On the afternoon of December 19, 2021, our team of amateur astronomers in two towns in Italy, Cremona and Salerno, observed the close passage of the near-Earth asteroid 163899 (2003 SD220). Our observations enabled us to calculate its distance using the parallax method.
The parallax of an object is its apparent shift based on the angle from which we’ve viewing it, in the same way that a finger held close to your eyes appears to move depending on whether you’re watching it with your left or right eye.
Our team has undertaken similar projects in the past. We take satisfaction in coordinating work over hundreds of kilometers, obtaining the utmost precision from our amateur equipment, and braving the cold of an evening close to the winter solstice.
To calculate the parallax, it’s first necessary to calculate the chord, or the distance between the two shooting locations based on their latitude and longitude. Our towns are relatively close to each other, 636.74 kilometers, but far enough apart to make a parallax calculation feasible.
Starting around 5:30 p.m. on December 19th, we connected over audio and video with Cristian Gambarotti, who helped coordinate the efforts. From Cremona, Gerardo Sbarufatti captured the view through a refractor with a focal length of 800 mm, while from Salerno, Andrea Mattei used an ATIK 383L CCD attached to a 10-inch Ritchey–Chrétien with 2000mm focal length.
Taking into consideration our own planet’s rotation, which makes the sky appear to rotate by12.54 arcseconds per minute, and the CCD’s theoretical resolution of 1.11 arcsecond per pixel, we initially thought to take a 5.3-second exposure. However, considering atmospheric turbulence, light pollution, and the faintness of the asteroid at 14th magnitude, we considered it necessary to expose for at least 8 seconds to obtain an acceptable signal. Accurately synchronizing our computers, we each took several shots at 30-second intervals.
Then, after acquiring the images, we synchronized them by the time they were taken and obtained the exact location of the asteroid on the sky. Then from this astrometry, we calculated the parallax of the asteroid as it passed near Earth, a shift of 23.5426 arcseconds. Overlapping the images taken from the different locations at the same instant highlights the asteroid’s apparent change in position:
Then, using simple geometry, we converted the parallax to an exact distance: 5,578,700 km
We compared this result to the ephemeris given by JPL’s Horizons Ephemeris Service, finding a difference of only 68,615 km, and therefore an error of only 1.22%.
The experience highlighted the limits of our equipment: Even using precise astrometric measurements, made meticulously and with low residuals, we nevertheless found that an error of only one hundredth of an arcsecond in the asteroid’s location on the sky could shift the distance measurement by about 900 km.
Nevertheless, the measurements are relatively accurate. By performing the same types of measurements on subsequent pairs of images, we could even notice the progressively increasing distance to the asteroid as it moved away from Earth.
Andrea Mattei is the president of the Astrofili Salernitani association. As a mathematician and programmer passionate about astronomy for more than 40 years, he mainly deals with astrometry and photometry. Gerardo Sbarufatti, an astrophotographer with more than 30 years of experience, is a member of the Astrofili Cremonesi Group. Cristian Gambarotti is associate professor of chemistry at the Milan Polytechnic and president of the Astrofili Cremonesi Group.