Skip to content
The Science 360
Space 16 min read

Why Stars Twinkle but Planets Don't (With the Math)

Observation recorded
Cinematic poster of a brilliant star burst rising over Earth's glowing horizon, with the title "Stars Twinkle" in large condensed type and the line "Planets don’t. Here’s why.".
#Space #Atmosphere #Optics #Astronomy

Sirius, the brightest star in the night sky, is about 0.006 arcseconds across as seen from Earth. Jupiter, which often hangs near it in winter skies, is around 40 arcseconds across. That is a ratio of nearly seven thousand. Both look like dots to your eye, yet one sparkles like a cut diamond and the other sits there as calm as a streetlight. The whole difference between twinkling and not twinkling lives inside that ratio, and you can work it out on the back of an envelope.

Quick answerStars twinkle because they are effectively points, so all their light crosses one small patch of turbulent air (about 7 cm wide, roughly 1.5 arcseconds of sky) at a time. A planet's disk is 4 to 66 arcseconds wide, so its light passes through dozens to hundreds of patches whose flickers average out.
Infographic: Why do stars twinkle but planets don't? A star's light reaches an eye through one patch of turbulent air 10 km up, while Jupiter's light crosses many patches. One patch is about 7 cm wide and spans 1.5 arcseconds, so every star twinkles fully while Jupiter's 40 arcsecond disk averages about 680 patches. A log-scale chart of relative twinkle against angular size is flat for Sirius at 0.006 and Betelgeuse at 0.045 arcseconds, then falls: Mars at 3.5 arcseconds is 2.3 times calmer, Jupiter 26 times. Tiles: simulated Jupiter flickers ±1.2% against a star's ±36%; twinkle is 4.8 times stronger 10° up; colors split below 26°. Myth: reflected light is not the reason.
Tap the image to view it full size. View the accessible, editable SVG.

Most explanations stop at "planets are disks, stars are points". That is correct, but it hides the useful part: how big a disk has to be, compared with what. Once you have the number, you can also predict when a planet will twinkle (and it does), and why Sirius flashes colors when it is low.

What actually makes a star twinkle?

Air bends light a tiny amount, and how much depends on its density, which depends on its temperature. The atmosphere is full of turbulent blobs that differ by a fraction of a degree. Each blob acts like a very weak lens. A single weak lens does almost nothing to the overall direction of starlight, but by the time the light has travelled a few kilometers past the turbulent layer, those slight bends have rearranged the light on the ground into a mottled pattern of brighter and darker patches. If you could see it on the ground, it would look like the wavy light on the bottom of a swimming pool. Astronomers call the effect scintillation.

The wind carries this pattern past you. Your pupil, at most about 7 mm wide at night, is much smaller than the patches, so your eye samples one patch at a time. When a bright patch slides across your pupil the star looks brighter, and when a dark one does it dims. That is twinkling: you are watching an interference-and-focusing pattern sweep across your eye at wind speed.

How big are the patches? Optics gives a clean answer. The characteristic size of the scintillation pattern is the radius of the first Fresnel zone, rF=λzr_F = \sqrt{\lambda z}, where λ\lambda is the wavelength and zz is the distance from the turbulent layer to you. Durham University researchers put it plainly in a 2015 paper on scintillation noise: a turbulent layer at 10 km observed at 500 nm makes patches about 0.07 m across, whatever the strength of the turbulence. Strength sets how deep the flicker is; distance sets the patch size.

Diagram of a turbulent air layer about 10 km up: light from a point star passes through a single 7 cm patch on its way to the eye, while light from a planet's disk arrives as a cone that crosses many patches.
Figure 1. A star's light reaches your eye through one patch of the turbulent pattern. A planet's light arrives from a whole disk, so it crosses many patches that brighten and dim independently.

The worked calculation: how many patches does a planet average over?

Here is the key step most explanations skip. We need the angle a single patch covers as seen from the ground, then we compare it with the planet's angular size.

Step 1. Patch size at the ground

For a layer h=10 kmh = 10\ \mathrm{km} up and λ=550 nm\lambda = 550\ \mathrm{nm} (green light):

rF=λh=550×10−9 m×10,000 m=5.5×10−3 m2≈0.074 m≈7 cm\begin{aligned}r_F &= \sqrt{\lambda h} = \sqrt{550\times10^{-9}\ \mathrm{m} \times 10{,}000\ \mathrm{m}} \\ &= \sqrt{5.5\times10^{-3}\ \mathrm{m^2}} \approx 0.074\ \mathrm{m} \approx 7\ \mathrm{cm}\end{aligned}

Step 2. Angle that patch subtends from the ground

θpatch=rFh=0.074 m10,000 m=7.4×10−6 rad×206,265 arcsec/rad≈1.5′′\begin{aligned}\theta_\text{patch} &= \frac{r_F}{h} = \frac{0.074\ \mathrm{m}}{10{,}000\ \mathrm{m}} = 7.4\times10^{-6}\ \mathrm{rad} \\ &\times 206{,}265\ \mathrm{arcsec/rad} \approx 1.5''\end{aligned}

Step 3. Jupiter's disk, about 40″ (NASA range: 30.5″ to 50.1″)

patches across=40/1.5≈26patches over the disk≈262≈680\begin{aligned}\text{patches across} &= 40 / 1.5 \approx 26 \\ \text{patches over the disk} &\approx 26^2 \approx 680\end{aligned}

Circle compared with circle, so the area ratio is just the diameter ratio squared.

Step 4. Independent flickers average down as 1/N1/\sqrt{N}

reduction=680≈26\text{reduction} = \sqrt{680} \approx 26

A star flickering by ±36% would become a Jupiter flickering by about ±1.4%.

Step 5. Betelgeuse, one of the largest stars in angular size, about 0.045″

0.045/1.5≈0.03 of one patch0.045 / 1.5 \approx 0.03\ \text{of one patch}

It is a point as far as the air is concerned.

So "smaller than the turbulence" understates it for a star: even the fattest star in the sky is about 30 times smaller than one patch, and Sirius is about 250 times smaller. Jupiter is 26 times bigger. Those two ratios point in opposite directions, and that is why one twinkles and the other does not.

A tidy way to state the rule: for a disk wider than one patch, the twinkle amplitude falls roughly as θpatch/θdisk\theta_\text{patch}/\theta_\text{disk}. Radio astronomers use exactly the same relation for quasars twinkling in the solar wind (a source wider than the "Fresnel angle" scintillates less, in proportion to its size), which is a nice sign the physics is general.

Log-log plot of relative twinkle amplitude against apparent angular diameter in arcseconds. Sirius and Betelgeuse sit on the flat full-twinkle line at the left; beyond a 1.5 arcsecond patch angle the line falls, passing Mars when far from Earth, Venus when far, Saturn's globe, Jupiter and Venus when near.
Figure 2. Relative twinkle amplitude versus angular diameter, using the 1.5" patch angle from the calculation above. Stars sit on the flat "full twinkle" plateau. Planets slide down the slope: Jupiter's flicker is diluted about 26 times, Mars at its smallest only about 2.3 times.

To check that the averaging argument holds up beyond hand waving, I simulated it. The code builds a random, smoothly varying brightness pattern with a known patch size, slides it past three "eyes" and records what each sees: a point, a disk 7 patches wide, and a disk 27 patches wide (Jupiter). Over the whole simulated field the point varies by ±36%, the 7-patch disk by ±4.7% and the Jupiter disk by ±1.2%. The ratios come out at about 7.6 and 29, close to the 7 and 27 the square-root rule predicts.

Simulated brightness versus time for a point star, a disk seven turbulence patches wide and a Jupiter-sized disk twenty-seven patches wide. The point star swings between about 0.4 and 3 times its average brightness, the small disk wobbles a few percent and the Jupiter-sized disk is almost a flat line.
Figure 3. Computed light curves from one simulated scintillation pattern. Same air, same wind; the only thing that changes is how much sky each target covers. The occasional tall spike on the star curve is typical: the brightness distribution of a twinkling star is skewed, with brief bright flashes.

The common misconception: planets don’t twinkle because they reflect light

You will still find this on quiz sites and in some school worksheets: stars twinkle because they make their own light, planets do not because they only reflect sunlight. It is wrong, and easy to disprove. The Moon reflects sunlight and a bright star emits its own; put a tiny reflecting asteroid next to that star and both would twinkle exactly the same, because the atmosphere has no idea where the light came from. What matters is angular size. Mars proves the point from the other side: it reflects sunlight like every planet, yet when it is far from Earth and its disk shrinks to 3.5 arcseconds it twinkles noticeably, as the calculation below predicts.

A second, subtler mix-up is treating twinkling and "seeing" as the same thing. They come from the same air but measure different things.

  • Seeing is blur and image jitter: the light arrives at slightly different angles. It is described by the Fried parameter r0, about 10 cm at a typical site in visible light, which gives a seeing disk of roughly λ/r0 ≈ 1 arcsecond. Seeing is dominated by turbulence near the ground and in the lowest kilometer.
  • Twinkling (scintillation) is the brightness change. It needs distance to develop, so it is dominated by high layers. In the standard small-aperture formula the turbulence at height h is weighted by h5/6, so a layer at 10 km counts about 46 times more, per unit of turbulence, than one at 100 m.

That is why a night with a ripping jet stream overhead makes stars dance even when the air near the ground is still, and why astronomers can have bad seeing with quiet twinkling, or the reverse.

Why do stars twinkle less through a telescope?

Same reason planets twinkle less. A 20 cm telescope collects light over about 800 times the area of your dark-adapted pupil, enough to span several 7 cm patches at once. The telescope's lens is doing to a star what Jupiter's disk does for Jupiter: averaging many independent patches. This "aperture averaging" is why photometry with large telescopes reaches precisions that would be impossible with a small lens, and why a star that seemed to sparkle by eye looks steadier, if wobblier, in the eyepiece.

When do planets twinkle?

Here is where the numbers earn their keep. "Planets don't twinkle" is a rule of thumb, and you can calculate when it breaks.

Look at a planet 10° above the horizon. Your line of sight now crosses the 10 km layer about 57 km away instead of 10 km, and passes through about 5.6 times as much air (the airmass). Two things change:

Airmass at 10° altitude:

X≈1sin⁡10∘≈5.8X \approx \frac{1}{\sin 10^\circ} \approx 5.8

With Earth's curvature included it is 5.6.

1. Patch angle shrinks as 1/X1/\sqrt{X}

θpatch≈1.5′′5.6≈0.64′′\theta_\text{patch} \approx \frac{1.5''}{\sqrt{5.6}} \approx 0.64''

2. Point-source twinkle grows

Scintillation variance scales as X11/6X^{11/6} (weak-turbulence theory, Dravins et al.), so amplitude scales as X11/12X^{11/12}:

5.611/12≈4.85.6^{11/12} \approx 4.8

So a star at 10° twinkles about 4.8 times as strongly as one overhead.

Mars, 4′′:4.8×(0.64/4)≈0.77Venus, 15′′:4.8×(0.64/15)≈0.2Jupiter, 40′′:4.8×(0.64/40)≈0.08\begin{aligned}\text{Mars, } 4'' &: 4.8 \times (0.64/4) \approx 0.77 \\ \text{Venus, } 15'' &: 4.8 \times (0.64/15) \approx 0.2 \\ \text{Jupiter, } 40'' &: 4.8 \times (0.64/40) \approx 0.08\end{aligned}

Each number is the planet's twinkle at 10° altitude as a fraction of an overhead star's.

So a small Mars low in the sky should twinkle almost as hard as a star overhead, and observers report exactly that. Mercury, which is 4.5 to 13 arcseconds across and is only ever seen low in twilight, is the planet most often caught twinkling. Venus low in a turbulent sky can shimmer noticeably. Jupiter rarely does.

One honest caveat. Close to the horizon the weak-turbulence formula overestimates the growth, because scintillation "saturates" once the light has been scrambled by several layers, and the amplitude stops climbing as fast. So read those numbers as an upper bound on the trend, not as precise predictions. The direction of the effect is solid; the exponent near the horizon is not.

Why does Sirius flash different colors?

Watch Sirius rising on a cold winter evening and it flickers red, green and blue, sometimes fast enough to look like a disco ball. The star is not changing. The atmosphere near the horizon acts like a weak prism: blue light is refracted slightly more than red, so the two colors reach your eye along slightly different paths.

Using the standard refractive index of air (n−1≈2.81×10−4n - 1 \approx 2.81\times10^{-4} at 450 nm and 2.76×10−42.76\times10^{-4} at 650 nm), the blue and red images of a star at 10° altitude are separated by about 5 arcseconds. Traced back up to the 10 km turbulent layer, the blue and red beams are something like 80 cm apart, while the patches there are only about 18 cm across. So the blue light and the red light are being twinkled by different pieces of air. When the blue happens to hit a bright patch and the red a dark one, the star flashes blue for a split second.

Plot against altitude above the horizon of two distances at the turbulent layer: the gap between blue and red light paths, which rises steeply toward the horizon, and the patch size, which grows slowly from about 7 to 25 centimeters. The curves cross near 26 degrees; below that, colors twinkle independently.
Figure 4. Computed gap between the 450 nm and 650 nm light paths where they cross a turbulent layer 10 km up, compared with the patch size. Below about 26° the gap is wider than a patch, so each color twinkles on its own. The crossover moves with the real turbulence profile; treat it as "roughly 20° to 30°".

Sirius sits at a declination of about −17°, so from 40° north it never climbs higher than about 33°, and from Britain or Germany it peaks around 20° to 25°. For most northern observers it spends its whole night in or near the color-flashing zone of Figure 4, and it is bright enough for your color vision to work. That combination, not anything special about the star, is why it has a reputation. Fainter low stars flash colors too; you just cannot see the color.

Do stars twinkle in space?

No. Every bit of twinkling comes from the last 20 kilometers or so of the light's trip, after it has crossed trillions of kilometers of empty space without a flicker. Astronauts describe stars from orbit as steady points, and space telescopes measure stellar brightness to parts per million precisely because there is no air in the way. On the ground, astronomers fight scintillation with large apertures, longer exposures and, on the biggest telescopes, adaptive optics, which corrects the image blur (although not the light lost to brightness fluctuations).

How to use this tonight

  • A bright point that is high and steady is almost certainly a planet. A bright point that is high and sparkling is a star.
  • Near the horizon, the test gets unreliable. Wait an hour for the object to climb, or compare it with a known star at the same height.
  • If the stars overhead are barely twinkling, the upper air is calm, and it is a good night to look at planets through a telescope; if they are dancing, the jet stream is probably right above you.

Twinkling is an optics problem with a size threshold of about one and a half arcseconds. Everything on the star side of that line sparkles; everything on the planet side averages itself into calm. The atmosphere that makes this happen also decides what color the Sun looks, which is a story for what color the Sun really is.

FAQ

Do planets ever twinkle?

Yes. A planet low on the horizon, or a small one such as Mars near its farthest from Earth or Mercury, can twinkle visibly. Near the horizon the light crosses about five times more air and the turbulence patches shrink in angle, so even a small disk no longer averages the flicker away.

Why do stars twinkle different colors?

Low in the sky, the atmosphere acts like a weak prism. Blue and red light from the same star take paths that are tens of centimeters apart when they cross the turbulent layer, so each color brightens or dims independently. Below roughly 25° altitude this makes bright stars like Sirius flash red, green and blue.

Do stars twinkle in space?

No. Twinkling is made entirely by Earth's atmosphere. Astronauts on the International Space Station and telescopes like Hubble and JWST see stars as steady points.

Is twinkling a reliable way to tell a planet from a star?

It is a good rule of thumb for objects well above the horizon: a bright, steady point is probably Venus, Jupiter, Saturn or Mars. It fails near the horizon, where planets can flicker, and on very calm nights, when even stars barely twinkle.

Why do stars twinkle more on some nights than others?

Twinkling depends mostly on turbulence high up, around jet-stream altitude. A strong jet stream overhead means strong twinkling. On nights when the upper air is calm, stars shine more steadily even if the air near the ground is moving.

Sources

  1. Osborn, J. et al. (2015), "Atmospheric Scintillation in Astronomical Photometry", MNRAS (Fresnel-zone patch size, ~0.07 m for a 10 km layer at 500 nm; small-aperture formula with (cos γ)−11/6): arxiv.org/abs/1506.06921
  2. Astronomical seeing (Fried parameter, r0 ≈ 10 cm and ~1" seeing): en.wikipedia.org/wiki/Astronomical_seeing
  3. Isaac Newton Group, DIMM seeing monitor (median r0 ≈ 15 cm at La Palma): ing.iac.es
  4. NASA NSSDC, Jupiter Fact Sheet (apparent diameter 30.5" to 50.1"): nssdc.gsfc.nasa.gov/planetary/factsheet/jupiterfact.html
  5. NASA NSSDC, Planetary Fact Sheets (Venus 9.7" to 66", Mars 3.5" to 25.1"): nssdc.gsfc.nasa.gov/planetary/factsheet/
  6. Davis, J. et al. (2011), "The Angular Diameter and Fundamental Parameters of Sirius A", PASA (6.04 mas): arxiv.org/abs/1010.3790
  7. Betelgeuse angular diameter measurements (~0.042" to 0.056" depending on epoch and wavelength): en.wikipedia.org/wiki/Betelgeuse
  8. Interplanetary scintillation of compact radio sources, source size versus Fresnel angle: arxiv.org/abs/1711.00393
  9. EarthSky, "Why don't planets twinkle as stars do?": earthsky.org
  10. BBC Sky at Night, Sirius flashing colors near the horizon: skyatnightmagazine.com

Header image: NASA (image iss073e0982823), regraded for this article.

Related observations
Physics 10 Cosmic Objects That Will amaze you Space Why the 2027 Solar Eclipse Lasts 6 Minutes 23 Seconds Space How Fast Must a Space Station Spin for 1 g?
Transmit