The composition of a planet's atmosphere can be measured during a transit by analyzing what?

Assume that someone is watching Earth from a distance.

When they observe our Sun, they notice that it has a blue component. However, when the Earth passes in front of the Sun, the blue component is scattered by our atmosphere, which explains why the sky appears blue, while the red component is not scattered, which explains why the Moon appears red during a lunar eclipse.

Who, then, is watching us and determining that our atmosphere scatters blue light but not red light?

For example, on Mars, where the air is thinner, the planet scatters more red light than blue light. A wavelength is scattered if the object it encounters along its path is the same size as the wavelength. Consequently, the average size of air molecules is in the order of the blue wavelength.

Using this system, you can infer which molecules the atmosphere ought to contain in order to disperse those colors and have that size.

By examining the light that travels through a planet's atmosphere during a transit, one can determine the composition of that atmosphere.