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Exoplanets: how we find other worlds

.text:0041B320; author: Can Ozdemir date: 2025-01-05 size: 0x34E0 tags: science, astronomy, exoplanets
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A planet around another star is a faint object sitting next to a dazzling one: in visible light a Sun-like star outshines an Earth-like planet by billions of times. So most exoplanets have never been seen at all. We infer them from side effects, the way you can tell a hidden function exists because a register changes at regular intervals. This post is about the four main ways of reading those side effects, and about what the word "habitable" really promises.

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1995: the first hot Jupiter

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The first confirmed planets were found in 1992 around a pulsar, a dead star, from tiny timing irregularities in its radio pulses. The first around a Sun-like star came on 6 October 1995, when Michel Mayor and Didier Queloz of Geneva announced a planet orbiting 51 Pegasi, a star about 50 light-years away that is faintly visible to the naked eye under dark skies. The planet, 51 Pegasi b, has at least half the mass of Jupiter and circles its star in just 4.2 days, at 0.05 AU, seven times closer than Mercury is to the Sun.

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That was a shock. Theories built on our own Solar System expected giant planets to sit far from their stars. A "hot Jupiter" was not in the plan. Mayor and Queloz shared the 2019 Nobel Prize in Physics for it. (The IAU later named the star Helvetios and the planet Dimidium, Latin for "half".)

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Method 1: the wobble

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A planet does not orbit its star; both orbit their common centre of mass.

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         ................
      ....              ....
     ..                    ..       O  planet: big, slow orbit
   ..                        .O
  ..                          ..    *  star: tiny, quick circle
  .                            .
  .           ::::::           .    x  barycentre, the common
  .           : x  ::          ..      centre of mass
  .           *:::::           .
  .                            .    Sun + Jupiter: x sits 1.07 solar
  ..                          ..    radii from the Sun's centre,
   ..                        ..     just outside its surface
     ..                    ..
      ....              ....        (not to scale)
         ................
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The star's little circle makes it move toward us and away from us, and by the Doppler effect its spectral lines shift slightly blue, then red. The shift in wavelength, divided by the wavelength, equals v/c, where v is the speed along our line of sight and c the speed of light. Jupiter makes the Sun wobble at 12.5 m/s, Earth at only 9 cm/s, and 51 Pegasi b makes its star move at about 56 m/s.

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+56 m/s |      ****                          ****
        |    **    **                      **    **
        |   *        *                    *        *
        |  *          *                  *          *
        | *            *                *            *
    0   |*..............*..............*..............*..............
        |                *            *                *            *
        |                 *          *                  *          *
        |                  *        *                    *        *
        |                   **    **                      **    **
-56 m/s |                     ****                          ****
        +------------------------------------------------------------>
         0                           4.2 d                         8.5 d
+ : star receding (lines red-shifted)   - : approaching (blue-shifted)
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For a 12.5 m/s wobble, a spectral line at 550 nm moves by about 0.00002 nm, thousands of times less than the width of an atom. Modern spectrographs such as HARPS reach about 1 m/s, and newer ones are built to reach 10 cm/s. The method has limits: because the tilt of the orbit is unknown, you get only a minimum mass, and starspots can fake a signal. The Doppler idea returns on a much larger scale in How we know the universe is expanding.

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Method 2: the shadow

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If we happen to look along the orbit's plane, the planet crosses the star's disc once per orbit and blocks a little light.

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         #####         #####         #####         #####     #####
        #######       #######       #######       #######   #######
    o  #########     o########     ####o####     ########o #########  o
        #######       #######       #######       #######   #######
         #####         #####         #####         #####     #####
        before        ingress         mid         egress     after

100.0% |________________\                            /__________________
       |                 \                          /
 99.0% |                  __________________________
       +--------------------------------------------------------------->
                                                                  time

A Jupiter-size planet dims a Sun-like star by about 1%. An Earth-size
planet dims it by only 0.0084%: over 100 times shallower than drawn.
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The dip has depth (planet radius / star radius) squared. Real numbers, from a few lines of Python:

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import math
R_sun, R_jup, R_earth = 695_700, 71_492, 6_371     # km
for name, r in (("Jupiter", R_jup), ("Earth", R_earth)):
    print(f"{name:8} transit depth = {(r / R_sun)**2 * 100:.4f} %")

G, M_sun, AU = 6.674e-11, 1.989e30, 1.496e11
def k_ms(m_planet_kg, period_days):             # star's speed wobble, circular orbit
    P = period_days * 86400
    return (2 * math.pi * G / P) ** (1/3) * m_planet_kg / M_sun ** (2/3)

print(f"Jupiter  -> Sun wobble {k_ms(1.898e27, 4332.6):6.2f} m/s")
print(f"Earth    -> Sun wobble {k_ms(5.972e24, 365.25):6.3f} m/s")
print(f"Earth transit chance = 1 in {AU / (R_sun * 1000):.0f}")
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Jupiter  transit depth = 1.0560 %
Earth    transit depth = 0.0084 %
Jupiter  -> Sun wobble  12.46 m/s
Earth    -> Sun wobble  0.089 m/s
Earth transit chance = 1 in 215
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Two lessons follow. An Earth-sized dip of 0.0084 percent is too small for most ground-based telescopes, so we needed space. And only about 1 in 215 Earth-like orbits would line up with us, so you must watch thousands of stars at once. That is what NASA's Kepler telescope did. Launched in 2009, it stared at about 150,000 stars in one patch of sky (roughly 0.3 percent of the whole sky) until a reaction wheel failure in 2013; a second mission, K2, continued until 2018. It showed that small planets are common. Its successor TESS, launched in April 2018, scans nearly the whole sky in 27-day sectors, aimed at nearby, bright stars. Combine a transit (radius) with a wobble (mass) and you get density, so you can tell a rocky world from a gas ball.

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Method 3: direct imaging

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Block the star and look at what is left. A coronagraph does that with a small mask inside the telescope, but starlight always scatters around it.

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                 ..........                 X  coronagraph mask
              ................                 (hides the star)
            .....::::::::::.....
           ....::--==++==--::....   O       shaded: leftover glare,
          ....:-=+*@XXXX@*+=-:....          far brighter than the
         ....:-=+%XXXXXXXX%+=-:....         planet
         ....:-=*@XXXXXXXX@*=-:....
         ....:-=+%XXXXXXXX%+=-:....         O  planet, 1e-9 of the
          ....:-=+*@XXXX@*+=-:....             star (Jupiter);
           ....::--==++==--::....              1e-10 for an Earth twin
            .....::::::::::.....
              ................
                 ..........
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Only young, massive, far-out planets are bright and wide enough to show: the four giants of HR 8799 (the first three imaged in 2008) are the classic example. A planet like Earth, a tenth of a billionth as bright as its star, remains out of reach for now.

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Method 4: gravity as a lens

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Einstein's general relativity says gravity bends light. When one star drifts almost exactly in front of a more distant one, the foreground star acts as a lens and the background star brightens smoothly for days to weeks. A planet around the lens star adds a short extra blip.

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 x5.5  |
       |                              **
       |
       |                             *  *   <- star alone: smooth hump
       |
       |                            *    *
       |          planet's blip (hours-days) ->  #
       |                           *      *      #
       |                         **        **    #
       |                       **            ** ###
       |                 ******                ******
  x1   |*****************............................*****************
       +-------------------------------------------------------------->
        weeks                                                     time
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Microlensing is good at finding cold planets several AU from their stars, even planets floating alone, but each event happens only once. Surveys using it indicate that, on average, every star has at least one planet.

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MethodWhat it measuresFinds bestBlind spot
Wobblestar's Doppler shiftmassive planets, close orbitsonly a minimum mass
Transitdip in starlightplanets whose orbit is edge-on; gives sizemost orbits are not edge-on
Imagingthe planet's own lightyoung giants far from the starsmall, old or close-in planets
Microlensingbrief extra brighteningcold, distant planetsone-shot, cannot be repeated
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What the catalogue says

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As of the start of 2025 there are well over 5,000 confirmed exoplanets, and the number grows every month. Most were found by transits. Hot Jupiters were found first not because they are common (about 1 percent of Sun-like stars) but because they are easy. The commonest planets are sizes between Earth and Neptune, a kind our Solar System lacks. Some systems are crowded: TRAPPIST-1, a dim red star 40 light-years away, has seven Earth-sized planets, all orbiting closer to their star than Mercury does to the Sun.

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Reading atmospheres with JWST

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During a transit a sliver of starlight passes through the planet's atmosphere, and molecules absorb particular wavelengths, so the planet looks very slightly larger at those colours. The James Webb Space Telescope (launched on 25 December 2021, science since July 2022) used this on WASP-39 b, a hot Saturn-mass planet, and made the first clear detection of carbon dioxide in an exoplanet atmosphere, along with water vapour. Here is a schematic of what such a spectrum looks like:

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transit |
depth   |                                                  CO2
        |                            H2O                    **
        |                             *                    *
        |                 H2O        * *
        |          H2O     *                                  *
        |           **    * *       *   *                 *
        |          *     *   *     *     *                     *
        |**********   ***     *****       **            **      *
        |                                   ************         ******
        +-------------------------------------------------------------->
micron:        1            2             3             4             5
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For rocky planets the signal is far fainter. Early JWST measurements suggest the two innermost TRAPPIST-1 planets have no thick atmosphere, but these are first results and could change.

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The habitable zone, and what it is not

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The habitable zone is the band of distances where a planet with an Earth-like atmosphere could keep liquid water on its surface. For the Sun, conservative estimates give roughly 0.95 to 1.37 AU, and wider ones 0.75 to 1.77 AU. For a dim red dwarf the band lies much closer in.

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THE SUN (36 columns per AU)
0.0              0.5               1.0               1.5    AU
+-----------------+--------~~~~~~~==+=============~~~~+~~~~~~~~~~-------
             Me           V         E                 Ma
== conservative zone 0.95-1.37 AU;  ~ wider estimates 0.75-1.77 AU

TRAPPIST-1 (1000 columns per AU: Mercury would be at column 387)
0.00              0.02                0.04                0.06    AU
+-----------------~~+~~~~~~~~~~~~~~~~~~~+~~-----------------+-----------
            b   c     d      e        f        g              h
~ rough habitable zone for this dim red dwarf (estimates vary)
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Notice that Venus (0.72 AU) and Mars (1.52 AU) sit at the two edges, and neither is habitable today: Venus is a greenhouse furnace and Mars lost most of its air. The zone only describes the amount of starlight received, under a fixed assumption about the atmosphere. It says nothing about atmosphere, magnetic field, water supply, stellar flares or tidal locking, all of which matter. And life might exist outside the zone, for instance in the oceans under the ice of Europa and Enceladus, heated by tides.

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So "habitable" means could have liquid water on the surface under favourable assumptions, not has life. A claim of life would need a biosignature, a combination of gases hard to explain without biology, and extraordinary claims need extraordinary evidence. None has been found.

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Try it

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Pick a bright star in tonight's sky and look up whether it has known planets; many do. Then adapt the Python above: for any transiting planet the dip is just its radius ratio squared. The Solar System itself is the calibration case: see A tour of the solar system for the planets, and The Moon, tides and eclipses for the centre-of-mass wobble that makes the first method work.

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.text:0041E707; © 2026 Can Ozdemir. All rights reserved. terms
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