1. PY4A01 Solar System Science Lecture 2 - Minimum mass model of solar nebula oTopics to be covered: oComposition and condensation oSurface density profile oMinimum mass of solar nebula

2. PY4A01 Solar System Science Terrestrial planets’ composition oMercury has a very large iron core about 3,500 km in diameter that makes up 60% of its total mass, surrounded by a silicate layer ~700 km thick. Its core is probably partially molten. oMars has a solid Fe and/or iron-sulfide core ~2,600-4,000 km in diameter, surrounded by a silicate mantle and rocky crust that is probably several hundred km thick. oVenus' interior is like the Earth's, except its Fe-Ni core probably makes up a smaller percentage of its interior.

3. PY4A01 Solar System Science Jovian planets’ interiors oJupiter's H/He atmosphere is ~1,000 km thick and merges smoothly with the layer of liquid molecular H, which is ~20,000-21,000 km thick. Pressure near center is sufficient to create a liquid metallic H layer ~37,000-38,000 km thick. Probably has silicate/ice core twice diameter of Earth with ~14 times Earth's mass. oSaturn is smaller version of Jupiter: silicate core ~26,000 km in diameter, ice layer about 3500 km thick, beneath a ~12,000 km thick layer of liquid metallic H. Then liquid molecular H layer around 28,000 kilometers thick, and atmosphere about 2,000 km thick. oCompression on Uranus/Neptune probably not enough to liquefy H. Uranus/Neptune have silicate cores ~8,000-8,500 km in diameter surrounded by a slushy mantle of water mixed with ammonia and methane ~7,000-8,000 kilometers thick. At top is a 9000 -10000 km thick atmosphere of H and He.

4. PY4A01 Solar System Science Minimum mass of the solar nebula oCan make approximation of minimum amount of solar nebula material that must have been present to form planets. Know: 1.Current masses, composition, location and radii of the planets. 2.Cosmic elemental abundances. 3.Condensation temperatures of material. oGiven % of material that condenses, can calculate minimum mass of original nebula from which the planets formed. oSteps 1-8: metals & rock, steps 9-13: ices

5. PY4A01 Solar System Science Nebula composition oAssume solar/cosmic abundances: Representative elements Main nebular Low-T material Fraction of nebular mass H, HeGas H 2, He 98.4 % C, N, OVolatiles (ices) H 2 O, CH 4, NH 3 1.2 % Si, Mg, FeRefractories (metals, silicates) 0.3 %

6. PY4A01 Solar System Science Minimum mass for terrestrial planets oMercury:~5.43 gcm -3 => complete condensation of Fe (~0.285% M nebula ). 0.285% M nebula = 100 % M mercury => M nebula = (100/ 0.285) M mercury = 350 M mercury oVenus: ~5.24 g cm -3 => condensation from Fe and silicates (~0.37% M nebula ). =>(100% / 0.37% ) M venus = 270 M venus oEarth/Mars: 0.43% of material condensed at cooler temperatures. => (100% / 0.43% ) M earth = 235 M earth oAsteroids: Cooler temperatures produce more condensation ~ 0.5 %. => (100% / 0.5%) = 200 M asteroids

7. PY4A01 Solar System Science Minimum mass for terrestrial planets oWhat is the minimum mass required to make the Terrestrial planets? oTotal of the 4 th column is 29881x10 26 g. This is the minimum mass required to form the Terrestrial planets =>2.9881x10 30 g ~ 500 M earth. PlanetFactorMass (x10 26 g) Min Mass (x10 26 g) Mercury3503.31155 Venus27048.713149 Earth23559.814053 Mars2356.41504 Asteroids2000.120

8. PY4A01 Solar System Science Minimum mass for jovian planets and pluto oJupiter: Almost nebula composition due to gas capture ~20%. => M nebula =100 / 20 M jupiter ~ 5 M jupiter is minimum mass required. oSaturn: Cooler than Jupiter, with slightly different composition ~12.5%. => M nebula = 100/12.5 M saturn ~ 8 M saturn oUranus: Less gas capture ~6.7% condensed to form planet. => M nebula = 100/6.7 M uranus = 15 M uranus oNeptune: ~5% of solar nebula material condensed to form planet. => M nebula = 100/5 M neptune = 20 M neptune oPluto: Main fraction due to ices ~1.4 % => M nebula = 100/0.14 M pluto = 70 M pluto

9. PY4A01 Solar System Science Minimum mass for jovian planets oWhat is the minimum mass required to make the Jovian planets? oTotal mass is therefore = 184450 x 10 26 g = 3085 M earth. oThis is minimum solar nebula mass required to make the Jovian planets. PlanetMass (x10 26 g) FactorMin Mass (x10 26 g) Jupiter19040595200 Saturn5695855560 Uranus8901513050 Neptune10322020640

10. PY4A01 Solar System Science Minimum nebula mass oThe minimum mass required to condense the nine planets is therefore: PlanetM (x M earth ) Terrestrial500 Jovian3085 Pluto0.119 3585 M earth oThis is the minimum mass required to produce the planets. oAs M sun ~ 2 x 10 33 g, the mass required to make the planets is therefore ~0.01 M sun. oDisk contained 1/100 of the solar mass.

11. PY4A01 Solar System Science Nebular surface density profile oTo make a more precise estimate, distribute min mass requirements over series of annuli, centred on each planet. oChoose boundaries of annuli to be halfway between the orbits of each planet. i.e., Mercury @ 0.38 AU and Venus @ 0.72 AU = > (0.72-0.38)/2 = 0.17 AU. oWe therefore estimate that Mercury was formed from material within an annulus of 0.38±0.17 AU => 0.33 - 0.83 x 10 13 cm. oThe surface density of an annulus,  = mass / area, where area =  r outer 2 -  r inner 2 =  [(0.83 x 10 13 ) 2 - (0.33 x 10 13 ) 2 ] = 1.82 x 10 26 cm 2 oSurface density of disk near Mercury is therefore: 1160x10 26 / 1.82 x 10 26 = 637 g cm -2 0.33x10 13 cm 0.83x10 13 cm

12. PY4A01 Solar System Science Nebular surface density profile oFor Venus at 0.72 AU, Mercury is at 0.38 AU and Earth is at 1 AU => Venus’ annulus extends from (0.72 - 0.38)/2 = 0.17 to (1 - 0.72)/2 = 0.14 oThe material that formed Venus was located between 0.72 - 0.17 AU and 0.72 + 0.14 or 0.55-0.86 AU. This is 0.83-1.29 x 10 13 cm. oArea is then =  r outer 2 -  inner 2 = 3.06 x 10 26 cm 2. =>  = 13150 x 10 26 / 3.06 x1 10 26 = 4300 g cm -2. oThis is the approximate surface density of the disk where Venus formed. oFor Jupiter at 5.2 AU, the Asteroids are at 3 AU and Saturn is at 9.6 AU. The annulus therefore ranges from 4 - 7.2 or 6 - 11 x 10 13 cm. oAs the area = 267 x 10 13 cm 2 =>  = 95200 x 10 26 / 267 x 10 26 = 356 g cm -2

13. PY4A01 Solar System Science Minimum mass and density

14. PY4A01 Solar System Science Surface density of solar nebula oSurface density of the drops off as:  (r) =  0 r -  o1 <  < 2,  0 ~ 3,300 g cm -3. oLocal deficit of mass in asteroid belt. Mars is also somewhat deficient in mass. oInside Mercury’s orbit, nebula material probably cleared out by falling in on Sun or blown out. oOuter edge may be due to a finite scale size of the original nebular condensation.

15. PY4A01 Solar System Science Surface density of solar nebula oHayashi et al. (1981) widely used:  (r) = 1700 (r / 1AU) -3/2 g cm -2 oWeidenschilling (1977) produced figure at right which shows similar trend. oMars and asteroids appears to be under-dense.

16. PY4A01 Solar System Science Surface density of solar nebula oDesch (2007) - disk much denser. oDisk much more massive: o0.092 M  in 1-30AU vs 0.011 M  oDensity falls steeply (as r -2.2 ) but very smoothly and monotonically. Matches to < 10%. oNepture and Uranus must be switched in position => planetary migration?

17. PY4A01 Solar System Science Minimum mass estimate oCan also estimate minimum mass from  : where R S is the radius of the Sun and R F is the max distance of Pluto. o Assume that  ( r ) = 3300 ( r / R E ) -2, where R E = 1 AU. Therefore, oSetting R E = 1.49 x 10 13 cm, and R S = 6.96 x 10 10 cm, and R F = 39 AU = > M  0.02 M Sun oIe approximately a factor of two of previous estimate.

18. PY4A01 Solar System Science