Exoplanet Transit Simulator

Adjust planet and orbital parameters to see how the transit depth and duration change.

Worked example — Exoplanet Transit Simulator

Transit depth: 84	84 ppm
Transit duration: 12.97 hours	12.97 h
Radial velocity semi-amplitude K: 0.0895 m/s	0.0895 m/s
Planet density: 5.51 g/cm³	5.51 g/cm^3
Estimated equilibrium temperature: 255 K	255 K
Semi-major axis: 1.00 AU	1.00 AU

These are the values the calculator shows when the page opens. Change any input above to recompute them.

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The transit catalogue is a census of what lines up, not of what exists 🖖

A transit needs the orbit to cross our line of sight, and that window is narrow: for an Earth-like orbit at 1 AU it spans 0.538° of inclination, so only about one random orientation in 213 would show it at all. Kepler still confirmed more than 2,600 planets this way — but every one of them had to happen to be pointing at us. The shape of the catalogue is therefore a fact about geometry and mission length before it is a fact about which planets are common: it over-reports whatever is easiest to catch, meaning large planets, close in, around small stars.

A shadow that measures a world 🖖

When a planet crosses in front of its star, it blocks a sliver of light — the depth of the dip equals the ratio of their disk areas, (Rp/R★)². So the light curve hands you the planet's size directly, with no image required. A Jupiter-sized planet dims a Sun-like star by about 1%, while an Earth-sized one dims it by only 0.008% (roughly 84 ppm).

A transit can reveal a backward orbit 🖖

During a transit the planet first hides the half of the spinning star rotating toward us, then the half rotating away, warping the star's measured velocity — the Rossiter–McLaughlin effect. The distortion's shape reveals whether the planet orbits with the star's spin or against it. Astonishingly, some hot Jupiters orbit backward: WASP-17b, confirmed in 2009, was the first known retrograde exoplanet.

The orbit buys frequency, never depth 🖖

Drag the period from 365 days down to 3 and watch the depth readout: it does not move by a single ppm. There is no distance term in the depth at all — the tool derives the orbital distance from the period by Kepler’s third law and spends it entirely on the duration. What a tight orbit buys is a more frequent transit, and a shorter one: the Earth preset crosses its star for 12.97 hours once a year, while the hot Jupiter preset crosses the same star in 2.62 hours — quicker, because a closer planet moves faster — but does it 122 times a year. Two years of watching yields two Earth transits, or 243 hot-Jupiter ones.

Problem solved in full

An alien astronomer watching the transit our planet actually produces 5 steps
Could an alien astronomer, watching from another star, discover the Earth? Work out the transit our planet actually produces, and then the odds that anybody is positioned to see it.
1. Transit depth is pure geometry — the fraction of the stellar disc the planet covers, which is the ratio of the two areas. Earth against the Sun comes to 84 parts per million: a hundredth of one per cent of dimming.
  
  $δ = (\frac{R _{p}}{R _{⋆}})^{2} = (\frac{6371}{696 000})^{2} = 8.39 \times 1 0^{- 5} = 84 ppm$
2. The orbital distance follows from Kepler's third law with the star's mass, and returns 1 AU. That is the check that this is the Earth being modelled and not merely something Earth-like.
  
  $a = (\frac{G M _{⋆} P ^{2}}{4 π ^{2}})^{1/3} = 1.50 \times 1 0^{11} m = 1.00 AU$
3. The duration is the time taken to cross the disc — the fraction of the orbit spanned by the star's diameter. Thirteen hours, once a year.
  
  $t_{tr} = \frac{P}{π} arcsin \frac{R _{⋆}}{a} \approx \frac{P R _{⋆}}{π a} = 12.97 h$
4. Now the step that governs the whole field. A transit happens only if the orbit is edge-on as seen from the observer, to within R★/a of exactly edge-on. That is 0.465%.
  
  $p_{tr} = \frac{R _{⋆}}{a} = \frac{6.957 \times 1 0 ^{8}}{1.496 \times 1 0 ^{11}} = 0.00465 = \frac{1}{215}$
5. So the alien has to be one of roughly 1 observer in 215 placed correctly, then needs photometry good to one part in twelve thousand, then has to watch for years to catch a repeat. A hot Jupiter is 121 times deeper and transits every few days.
  
  $(\frac{11 R _{\oplus}}{R _{⊙}})^{2} = 1.015% = 121 δ_{\oplus}$
Answer

The tool prints 84 ppm, a 12.97-hour transit, 1.00 AU and a density of 5.51 g/cm³. The figure it does not print is the one that shapes the catalogue: a randomly placed observer has about a 1-in-215 chance of seeing any transit at all. Multiply that by the depth and it is obvious why the first transiting planets found were all hot Jupiters — 1% deep, and a fresh transit every three days. The selection effect is not a footnote to the exoplanet census; it is most of its shape. Click the hot-Jupiter preset and compare the two depths directly.

$δ = 84 ppm, t_{tr} = 12.97 h; p_{tr} = \frac{R _{⋆}}{a} = \frac{1}{215}$

References (4)

Where the depth-to-radius relation and the light-curve geometry come from: S. Seager & G. Mallén-Ornelas, "A Unique Solution of Planet and Star Parameters from an Extrasolar Planet Transit Light Curve." The Astrophysical Journal 585, 1038–1055, 2003.
The first planetary transit ever observed — HD 209458 b, reported alongside Henry et al. in the same issue: D. Charbonneau, T. M. Brown, D. W. Latham & M. Mayor, "Detection of Planetary Transits Across a Sun-like Star." The Astrophysical Journal 529, L45–L48, 2000.
The mission behind the catalogue this tool’s first block describes: W. J. Borucki et al., "Kepler Planet-Detection Mission: Introduction and First Results." Science 327, 977–980, 2010.
The retrograde hot Jupiter named in the Rossiter–McLaughlin block: D. R. Anderson et al., "WASP-17b: An Ultra-Low Density Planet in a Probable Retrograde Orbit." The Astrophysical Journal 709, 159–167, 2010.

By the 42Math team · Updated 2026-06-29

Reviewed against published sources. Corrections welcome. Editorial policy · Corrections

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Example problems

Earth - Earth as seen from outside: an 84 ppm dip, one part in twelve thousand, lasting 12.97 hours once a year. The panel also gives the wobble Earth puts on the Sun, 0.0895 m/s — under nine centimetres a second. Both are correct and only one is measurable, which is why nearly every small planet we know was found by watching a star dim rather than watching it wobble.
Hot Jupiter - A Jupiter-mass planet in a 3-day orbit: 1.015% of the star's light blocked, 141 m/s of radial-velocity wobble, 1263 K at 0.0407 AU. The transit lasts 2.62 hours of that 3-day orbit — visible 3.6% of the time, which is why transit surveys stare instead of sampling.
Super-Earth - Super-Earth around M-dwarf: deeper dip, shorter period
Kepler-22b - The transit measures one thing and it is here: 503 ppm, which is a radius. The 14.4 g/cm³ below it, denser than lead, comes from a mass nobody has measured — the preset supplies 36 Earth masses because Kepler-22b’s real mass is still unknown. Halve that number and the depth does not move a digit while the density halves with it.