Exoplanet Transit Light Curve

Lesson notes

Overview

A planet passing in front of its star dims the light slightly; the dip reveals its size. This topic is rated advanced and is number 40 of 98 in Earth & Space. Deeper models, formal results and harder reasoning.

What you are seeing

The panel above shows a graph of the function. Each slider changes one parameter, so you can see exactly how the curve bends, shifts or stretches. The animation is drawn live from the model, so everything you see responds to the sliders. Press Space to pause, use Restart to replay from the start, and change the speed to slow down quick events.

In depth

When a planet passes in front of its star, it blocks a small fraction of the light, so the star dims briefly and periodically. The fractional drop in brightness, depth = (R_p/R_s)², gives the planet’s size relative to the star: Jupiter transiting the Sun would block about 1%, and Earth about 0.008%. The time between dips gives the orbital period and the duration of the dip the orbit’s shape. Kepler and TESS found thousands of planets this way.

Reading the relationship

The expression "depth = (R_p/R_s)²" is a compact summary of the idea. It uses the symbols d, e, p, t, h, R_p; name what each one stands for before you start. Notice that it contains a squared term, so doubling that quantity changes the result by a factor of four, and a ratio, so increasing the denominator makes the result smaller. Then use the sliders to see how changing one quantity changes the others.

A guided exploration

1. Set every slider to its middle value and note the shape of the curve. 2. Move one slider at a time and describe whether the curve shifts, stretches or turns. 3. Find the value where the behaviour changes sharply, then connect it to the formula.

Try this

Try to explain why the pattern holds, not just what it is. Look for limiting cases and what happens at the edges.

Common pitfalls

Earth and space systems work on very different scales of time and distance. Check which scale a number refers to before comparing it with another.

How it connects

It builds on “Schwarzschild Radius of a Black Hole”, the topic before it in Earth & Space. Once you are comfortable, continue with “Galaxy Rotation Curves and Dark Matter”.

Why it matters

Earth and space science helps us understand our planet, its climate and the wider universe.