Estimate how many planetary embryos of mass 5 × 10²² kg would have been required to assemble:

(a) Mercury, and

(b) Earth. The mass of each planet is available in AppendixA, TableA1.

Table A1

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Table Al Basic data on the planets (plus the Moon and Pluto). Mercury Venus Earth Mass /1024 kg /Earth masses Orbital semimajor axis /106 km /AU Orbital eccentricity Orbital inclination/ degrees Orbital period Axial rotation period/days Axial inclination/ degrees Polar radius/km Equatorial radius/km Mean radius /km Density/10 kg m- Surface gravity/ms2 Mean surface temperature/K Effective cloud-top temperature/K Temperature at 1 bar pressure/K Rings Satellites 0.330 0.055 57.91 0.39 0.206 7.0 88.0 days 58.6 0.1 2440 2440 2440 5.43 3.7 443 0 0 O Na 4.87 0.815 H (He) 108.2 0.72 0.007 3.4 224.7 days 243 177.3 6052 6052 6052 5.20 8.9 733 Atmospheric surface 10-15 pressure/bard Atmospheric surface ~10-3 67 density/kg m-3 Atmospheric column *10-1 mass/kgm Atmospheric main components (relatively minor components in parentheses) 0 92.1 5.97 1.00 CO (N) 149.6 1.00 0.017 0.0 365.3 days 0.997 23.5 6357 6378 6371 5.51 9.8 288 0 1 1.01 1.293 Moon Mars N 0 (HO) (Ar) 0.074 0.642 0.012 0.107 149.6 227.9 1.00 1.52 0.055 0.093 5.2 1.9 27.3 days 27.3 6.7 1738 1738 1738 3.34 1.6 250 0 -11 1.03 10 1.03 104 10 X 687.0 days 1.03 Ar H He Na 25.2 0 2 10-4 6.3 10 10-13 0.018 3375 3397 3390 3.93 3.7 223 1.69 10 CO (N) (Ar) Jupiter Saturn Uranus Neptune Pluto 1900 569 318 95.2 778.4 1427 2871 5.20 9.54 19.19 0.048 0.054 0.047 1.3 2.5 0.8 3.1 11.86 29.46 84.01 164.8 days days days days 0.412 0.444 0.718 0.671 66 850 71 490 69 910 1.33 0.69 23.1 9.0 120 165 26.7 few 269 54 360 60 270 58 230 86.8 14.4 97.9 many 262 24 970 25 560 25 360 1.32 8.7 89 53 135 75 several 227 102 0.013 17.1 0.002 H H H He He He (CH) (CH) (CH) 4498 30.07 0.009 1.8 29.6 24 340 24 770 24 620 1.64 11.1 54 70 5906 39.48 0.249 17.1 H He (CH,) 247.7 days 6.39 119.6 1187 1187 1187 1.86 0.62 38 few 0 213 5 10-$ =104 =1 N (CH) (CO,)