Determining the orbital radius of extrasolar planets

AI Thread Summary
To determine the orbital radius of extrasolar planets, one can use a formula that relates the orbital period to the radius. The period is relatively easy to observe, but the mass of the star, which is also needed for the calculation, is more challenging to determine. By applying the concept that the centripetal force required for circular motion is equal to the gravitational force between the planet and the star, one can derive the necessary equations. Observations of the star's characteristics can help estimate its mass, facilitating the calculation of the orbital radius. Understanding these relationships is crucial for analyzing extrasolar planetary systems.
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Homework Statement


Basically I don't understand how you do this - the course I'm doing keeps mentioning the orbital radius of extrasolar planets but doesn't tell you HOW to find it?
Can anyone please help - in plain English, please, I'm not a natural scientist!


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The Attempt at a Solution

 
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We have a formula relating the period of the orbit to its radius. It is easy to observe the period, so the radius can then be calculated. The longer answer is that the formula has the mass of the star in it and that mass is not easy to observe. I think some guessing is involved but I don't really know. Stars are very interesting and a lot is known about how they work, so perhaps there is a way to guess the mass fairly well from observations of the star's characteristics.
 
Delphi51 said:
We have a formula relating the period of the orbit to its radius. It is easy to observe the period, so the radius can then be calculated. The longer answer is that the formula has the mass of the star in it and that mass is not easy to observe. I think some guessing is involved but I don't really know. Stars are very interesting and a lot is known about how they work, so perhaps there is a way to guess the mass fairly well from observations of the star's characteristics.

Hi Delphi
Yes, it's actually the formula I'm trying to find
Best wishes
AggieG
 
There is a lovely way to find the satellite formula for circular motion. You begin by saying Fc = Fg
meaning that the centripetal force required to hold the planet in circular motion is provided by the gravitational force between planet and star. Then fill in the detailed formulas for Fg and Fc (choosing the one with the period T in it rather than the one with velocity).
 
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