how does the size of planet eclipsing a star effect the brightness of the star?
think about when the moon gets in the way of the sun.
Picture the star as a disk of light. And the planet, as a disk of darkness.
Subtract the area of the planet's disk from the area of the star's disk to compare eclipse / non-eclipse brightness. Limb darkening complicates it a bit, so you'll see a rise, a sharp peak and a decline. (Area = pi r^2)
This is a bit different than an eclipse of the Sun by the Moon. Both Sun and Moon are close enough to affect the ratio of their actual sizes and their appearant sizes. But at their distances, the ratio of their actual sizes and their appearant sizes is very, very close to 1. A star and its planet can be treated as if at an infinate perspective.
right, but is brightness directly proportional to the apparent area we see? probably a stupid question, but thanks
Roughly proportional to the visible fraction of the surface area, yes. There are effects like limb darkening that complicate the picture a bit, but for the most part, eclipses can be modelled as simply as this.
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