Help with an Equation Please
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Help with an Equation Please

[From: ] [author: ] [Date: 12-09-28] [Hit: ]
but Im not understanding it. A newly discovered planet orbits a distant star with the same mass as the Sun at an average distance of 108 million kilometers. Its orbital eccentricity is 0.5.1. Find the planets orbital period.......
Help with Astronomy please? Im not asking for an explanation how, but an explanation WITH the answers. I have an explanation in my book, but I'm not understanding it.
A newly discovered planet orbits a distant star with the same mass as the Sun at an average distance of 108 million kilometers. Its orbital eccentricity is 0.5.
1. Find the planet's orbital period.

2. Find the planet's nearest orbital distance from its star.

3. Find the planet's farthest orbital distance from its star.


This may seem stupid but I cant figure this out! I really don't want to fail this assignment!
Thanks!

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When you do these types of problems, the best approach, in my opinion, is to list out all the information you know and everything you need to find out. This allows you to look for relevant equations which have either all the terms you know or terms you are trying to find. So lets go through question 1:

1) Find the planet's orbital period - We know the mass of the sun (1 solar mass) and the orbital distance of 108 million km (in scientific notation is 1.08E8 km or 0.722 AU). We also know the eccentricity is 0.5 and we want to know the period. Given all of this, you should be thinking "Kepler's Third Law".

The general form of Kepler's Third Law is a bit long, but fortunately they told us the sun has a mass of 1 solar mass. This means that if we use the period (which I'm going to denote by the letter P) in units of years and the distance (denoted by the letter a) in units of AU, we can say that:

P^2 = a^3

P = a^(3/2)

P = (0.722 AU)^(3/2)

P = 0.613 years

2) Find the planet's nearest orbital distance from it's star. - At this point we have only not used the eccentricity. That should at least tell you that it should play a part in this problem. I think it would be best to read this section of the wikipedia page on ellipses.
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