The dwarf planet Pluto has an elliptical orbit with a semimajor a...

Question

The dwarf planet Pluto has an elliptical orbit with a semimajor axis of 5.91 * 1012 m and eccentricity 0.249. (b) During Pluto’s orbit around the sun, what are its closest and farthest distances from the sun?

Accepted Answer

Welcome back everybody. We are taking a look at the most eccentric planet HD 2782 B. And it is rotating around or orbiting around its parent star. Now we are told that its orbital eccentricity, it has a value of 0.96. And we are also told that the distance or the length of its semi major axis is 2.3 times 10 to the eight kilometers. And we are asked to find two things during its orbit. What is the maximum distance between the star and the planet and the minimum distance between the star and the planet? Let's go ahead and start out with the maximum distance here. The formula for maximum distance is pretty simple. It's just our semi major access length, axis length times one plus our orbital eccentricity. So let's just go ahead and plug in our values here we have 2.3 times 10 to the eighth times one plus 0.96. Which when you plug into your calculator, you get that. The maximum distance during orbit is 3. times 10 to the eighth kilometers. Great. So now let's go ahead and find that minimum distance, in part the minimum distance. Very similar formula. Here we are going to have the length of our semi major axis times one minus our orbital eccentricity. Plugging in our values again, we have 2.3 times 10 to the eighth times one minus 0.96. Which when you plug this into your calculator, you get the minimum distance is 8.12 times to the six kilometers. So now we have found our maximum distance and our minimum distance corresponding to answer choice. A thank you all so much for watching. Hope this video helped. We will see you all in the next one.

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