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I’ve been watching a lecture about how in astronomy one would be able to calculate the radius of 2 stars by measuring the velocity of the orbit and then measure the time how long the luminosity of a star dims when one star is behind the other.

After thinking this a bit through, I came up with a scenario of a planet orbiting a star and how to formulate the radius of the planet if we know the apparent luminosity of a star. This is just merely a scenario without taking influencing factors into account and I want to know if the way I’m reasoning this is logical or not.

Suppose we measure the apparent luminosity of a star ##L## and we wait until the orbiting planet is in front of the star right in the middle with respect to us. Since the planet obscures a part of a star, the apparent ##L## of that star would dim a bit by a factor, let us call that dimmed luminosity L_{dim}. We can say that this factor is caused by a decrease in area of that star. Since luminosity is proportional to the area, we can say that:

Here, R_{dim}obviously doesn’t mean that the star has reduced in size, but it just states that the area has decreased by a factor because of the planet. We've yet to reformulate R_{dim}.

We can imagine that the reduction in area of the star is caused by a substraction of the circular area of the planet that is in front of the star, since the obscuring is caused by the planet’s circle area and not its total spherical area from our perspective. Of course the distance of the planet from the star must not be too large otherwise we’d be overestimating the radius of the planet.

So, we can say that the factor by which the star has reduced in its total area is equal to:

In which the small ##r## is the radius of the planet.

Is this reasoning correct? If so, what might be outside influencing factors that make this calculation impossible?

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# I Calculating planet's radius using a star's luminosity

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