Maciej Woloszka and Alexander Putz
Contact: kontakt@sternfreunde.berlin
Introduction
Parallax measurements are usually know in the context of stellar parallax. The first successful stellar parallax measurement was already done in the 19th century by Friedrich Bessel, Thomas Henderson and Friedrich Wilhelm Georg von Struve in the year 1832-1838.
However, the resulting parallax, and thus the distance to the measured star, could only be achieved after 6 months of waiting since the baseline was formed by earths rotation around the sun. For an “instant” measurement, two telescopes are needed which are as far apart as possible. Unfortunately, the maximum baseline is limited by earths diameter, reducing the possible baseline by a factor of 25.000 (under practical conditions even more)!
The distance to asteroids is by orders of magnitudes lower than to the next stars, increasing the parallax effect by magnitudes as well. Since asteroids move significantly over a period of 6 months, the baseline of earths orbit can not be used, restricting it to several thousand kilometers on earth. Nevertheless these distances are enough to produce a parallax in the range of arcseconds. Since modern telescopes and cameras are able to measure the relative position of stars in the sub-pixel range, asteroid parallax measurements have become feasible even for amateur astronomers. We will present here a parallax measurement of the asteroid “(16) Psyche” which was done in the beginning of January.
Setup and Asteroid
For this measurement we rented the telescope T11 and T72 of the company iTelescope simultaneously. Although they had different pixel scales, they provided a large baseline of about 8.000km.
Parameters T11:
Parameters T72:
We chose the asteroid “(16) Psyche”, because it is a well known asteroid and was well visible in to this time. It consists mostly of metal. In 2029 the probe “Psyche” will visit the asteroid and analyse its internal structure. The asteroid has a mean diameter of about 222km and has a distance from 1.5AU to 4AU towards earth.
In Figure 1, exemplary parallaxes are calculated and displayed for different asteroid distances.
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| Figure 1: Exemplary calculated parallax for a baseline of 8000km for different asteroid distances. |
Note that contrary to the definition of the stellar parallax, here the full baseline and full angle (the stellar parallax is defined as the half opening angle and half baseline (1 AU)) are used since the telescopes do not rotate around a central point. The parallax is proportional to the baseline, so you can simply scale it to your baseline.
Current amateur telescopes equipment allows to measure relative positions with accuracies better than 0.5”. This depends of course on the pixel resolution and SNR of the star.
With such high precision it becomes possible to measure the distance of asteroids in the range of several astronomical units, even with a lower baseline.
Observation
The observations were done from two different locations at 13. of January 2026. T11 is located in Utah desert (USA) and T72 is located in Rio Hurtado valley (Chile). Their exact, direct distance d is 8093km.
T11 was taking 30s exposures consecutively from 03:04:48 to 3:28:54 UTC and T72 was taking 30s exposures consecutively from 03:01:06 to 03:18:11 UTC. Both were using the Luminance channel.
Analysis and Conclusion
As described in the observations part, not only one, but consecutive images were taken. This reduces errors due to e.g. tracking, seeing, etc.. The images of both telescopes, which can be seen in Figure 2, do not share the same field of view and pixel scale, which is why they were registered in the software Pixinsight. The interpolation introduces minimal errors. Since the image scale is relatively low and the asteroids Point-Spread Function has a FWHM of 4 pixels the interpolation is expected to not introduce too much error. It might look in the images like the asteroid is oversaturated, but the pixels reached only about 60% of their maximum intensity.
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| Figure 2: Annotated, unregistered, original images. Both images share the same pixel scale. |
The parallax p becomes clearly visible with bare eye by blinking two pictures taken at the same time (only a couple of seconds off).
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| Figure 3: Blinked images of both telescopes with visible parallax. |
After registering the images, the position (in pixel) of the asteroid was determined for every image with Fitswork and saved into a textfile for further analysis via Python.
In Figure 4, the positions of the asteroid on the registered images is shown. The position in pixels is scaled to arcseconds. Keep in mind, that this is no absolute position. An absolute position is not necessary since only the distance is relevant. Additionally an interpolation (straight red and blue lines) of the asteroid's path is shown. The movement of the asteroid can well be approximated by a straight, uniform movement. Both paths start and end at the same time.
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| Figure 4: Measured and linearly interpolated movement of the asteroid Psyche (16) from two different telescopes (T11,T72). By averaging the distance at same time points of the linear interpolation the parallax of the asteroid can be determined. |
By averaging the 20 distances, the final distance (i.e. parallax p) is 5.676”+-0.074”. The uncertainty corresponds to the standard deviation of the 20 points.
The baseline needs to be considered separately. The direct distance does not necessarily correspond to the true baseline. For the baseline only components perpendicular to the line of sight towards the asteroid are relevant. Imagine the two observers on a straight line towards the asteroid. Their effective baseline would be zero. Therefore the position of the asteroid in the sky and the location of the telescopes on earth need to be considered. We computed the observing baseline in a few steps.
First, we converted each telescope’s latitude, longitude, and altitude into Earth-centered Cartesian coordinates (ECEF) using the WGS84 ellipsoid: r1 and r2.
Subtracting these two position vectors gives the 3D baseline vector b=r1−r2.
Its length in our case is B=∥b∥=8093.76 km (the straight-line distance through space between the sites).
To get the effective baseline for parallax, we turned the asteroid’s RA/Dec (plus the observation time via GMST) into a unit line-of-sight vector s expressed in the same ECEF frame.
The effective baseline is then the part of vector b perpendicular to vector s. For our setup and time, we calculated an effective baseline of 7925km.
With these parameters a final distance of d=1.925AU+-0.025AU is obtained. The Minor Planet Center (MPC) gives a distance of d=1.907AU for the given date. The result fits very well to the literature value and is only 0.94% off.
We have shown that amateur distance measurement to solar system asteroids are possible with surprisingly small errors and we encourage readers to perform their own experiments.
