# 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.

Course: [Orbits, missions and exoplanets](https://studybrix.com/en/courses/orbits-missions-and-exoplanets/index.md)
Level: university
Prerequisites: Ratios, graphs and Newtonian orbits.

## Notes

### 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.

## Practice questions

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

Answer: 0.01

Explanation: Square the radius ratio.

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

Answer: 0.02

Explanation: Take the positive square root of the depth.

### 3. What does a radial-velocity measurement directly trace?

A. Line-of-sight stellar motion
B. The planet's surface photograph
C. The star's name
D. A guaranteed biosignature

Answer: Line-of-sight stellar motion

Explanation: Spectral shifts constrain motion along the line of sight.

### 4. Why are many planetary systems not seen in transit?

A. Only Earth has gravity
B. Planets never block light
C. All stars have identical noise
D. Their orbital alignment does not produce a crossing from our viewpoint

Answer: Their orbital alignment does not produce a crossing from our viewpoint

Explanation: Transit visibility is strongly geometric.

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

Sample answer / marking guidance: An eclipsing stellar system or stellar activity can mimic aspects of a candidate signal. Follow-up and model comparison help distinguish explanations.

Explanation: 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.

Answer: 5 days

Explanation: 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 / marking guidance: Limb darkening, geometry, stellar contamination and finite planet size can alter the shape and inferred parameters.

Explanation: Credit explicit deviations from the simplified assumptions.

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

A. No
B. Yes, every transit does
C. Only when the dip is deep
D. Only when the period is short

Answer: No

Explanation: Planet detection and evidence of life are different questions.

## Further reading

- https://science.nasa.gov/exoplanets/how-we-find-and-characterize/

Original AI-assisted educational draft; not independently teacher-reviewed. References support further study, not copied exercises, affiliation or curriculum accreditation.