StudyBrixFree worksheets, study guides and courses

Astronomy & space · lesson 3 of 4

Exoplanet transits and radial velocities

A planet crossing a star's visible disk can cause a periodic brightness dip. For an idealized small dark planet and uniform stellar disk, depth≈(Rp/Rstar)².

University8 practice questionsNotes + worked examples
Take the quizStudy guideRevision sheet

Learn the ideas

Prerequisites: Ratios, graphs and Newtonian orbits.

Transit method

A planet crossing a star's visible disk can cause a periodic brightness dip. For an idealized small dark planet and uniform stellar disk, depth≈(Rp/Rstar)².

Radial velocity

A star and planet orbit their common centre of mass. Periodic line-of-sight stellar velocity changes can be inferred from spectral shifts.

Selection

Neither method detects every planet equally well. Orbital orientation, noise, stellar activity and observational duration affect sensitivity.

Confirmation

A candidate signal needs checks against false positives. A transit alone is not proof of life or a complete atmospheric measurement.

Worked examples

Example 1

In the idealized transit model, Rp/Rstar=0.1. Find fractional transit depth.

Square the radius ratio.

0.01

Example 2

For idealized transit depth 0.0004, find Rp/Rstar.

Take the positive square root of the depth.

0.02

Check your understanding

8 questions

Decimals or fractions are accepted for numeric answers. Proofs and written responses use sample answers and require human marking. This is practice, not a protected examination.

1 In the idealized transit model, Rp/Rstar=0.1. Find fractional transit depth.

Show answer and explanation

0.01

Square the radius ratio.

2 For idealized transit depth 0.0004, find Rp/Rstar.

Show answer and explanation

0.02

Take the positive square root of the depth.

3 What does a radial-velocity measurement directly trace?

Show answer and explanation

Line-of-sight stellar motion

Spectral shifts constrain motion along the line of sight.

4 Why are many planetary systems not seen in transit?

Show answer and explanation

Their orbital alignment does not produce a crossing from our viewpoint

Transit visibility is strongly geometric.

5 Give one false-positive or confounding effect that should be checked in a planet search.

Sample answer and marking guidance

An eclipsing stellar system or stellar activity can mimic aspects of a candidate signal. Follow-up and model comparison help distinguish explanations.

Credit a plausible confounder and validation.

6 A repeating dip occurs at days 2, 7 and 12 in a simple periodic model. Find its period.days

Show answer and explanation

5 days

Consecutive dip times differ by five days.

7 Why does the uniform-disk transit-depth formula not describe every detailed transit light curve?

Sample answer and marking guidance

Limb darkening, geometry, stellar contamination and finite planet size can alter the shape and inferred parameters.

Credit explicit deviations from the simplified assumptions.

8 Does detecting a planet by transit establish that it supports life?

Show answer and explanation

No

Planet detection and evidence of life are different questions.

Further reading and review references

These are reference links, not copied exercises, institutional endorsement or proof of independent review.