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Teslarati's SpaceX just expanded the envelope of rocket recovery with 50th booster landing includes some beautiful examples of Richard Angle's work portraying time and motion and physical processes. The sequence of launch, stage separation, boost-back and landing is many minutes, and this results in star trails.

Question: Why are the star trails so non-uniform? Why is each star trail non-uniform along its length and why does every trail show the same pattern of brightness variation along its length?

Falcon 9’s MECO (the gap) and boostback burn (backwards curly-cue) Richard Angle

Falcon 9’s MECO (the gap) and boostback burn (backwards curly-cue). The lefthand arc is the rocket’s upper stage and Cargo Dragon payload continuing on its way to orbit. (Richard Angle)

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They are not uniform but they all show the same bright-dim-bright pattern. One explanation is that this is a composite picture of several exposures and that the middle exposure(s) was/were dimmed a bit to compensate for a brighter subject (booster separation).

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    The article describes the image as single-exposure. – Asteroids With Wings Mar 9 at 15:55
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    I'm not necessarily discounting that possibility. Whether the variance must necessarily indicate a composite image, or whether perhaps, say, the ISO sensitivity could have been varied mid-exposure, I can't say. I do think this answer should at least acknowledge the article's claim, though. :) – Asteroids With Wings Mar 9 at 16:39
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    @AsteroidsWithWings It says "pictured in a single long-exposure photo". "Single" can apply to the result (several events in one single image). It is common in astrophotography to describe as "long exposure" a series of semi-long exposures assembled into one. In fact there are still EXIF data in the image that give an exposure of 47s, while the whole process (from launch to booster landing) is over 8 minutes... – xenoid Mar 9 at 16:44
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    Also i've never heard of ISO or whitebalance changing in the middle of a frame, photons just collect in the wells and then get dumped at the end and then iso multiplies the count on the way out. Never seen a camera that could do that or processing software that would know how to handle it. – user1169420 Mar 9 at 20:17
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    @user1169420 On a very long exposure you could tweak a variable ND filter for some part of the exposure duration. Details of the launch process are known in advance so you would know when some bright event is going to happen. Not very practical, but doable by someone with dedication, possibly an assistant, and a rock-solid tripod:) – xenoid Mar 9 at 21:05
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You aren't clear about what you mean by "non-uniform".

As @xenold says, exposure could be a factor in the variation in brightness. Changing image exposure to adjust for the booster brightness could be a factor, as could exposure adjustment to allow for differing brightness of the moon depending on cloud cover, and any subsequent processing to equalise brightnesses and colours. The fact that stars seem to cut out altogether suggests that black level adjustment or gamma correction has been used. On a long exposure with a digital camera there can be significant "speckling" in the background from random thermal noise, and these two techniques can help to reduce that.

If by "non-uniform" you simply mean that the stars are different brightnesses - well, some stars are brighter than others. :)

And if by "non-uniform" you mean that the stars do not all appear to follow the same lines, that would be an feature of the lens used. The photographer appears to have used a fisheye lens and cropped to the lower-right section of the image where the rocket trail appears. Since rocket launches are infrequent and their exact track is hard (for civilians!) to predict, the photographer was sensible in choosing to use a lens which would maximise the chance of obtaining a good shot.

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  • "Why are the star trails... so non-uniform?" I perhaps I could have asked why each trail was non-uniform along its length and why every trail shares the same variation in brightness along its length. While this answer figured it out you're right it's not 100% clear. I've now added a clarification to the body of the question. thanks! – uhoh Mar 9 at 11:52
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The most likely cause of this variation along every trail in a single exposure image is variation in air clarity during the exposure. This might happen due to fast moving clouds (as I recall, for this launch the wind was relatively high, above previous "no-fly" limits for Falcon 9 landings attempts).

While this wouldn't produce variations that are uniform from one trail to another, if the clouds passed across the entire field during a fraction of the exposure, they'd produce very similar brightness variations (one could even analyze the difference in trails to get an idea of the shapes of the individual clouds, as is done with occultation timings to to get the shape of an asteroid or section of the Lunar limb).

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Radial Blur

I think you're seeing a combination of the camera moving and rotating slightly during the shot. It looks like there's a circular blur whose center is off the image, far to the left and a little above it. Imagine the camera on a long circular boom, slowly moving in a small arc. This is probably not literally what happened, but you can imagine the camera operator emulating a similar motion.

Here's an example of the effect made artificially. I started with a few stars:

fake stars on a black background

Then I applied a 3-degree radial blur about a point on the left edge of the picture, 25% of the way down (center and rotational arcs in purple):

fake stars with radial motion blur

Then I cropped to roughly the bottom-right quadrant to get what seems reasonably close to the original image.

fake stars with radial motion blur, cropped to bottom right

The differences in brightness can be explained by the camera spending different amounts of time in the different orientations along that path.

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    This is a great explanation of radial blur, thanks! This comment mentions that the time from launch to landing was about 8 minutes. I don't know how far the camera was from the launch site or the field of view of these images, but can we rule out that the radial motion isn't just the rotation of the Earth? For example the time it takes the Earth to rotate 3 degrees is 12 minutes. – uhoh Mar 11 at 0:24
  • The software discussed in How (the heck) does Astrometry.net work? might be useful for nailing down the patch of sky viewed and coordinates of these stars and therefore if the pole is also the point where the radial motion is centered, and Flightclub.io can be used to reconstruct the launch and that combined with the deduced star field can locate the photographer. – uhoh Mar 11 at 0:30
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    @uhoh It surely is the earth's rotation. The rocket's trail is very crisp which would be hard to achieve with a moving camera. Tracking the rocket would also contradict the images' purpose: To show a movement through space. – Peter - Reinstate Monica Mar 11 at 9:33
  • @Peter-ReinstateMonica the rocket's trail is crips because it's moving a zillion meters per second (where zillions are actually thousands) so spends a fraction of a second at each pixel, whereas the stars in the background behave differently. A camera slowly and steadily moving over minutes would not blur the rocket trail no matter it was related to the Earth's rotation or not. – uhoh Mar 11 at 10:18
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    The camera doesn't have to move at all to explain radial blur. It's a natural consequence of the Earth's rotation. The locus of the curves would be at the celestial pole. If the camera moved during the flight, the trail would still be crisp, but the shape of it would be distorted by the movement of the camera. – Michael C Mar 12 at 0:54

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