Radar provides finer spatial resolution of near-Earth asteroids than any other type of ground-based observation. A powerful series of radio waves is transmitted toward the asteroid, and then some of the reflected echoes are received and recorded. These echoes can be decoded in round-trip light travel time (delay) and Doppler-shifted frequency to generate two-dimensional delay-Doppler images of the target. Given a set of delay-Doppler images from a range of times and viewing geometries, it is possible to determine the target’s size, shape, and rotation state (e.g., Magri et al. 2007, Icarus 186).
We present shape models of three near-Earth asteroids that have been observed with the planetary radar systems at Arecibo Observatory and at NASA’s Goldstone Deep Space Communications Complex: 1981 Midas, 3200 Phaethon, and 2015 DP155. For Midas and 2015 DP155, we found it helpful to make manual adjustments to the model using the 3D graphics software Blender, which was first used for asteroid shape modeling by Crowell et al. (2017; Icarus 291).
Midas was observed from Arecibo and Goldstone during its close approach in March of 2018. Using those radar data, plus lightcurves from four apparitions, we find that Midas is a contact binary with dimensions 3.4 × 1.9 × 1.3 kilometers (McGlasson et al., submitted to PSJ). Its larger lobe is approximately double the volume of the smaller lobe.
Phaethon is one of the largest potentially hazardous asteroids. It is also the parent body of the Geminid meteor stream (Whipple 1983, IAUC 3881; Gustafson 1989, A&A 225) and the target of JAXA’s upcoming DESTINY+ mission (Arai et al. 2018, LPSC 49). For shape modeling, we used radar data from Arecibo and Goldstone in 2007 and 2017 (Taylor et al. 2019, P&SS 167), stellar occultations from 2019 (Arai et al. 2020, LPSC 51; Dunham et al. 2020, DPS 52), and lightcurves from many apparitions (Kim et al. 2018, A&A 619; Hanuš et al. 2018, A&A 620; and others). Phaethon is approximately spheroidal with an equatorial ridge, resembling the shapes of 101955 Bennu (Lauretta et al. 2019, Nature 568) and 162173 Ryugu (Watanabe et al. 2019, Science 364), though Phaethon is larger, with a volume-equivalent diameter of about 5.3 kilometers (Marshall et al. 2021, PDC).
All available radar and lightcurve data for 2015 DP155 come from its May-June 2018 apparition. The shape model (Repp et al. 2020, LPSC 51) is elongated with several bumps. It looks approximately triangular when viewed along its rotation axis. Its maximum breadth is about 200 meters, and its volume-equivalent diameter is about 140 meters, making it one of the smallest asteroids with a shape model.