Each star below was watched by NASA's TESS satellite for about a month, taking a brightness reading every two minutes. Some of these stars have planets passing in front of them. One of them is an impostor. Find the dips, work out how often they repeat, and measure how big the thing blocking the light must be.
Transit Explorer: how the method works
From many light-years away, a star is just a dot. We can't see its planets, but we can watch its brightness. If a planet's orbit happens to be lined up edge-on with Earth, once per orbit the planet passes in front of the star and blocks a little of its light. Every slider below changes something real about the star or planet. Watch how each one changes the dip.
Axes rescale automatically to fit each dip. Lock them to see the real, absolute changes as you move the sliders.
What each slider does
Planet size sets the planet's radius. The depth depends on how big it is compared to the star: depth ≈ (Rplanet ÷ Rstar)². Twice as wide means four times deeper. It also sets how long the planet takes to cover the edge of the star (the sloped "ingress" and "egress").
Path across the star (astronomers call it the impact parameter, b): 0 is straight through the middle, 1 is skimming the edge. Off-center paths are shorter chords, so the transit is shorter. Near the edge the planet never fully fits on the star, giving a V shape.
Star size: the planet keeps the same size in Earth radii, so a bigger star is a bigger disk to cover (shallower dip) and a longer path to cross (longer transit). Lock the brightness axis to see the dip shrink.
Star mass and period set the orbit through Kepler's third law: a = ∛(Mstar × P²). A wider orbit means a slower planet, so the transit lasts longer, and the planet is less likely to be lined up with us.
Limb darkening: stars look darker near their edges because we see cooler, higher layers there. That rounds off the bottom of the dip into a U shape.
Noise: every real measurement scatters a little. When the noise is bigger than the dip, one transit can't be seen, and you need to fold many together.
Units cheat sheet: what do R☉, AU, ppm and K mean? (Tip: tap any underlined value on this page for a plain-language translation.)
R☉
One Sun radius, 696,000 km. The Sun is 109 times wider than Earth.
R⊕ / Earth radii
One Earth radius, 6,371 km. Jupiter is 11.2 Earth radii, Neptune 3.9.
M☉
One Sun mass, 333,000 Earths.
AU
Astronomical unit: the Earth–Sun distance, 150 million km. Mercury orbits at 0.39 AU.
pc
Parsec: 3.26 light-years, or 31 trillion km. The nearest star is 1.3 pc away.
ppm
Parts per million. 10,000 ppm = 1%. A 100 ppm dip means 1 in every 10,000 photons is blocked.
K
Kelvin. Same size steps as °C, but starting from absolute zero: °C = K − 273. Water boils at 373 K; the Sun's surface is 5,772 K.
d, h
Days and hours. TESS times are in days since it began watching that patch of sky.
1Scan the light curve
Click the bottom of each dip to mark it. Mark at least three dips that look alike.
No dips marked yet.
How the math works: reading a light curve
Each dot is one brightness measurement. TESS took a picture every 2 minutes. We averaged them into 10-minute chunks to cut down the noise. The vertical axis shows how much brighter or dimmer the star was than usual: 0% is normal, −1% means 1% of the light was missing.
A transit is a short, repeating dip. Real dips all have about the same depth and the same length. Single low dots scattered around are just noise.
The time between dips is the orbital period. If you mark the first and last dip, and there are N dips from first to last, then
P = (tlast − tfirst) ÷ (N − 1) Watch for gaps in the data (like TESS pausing to send data home): a missing dip still counts as a step.
2Fold the data on the orbital period
If the dips repeat every P days, stacking the data in chunks of P days lines all the dips up on top of each other. When the period is right, the dip snaps into one sharp shape.
How the math works: folding
Pick a starting transit. Call its time T0, the middle of one dip.
For every measurement, count how many orbits have passed since T0. orbits = (t − T0) ÷ P Keep only the leftover fraction (the part after the decimal point). That's how far the planet is around its orbit, like reading the minutes on a clock and ignoring the hour.
Plot every point at its leftover fraction. We convert it to hours from the middle of the dip so the axis is easy to read. If P is right, every transit lands in the same spot and the dips stack into one sharp shape. If P is a little off, each transit lands slightly shifted and the stack smears out.
Stacking beats noise. Averaging N transits together shrinks the random scatter by about √N. The dark line is that average. It's how TESS finds dips far too small to see in a single transit.
3Measure the depth
Drag the amber line on the folded plot (or use the slider) to the bottom of the dip. The fraction of starlight blocked equals the area of the planet's disk divided by the area of the star's disk.
How the math works: from depth to size
The dip is an area ratio. Seen from Earth, the star and the planet are both circles. A circle's area is π R², so the fraction of starlight blocked is
depth = (π Rplanet²) ÷ (π Rstar²) = (Rplanet ÷ Rstar)²
Undo the square. Taking the square root tells you how wide the planet is compared to the star:
Rplanet ÷ Rstar = √depth
Multiply by the star's size. Astronomers know each star's radius from its brightness, temperature and distance (measured by the Gaia satellite). One Sun radius equals 109 Earth radii, or 9.7 Jupiter radii.
Rplanet = Rstar × √depth × 109 Earth radii per Sun radius
Real stars look a little darker near their edges ("limb darkening"), which makes the middle of a transit slightly deeper than the simple formula assumes. Your answer may come out 5–10% bigger than the published value. That's normal.
4What did you find?
How the math works: how far, how hot, and how lucky?
Kepler's third law gives the orbit's size. A planet with a longer year orbits farther out. With the period in years, the distance in AU (1 AU = Earth–Sun distance) and the star's mass in Sun masses:
a³ = Mstar × P² so a = ∛(Mstar × P²)
Closer means hotter. A planet's temperature depends on how hot its star is and how much of the sky the star fills. Ignoring clouds and greenhouse gases:
Tplanet ≈ Tstar × √(Rstar ÷ 2a) For comparison, Earth would be about 280 K (7 °C) by this formula and Mercury about 450 K.
Why don't we see every planet transit? Orbits point in random directions. We only see a transit if we happen to sit close to the plane of the orbit. The chance is about
chance ≈ (Rstar + Rplanet) ÷ a Close-in planets have a much better chance. For Earth seen from a random star, it's only about 0.5%, so for every Earth twin that transits, about 200 others are hidden from us. That's why TESS watches hundreds of thousands of stars.
Bonus: load any star TESS has observed
Type a star name (like WASP-126, TOI-700, HD 209458) or a TIC number, then pick a sector. The page downloads the real light curve from NASA's MAST archive.