Answer key: Exoplanet Transit Worksheet

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Goal: Explain how astronomers find planets from tiny dips in starlight, and use the transit depth to estimate a planet’s size.

Completed results table

Values are the lab’s own readouts for each setting.

Answers

1. How much does a Jupiter-sized planet dim a Sun-like star? How much does an Earth-sized planet dim it?

   Jupiter-sized: about 1.05%. Earth-sized: only about 0.0084%. The Jupiter-sized dip is about 125 times deeper.

2. Show that transit depth ≈ (planet radius ÷ star radius)² for the Jupiter-sized planet.

   The radius ratio is 0.1026, and 0.1026² ≈ 0.0105, which is 1.05%.

3. What happened to the Earth-sized planet’s dip around the small star? Why do astronomers search small stars for Earth-sized planets?

   The dip grew to about 0.21%, 25 times deeper: the star is 5 times narrower and 5² = 25. Small planets are much easier to detect around small stars.

4. Why is the grazing transit’s dip shallower than the central one, even though the planet is the same size?

   In a grazing transit the planet only clips the edge of the star, so part of the planet never covers the star’s disk. Less light is blocked: about 0.64% instead of 1.05%.

5. Astronomers measure a 1% dip from a Sun-like star. Estimate the planet’s radius in Earth radii. (Hint: Rp ≈ R★ × √depth, and the Sun is about 109 Earth radii wide.)

   Rp ≈ 1 Sun × √0.01 = 0.1 Sun. The Sun is about 109 Earth radii wide, so that is about 10.9 Earth radii, roughly the size of Jupiter.

6. Can a transit tell you a planet’s mass? What else would astronomers need?

   No. A transit measures the planet’s size relative to its star. The mass usually comes from other observations, such as measuring the star’s tiny wobble with spectroscopy (the radial-velocity method).