1 / 18

Lecture 2 - Minimum mass model of solar nebula

Lecture 2 - Minimum mass model of solar nebula. Topics to be covered: Composition and condensation Surface density profile Minimum mass of solar nebula. Terrestrial planets’ composition.

tanek-romero
Download Presentation

Lecture 2 - Minimum mass model of solar nebula

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Lecture 2 - Minimum mass model of solar nebula • Topics to be covered: • Composition and condensation • Surface density profile • Minimum mass of solar nebula PY4A01 Solar System Science

  2. Terrestrial planets’ composition • Mercury 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. • Mars 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. • Venus' interior is like the Earth's, except its Fe-Ni core probably makes up a smaller percentage of its interior. PY4A01 Solar System Science

  3. Jovian planets’ interiors • Jupiter'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. • Saturn 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. • Compression 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. PY4A01 Solar System Science

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

  5. Nebula composition • Assume solar/cosmic abundances: PY4A01 Solar System Science

  6. Minimum mass for terrestrial planets • Mercury:~5.43 gcm-3 => complete condensation of Fe (~0.285% Mnebula). 0.285% Mnebula = 100 % Mmercury => Mnebula = (100/ 0.285) Mmercury = 350 Mmercury • Venus: ~5.24 g cm-3 => condensation from Fe and silicates (~0.37% Mnebula). =>(100% / 0.37% ) Mvenus = 270 Mvenus • Earth/Mars:0.43% of material condensed at cooler temperatures. => (100% / 0.43% ) Mearth = 235 Mearth • Asteroids: Cooler temperatures produce more condensation ~ 0.5 %. => (100% / 0.5%) = 200 Masteroids PY4A01 Solar System Science

  7. Minimum mass for terrestrial planets • What is the minimum mass required to make the Terrestrial planets? • Total of the 4th column is 29881x1026g. This is the minimum mass required to form the Terrestrial planets =>2.9881x1030g ~ 500 Mearth. PY4A01 Solar System Science

  8. Minimum mass for jovian planets and pluto • Jupiter: Almost nebula composition due to gas capture ~20%. => Mnebula =100 / 20 Mjupiter ~ 5 Mjupiteris minimum mass required. • Saturn: Cooler than Jupiter, with slightly different composition ~12.5%. => Mnebula = 100/12.5 Msaturn ~ 8Msaturn • Uranus: Less gas capture ~6.7% condensed to form planet. => Mnebula = 100/6.7 Muranus = 15 Muranus • Neptune: ~5% of solar nebula material condensed to form planet. => Mnebula = 100/5 Mneptune = 20 Mneptune • Pluto: Main fraction due to ices ~1.4 % => Mnebula = 100/0.14 Mpluto = 70 Mpluto PY4A01 Solar System Science

  9. Minimum mass for jovian planets • What is the minimum mass required to make the Jovian planets? • Total mass is therefore = 184450 x 1026g = 3085 Mearth. • This is minimum solar nebula mass required to make the Jovian planets. PY4A01 Solar System Science

  10. Minimum nebula mass • The minimum mass required to condense the nine planets is therefore: Planet M (x Mearth) Terrestrial 500 Jovian 3085 Pluto 0.119 3585 Mearth • This is the minimum mass required to produce the planets. • As Msun ~ 2 x 1033 g, the mass required to make the planets is therefore ~0.01 Msun. • Disk contained 1/100 of the solar mass. PY4A01 Solar System Science

  11. Nebular surface density profile • To make a more precise estimate, distribute min mass requirements over series of annuli, centred on each planet. • Choose 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. • We therefore estimate that Mercury was formed from material within an annulus of 0.38±0.17 AU => 0.33 - 0.83 x 1013cm. • The surface density of an annulus,  = mass / area, where area =  router2-  rinner2 =  [(0.83 x 1013)2 - (0.33 x 1013)2] = 1.82 x 1026cm2 • Surface density of disk near Mercury is therefore: 1160x1026 / 1.82 x 1026 = 637 g cm-2 0.33x1013cm 0.83x1013cm PY4A01 Solar System Science

  12. Nebular surface density profile • For 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 • The 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 1013cm. • Area is then =  router2-  inner2= 3.06 x 1026 cm2. => = 13150 x 1026 / 3.06 x1 1026 = 4300 g cm-2. • This is the approximate surface density of the disk where Venus formed. • For 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 1013cm. • As the area = 267 x 1013cm2 =>  = 95200 x 1026 / 267 x 1026 = 356 g cm-2 PY4A01 Solar System Science

  13. Minimum mass and density PY4A01 Solar System Science

  14. Surface density of solar nebula • Surface density of the drops off as:  (r) = 0 r - • 1 <  < 2, 0 ~ 3,300 g cm-3. • Local deficit of mass in asteroid belt. Mars is also somewhat deficient in mass. • Inside Mercury’s orbit, nebula material probably cleared out by falling in on Sun or blown out. • Outer edge may be due to a finite scale size of the original nebular condensation. PY4A01 Solar System Science

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

  16. Surface density of solar nebula • Desch (2007) - disk much denser. • Disk much more massive: • 0.092 M in 1-30AU vs 0.011 M • Density falls steeply (as r-2.2) but very smoothly and monotonically. Matches to < 10%. • Nepture and Uranus must be switched in position => planetary migration? PY4A01 Solar System Science

  17. Minimum mass estimate • Can also estimate minimum mass from  : where RSis the radius of the Sun and RFis the max distance of Pluto. • Assume that ( r ) = 3300 ( r / RE )-2, where RE = 1 AU. Therefore, • Setting RE = 1.49 x 1013 cm, and RS = 6.96 x 1010 cm, and RF = 39 AU = > M 0.02 MSun • Ie approximately a factor of two of previous estimate. PY4A01 Solar System Science

  18. PY4A01 Solar System Science

More Related