Orbital period change of Dimorphos due to the DART kinetic impact

Abstract

The Double Asteroid Redirection Test (DART) spacecraft successfully performed the first test of a kinetic impactor for asteroid deflection by impacting Dimorphos, the secondary of near-Earth binary asteroid (65803) Didymos, and changing the orbital period of Dimorphos. A change in orbital period of approximately 7 min was expected if the incident momentum from the DART spacecraft was directly transferred to the asteroid target in a perfectly inelastic collision¹, but studies of the probable impact conditions and asteroid properties indicated that a considerable momentum enhancement (β) was possible^2,3. In the years before impact, we used lightcurve observations to accurately determine the pre-impact orbit parameters of Dimorphos with respect to Didymos^4-6. Here we report the change in the orbital period of Dimorphos as a result of the DART kinetic impact to be -33.0 ± 1.0 (3σ) min. Using new Earth-based lightcurve and radar observations, two independent approaches determined identical values for the change in the orbital period. This large orbit period change suggests that ejecta contributed a substantial amount of momentum to the asteroid beyond what the DART spacecraft carried.

Fig. 1. Post-impact Didymos system geometry.

We determine the new orbital period of Dimorphos using the times of mutual events, when a measurable decrease in the system brightness occurs because of an eclipse or occultation. Due to the geometry of the Didymos system during this time period, our lightcurve observations include primary eclipses (left), time outside mutual events (centre) and secondary eclipses (right). These diagrams simulate the view of the system from Earth on 10 October 06:09 (primary eclipse), 10 October 08:47 (outside events) and 10 October 12:06 (secondary eclipse) in geocentric UTC. The primary eclipses observed throughout our post-impact dataset are grazing, which resulted in a subtle decrease in system brightness (Fig. 3). During the secondary eclipse, Dimorphos is completely shadowed.

Fig. 2. Radar range-Doppler images of the post-impact Didymos system.

Radar range-Doppler images obtained on 4 October using Goldstone and 9 October using Goldstone to transmit and the Green Bank Telescope to receive. In each image, the distance from Earth increases from top to bottom and the Doppler frequency increases to the right, so rotation and orbital motion are anticlockwise. Each image was integrated for 20 min, with 10 min of overlap between successive images. Images have resolutions of 75 m × 0.5 Hz. The broader echo is from Didymos and the smaller, fainter echo shown using arrows is from Dimorphos. The open circles show Dimorphos positions predicted by the pre-impact orbit. The yellow ellipses show the trajectory of Dimorphos. Prediction uncertainties are smaller than the image resolution. On 4 October, the ellipse spans −870 m to +870 m along the y axis and −7 Hz to +7 Hz along the x axis, corresponding to line-of-sight velocity of −12 cm s⁻¹ to +12 cm s⁻¹. On 9 October, the ellipse spans −980 m to +980 m along the y axis and −8 Hz to +8 Hz along the x axis, corresponding to line-of-sight velocity of −14 cm s⁻¹ to +14 cm s⁻¹. The physical extents of the ellipse vary because of the viewing geometry.

Fig. 3. Post-impact photometric lightcurve of the Didymos system.

Measured photometry from UTC 2 October 2022 phase folded to the 2.26-h rotation period of Didymos (top) and the extracted mutual events (= observed data − 9th order Fourier fit to the rotation of Didymos) phase folded to the new orbit period of Dimorphos (bottom). These lightcurves, collected from five different telescopes, show photometric accuracy similar to all the lightcurve datasets in our analysis. The mutual event times are highly consistent across these datasets, although residual systematics in the photometry result in slightly different event depths.

Fig. 4. Observed mutual events of the Didymos system.

The data are marked as circles and the solid curve represents the synthetic lightcurve for the best-fit post-impact solution. The dashed curve is the pre-impact orbit prediction from ref. . The primary and secondary events are shown on the left and right sides of the plots, respectively. In some cases, the observations of a secondary event precede those of a primary event (that is, their order in the dataset is the inverse of that shown in the plot). We present these events in reverse order and they are separated by a ‘//’ symbol in the plot (0.4728 days are to be subtracted from the x coordinate of data points to the right from this separator). The y axis shows the magnitude on the night of the observation for each dataset and each tick mark has a range of 0.02 magnitudes.

Extended Data Fig. 1. Goldstone radar echo power spectra.

Selected radar echo power spectra obtained at Goldstone that were used to measure the Doppler separations in Extended Data Table 6. The spectra were obtained in the opposite sense of circular polarization as the transmitted wave. Each spectrum was integrated for 10–15 min to detect Dimorphos with minimum smear owing to orbital motion (<8°). Echoes from Didymos are centred on 0 Hz and have a bandwidth of between 22 and 34 Hz. The echo from Dimorphos appears as a narrow spike superimposed on the signal from Didymos, a pattern observed with radar observations of dozens of other near-Earth asteroids (for example, ref. ), indicated by the arrows. The Doppler frequency of Dimorphos varies with time between positive and negative values because of its orbital motion and estimated values can be found in Extended Data Table 6. Dashed vertical lines show the Doppler frequencies of Dimorphos predicted by the pre-impact orbit. Prediction uncertainties are smaller than the resolution of the spectra.