Question

You are trying to detect transiting planets around stars that are the same size as our Sun. If your instrument can detect 0.5% changes in the brightness of a star, what is the minimum radius (in km) of a planet you can detect?

Answer 1

As we know the brightness of the star depends on the area of the star.. When a planet transits over the star the effective area decreases.. Hence we can write

B=kA (here k is a constant, A is the area of the star and B is the brightness)

B=4*pi*k*R^2 (here R is the radius of the star)

Let the area of the planet that transits over the star be 'a' and it's radius be 'r'.

Hence new brightness

Hence the planet must have minimum radius of √0.05×695,510 km= 155,520 km