Question

A 1 solar mass star has two planets. One is observed to transit every year and the other twice a year. If their orbits are circular, how can you determine the distance between their orbits? How could the transits show that they are circular? How might transit observations provide estimates of the density of the planets? How could you tell if the orbits were parallel to the star's spin axis?

Answer 1

a) According to Kepler's third law of orbits,

The radius of opbit a is related to the period according to the relation

The period of tansit is the peropd of revolution T

Withthis the ratio of a can be estimated.

b) The transit speed and intnesity of light during transit is to be measured.

If the planet travels in the same speed to cross the star and theintensity of light from the star is constant during transit, the orbit is circular.

c) For getting information on the density of the planet, the light curve of the star is to be studied.

The light curve is the graph with time in x axis and intensity of light from star in y axis, for a time greater than the time difference between two transits.

d) IF the transit is occuring from diameter to diameter of the star, and occurs at the same position of the star every time, we can say that the planes coincide. (This is not the case for the transit of mercury and venus)