Of all the days that I gathered data on Lemmon (10-23 to 11-04), this image represents the most dynamic period where the tail and its features were changing very quickly. This presents a massive processing challenge since stacking the full capture would result in all the features being softened. Even using advanced methods, the features change sufficiently quickly make such methods ineffective.

This image is a composition of 5 × 3 groups of RGB (15 frames total) with 45s exposures + 1 90s luminance frame from SFRO, where the 2 most distant frames were manually warped and feathered to match coherent feature positions. It is clear and expected that the more distant features are changing more quickly, than those close to the comet nucleus, but it isn’t until blinking the frames can one appreciate how quickly things are changing.

A clearly defined plasma knot captured by the solar wind.

How quickly are things changing?

As an exercise and without claiming any scientific accuracy, I performed some rough calculations based on what is known about the collected data. I wanted to know how the solar wind was affecting the tail.

First, calculate the radial velocity of the comet, i.e. how quickly is it moving away from Earth. Of course, this infomation is captured in the minor body ephemerides published by JPL, but let’s see how our data compare. Using the timestamps of each of the 24 images in our dataset along with the distance to Earth at per second resolution (obtained from JPL ephemeris data), we get:

| Frame Transition | Velocity (away) (km/s) |

|----------------------|---------------------|

| A2 -> A3 | 50.825 |

| A3 -> A4 | 51.454 |

| A4 -> A5 | 51.153 |

| A5 -> A6 | 50.501 |

| A6 -> A7 | 51.153 |

| A7 -> A8 | 50.825 |

| A8 -> A9 | 51.454 |

| A9 -> A10 | 51.153 |

| A10 -> A11 | 51.053 |

| A11 -> A12 | 51.454 |

| A12 -> A13 | 51.153 |

| A13 -> A14 | 50.825 |

| A14 -> A15 | 51.784 |

| A15 -> A16 | 50.825 |

| A16 -> A17 | 50.825 |

| A17 -> A18 | 51.784 |

| A18 -> A19 | 50.825 |

| A19 -> A20 | 50.825 |

| A20 -> A21 | 51.784 |

| A21 -> A22 | 50.825 |

| A22 -> A23 | 50.825 |

| A23 -> A24 | 51.784 |

If we assume constant velocity, we get: Velocity (Mean): 51.140 km/s with Standard Deviation (the "Error"): ±0.394 km/s which is very close to the published velocity of 50.489 km/sec. This is the radial velocity (how fast the comet is moving away from us), not the tangential velocity (how fast the comet is moving across the field of view).

To estimate velocities in the tail I computed the flow speed by tracking small regions of features across consecutive frames. Each region is tracked using ECC image registration and optical flow on specific feature points, while attempting to suppress spurious behaviour.

Using this approach, for each frame pair, the resulting motion in pixels per second is measured and converted to an angular speed in arcseconds per second using the plate scale, derived from the telescope focal length and camera pixel size. This angular speed is then converted to a true physical velocity in kilometres per second using the comet–Earth distance at the exact imaging times. Since the tail is not parallel to the image plane, we estimate a correction factor to account for the tilt of the motion vector relative to the sky plane and use this to approximate the true flow velocity within the tail, correcting for its projection onto the sky plane.

This image shows the estimated velocities along different parts of the dust and ion tails. The labels R1 through R4 are tracking specific "knots" of ionized gas as they move away from the comet's head.

The velocities are different because the regions of gas are being constantly accelerated by the solar wind. This is how the tail is formed:

Gas Gets Ionized: The comet's nucleus releases neutral gas. Intense ultraviolet light from the Sun strips electrons from these gas molecules, turning them into ions (charged particles).
The Solar Wind: The Sun constantly blows a stream of its own charged particles, called the solar wind, into space at very high speeds (typically 300-800 km/s).
Acceleration: This fast-moving solar wind "grabs" the new, relatively slow-moving cometary ions (via magnetic field interactions) and sweeps them away, causing them to accelerate.

R1 is a "new" release of plasma, still relatively close to the comet's head. It has just begun to be accelerated by the solar wind, so its speed is the lowest at 79.5 km/s. As R2 and R3 are pushed farther down the tail, the constant force from the solar wind has had more time to act on them, accelerating them to 96.2 km/s and 181.5 km/s. R4 is the oldest of the group, and is therefore a greater distance away. It has been accelerated by the solar wind for the longest duration, and reaches the highest observed speed of 217.6 km/s as it tries to catch up with the speed of the solar wind itself.

If we measure the tail velocities on a visually less active day, we compute lower velocities and acceleration across the tail’s extent based on it’s motion. This confirms our visual observations.

Closer inspection of the tail motion shows what appears to be helical motion progressing away from the nucleus. This is consistent with spinning of the nucleus due to the ejection of material unevenly across the surface as it is heated by the Sun.

The tail motion is twisting. Focus on the top left.

Finally, to answer the question of how quickly things are changing with respect to that interesting knot of plasma mentioned above, we can estimate a lower bound for the knot's total 3D velocity relative to Earth. We measured the comet system's radial velocity (away from Earth) at ~51 km/s and the knot's independent tangential velocity (across the sky) at ~79.5 km/s (for R1). By combining these two perpendicular motion vectors using the Pythagorean Theorem, \(\sqrt{51² + 79.5²}\), we get a minimum 3D velocity of approximately 94.4 km/s.