can eliminate choice B.
Choices C and D: These two choices talk about the speed of the orbit.
As proved in the explanation for choice B, the force is greatest when Pluto is closest to the Sun, and lowest when Pluto is furthest from the Sun. Since, at these two points the gravitational force points toward the center of the orbit, we can set this equal to the centripetal force.
It is crucial to notice that as the gravitational force increases, the speed does as well. When the gravitational force is largest, the speed is greatest. Furthermore, as the distance between the masses decreases, the speed increases. So, Pluto will have its greatest speed at the point of the orbit closest to the Sun. Choice C must be true, but choice D is false.
Choice E: This choice can be quickly crossed out. In the explanation of choice B, we already proved that the gravitational force is greatest when Pluto is closest to the Sun and least when furthest from the Sun.
Answer: C
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