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Astronomy & space · University

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.

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Prerequisites

Ratios, graphs and Newtonian orbits.

Study 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.

Worked examples

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

Square the radius ratio.

0.01

For idealized transit depth 0.0004, find Rp/Rstar.

Take the positive square root of the depth.

0.02

Check your understanding

  1. What does a radial-velocity measurement directly trace?

    1. Line-of-sight stellar motion
    2. The planet's surface photograph
    3. The star's name
    4. A guaranteed biosignature

  2. Why are many planetary systems not seen in transit?

    1. Only Earth has gravity
    2. Planets never block light
    3. All stars have identical noise
    4. Their orbital alignment does not produce a crossing from our viewpoint

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

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

Answers and marking guidance

Answers and marking notes
  1. Line-of-sight stellar motion

    Spectral shifts constrain motion along the line of sight.

  2. Their orbital alignment does not produce a crossing from our viewpoint

    Transit visibility is strongly geometric.

  3. 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.

  4. 5 days

    Consecutive dip times differ by five days.

Further reading and review references

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