Why is a point source (star) more twinkling than a disc source (planet)?

Question

Most scintillation effects are caused by anomalous refraction caused by small-scale fluctuations in air density usually related to temperature gradients.

Stars twinkle because they are so far from Earth that they appear as point sources of light easily disturbed by Earth's atmospheric turbulence which acts like lenses and prisms diverting the light's path.

Large astronomical objects closer to Earth, like the Moon and other planets, encompass many points in space and can be resolved as objects with observable diameters. With multiple observed points of light traversing the atmosphere, their light's deviations average out and the viewer perceives less variation in light coming from them. https://en.wikipedia.org/wiki/Twinkling

But I don't understand why light coming from one point is more scattered than light coming from more points. I would expect the opposite because the lines to the receiver are more close together. Besides that, how is the deviated light of a planets averaged out. Is the light (of the edges) of the disc (planet) really capable of getting a constructive interference or something like that? How could this work?

Answer 1

The light from each point of a planet surface is scattered almost exactly as much as from a distant star. The trick is to figure out which part of our turbulent atmosphere affects the image of the whole object.

Let's assume your dilated pupil size is 6mm.

1) When you're looking at a star - you're looking at it through cylinder which has 6mm diameter and is ~10km long.

2) When you're looking at a planet with angular size of only 10 arcseconds (average size for a mars) you're looking through a cone which is 6mm in diameter on the one end and 484+6=490mm on the other end (tan(10 arcseconds)*10km=484mm).

Thus rays from different points of planet surface (even if it's beyond eye resolution) go through significantly different parts of the atmosphere (up to 490mm apart, compared to 6mm apart for a star), and got refracted randomly and thus averaged as each photon goes through significantly different path through atmosphere.

Now we can see that rays from mars "average" much larger volume of earth's atmosphere, even though you still see it as a single point (it's 6 times smaller than eye resolution).

Answer 2

It is related to the Rayleigh criterion. This states that the minimum angle with which two sources can be distinguished is the angle $$ \theta~=~1.22\frac{\lambda}{D}, $$ for $\lambda$ the wavelength, and $D$ the aperature diameter. The $1.22$ comes from the first Bessel function $J_1(x)$. Consider Venus, which does not twinkle. It has a diameter of about $6000km$ and we observe it across a distance of say $5\times 10^7km$. And this is an angle $1.2\times 10^{-4}rad$ or $7\times 10^{-3}$ degrees. For optical light around $500nm$ and an eye pupil of $.5cm$ the Rayleigh criterion is $\theta~=~1\times 10^{-4}$ That is very close, and if you think about it you can almost see Venus as a disk. The same is the case with the other planets. Now compare this to the angle to a distant star $\theta~<~10^{-8}rad$.

Optical turbulence is most pronounced below the Rayleigh criterion, which is why stars twinkle and planets do not. In order to resolve stars as a disk you have to have an optical aperture $10^3$ or $10^4$ times the eye pupil. This is on the order of $10m$ to $100m$, which is at the upper limit of modern telescopes.