Table 1

Potential Moon-forming giant impacts onto a fast-spinning proto-Earth. Mproj, projectile mass; Vi, impact velocity in kilometers per second; b, impact parameter (negative value indicates retrograde impact; all impacts in the equatorial plane); Mplanet, mass of post-impact planet including atmosphere; Req, estimated equatorial radius of post-impact planet in kilometers; f, flattening of post-impact planet (ReqRpole)/Req (where Rpole is the polar radius); T, spin period of post-impact planet in hours; LZ, z-component of angular momentum of planet and disk; Matm, mass of the atmosphere; Miron/Mdisk, iron core mass fraction in disk.

Embedded ImageVibEmbedded ImageReqfTEmbedded ImageEmbedded ImageEmbedded ImageEmbedded ImageEmbedded ImageEmbedded ImageprojEmbedded ImageResult
0.99ME target with 2.3 hours spin and 3.0LEM
0.02620.0–0.300.9677000.392.62.434.01.540.820.850.0640.0520.003*
0.02625.0–0.300.9475000.372.62.325.62.070.870.960.0490.0390.010*
0.02630.0–0.300.9173000.362.72.226.82.330.901.010.0460.0380.049*
0.02620.00.300.9681000.452.42.762.91.590.880.790.1670.1570.037*
0.05015.0–0.300.9878000.422.52.564.51.810.910.930.1130.0870.002*
0.05020.0–0.300.9475000.382.62.406.62.450.961.090.0860.0640.008*
0.05025.0–0.300.9073000.382.72.228.02.540.911.060.0770.0590.034*
0.05015.0–0.150.9879000.432.52.674.51.840.930.900.1220.0930.007*
0.05020.0–0.150.9476000.402.62.526.42.621.141.220.0900.0670.024
0.05015.00.000.9881000.462.52.844.21.971.020.950.1760.1470.015
0.05020.00.000.9478000.422.52.686.02.851.331.360.1150.0910.054
0.10015.0–0.300.9874000.382.82.308.12.160.890.900.1210.0690.021*
0.10020.0–0.300.9371000.352.92.0710.42.220.810.860.1030.0560.078*
0.10010.00.001.0481000.432.52.904.51.600.910.740.2550.1870.014*
0.10015.00.000.9978000.432.62.797.42.811.321.230.1680.1110.083
1.05ME target with 2.3 hours spin and 3.1LEM
0.05020.0–0.301.0175000.372.72.477.02.201.021.020.0810.0590.005†‡
0.05022.5–0.300.9974000.362.82.407.92.320.900.970.0700.0500.007*
0.05025.0–0.300.9773000.352.82.318.72.370.930.950.0660.0480.019*
1.05ME target with 2.5 hours spin and 2.5LEM
0.05025.00.000.9872000.303.12.158.72.141.291.090.0840.0610.092
0.05020.00.151.0375000.352.82.426.31.671.010.810.1870.1610.076*
1.05ME target with 2.7 hours spin and 2.1LEM
0.05020.00.301.0374000.352.82.255.11.260.910.700.1960.1740.098*
0.05§25.00.001.0071000.293.41.949.91.771.240.820.1010.0760.084

*Potential Moon-forming simulations with more relaxed criteria of 0.8 ≤ MS/MM ≤ 1.5, ∆proj ≤ 0.20, and Miron/Mdisk ≤ 0.1.

†Successful Moon-forming simulations with MS ≥ 1.0MM, ∆proj ≤ 0.15, and Miron/Mdisk ≤ 0.1.

‡Example in Fig. 1.

§Projectile with a 2.9-hour prograde spin; other projectiles have no spin. Targets have 1 to 2 × 105 SPH particles [additional simulation results and methods in (26)].