MINIMUM MASS SOLAR NEBULA

Short Description 1 Lecture 3 - Minimum mass mdel f slar nebula Tpics t be cvered: Cmpsitin and cndensatin Surchallenge density prfile Minimum ...

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0.72 AU = > (0.72-0.38)/2 = 0.17 AU.o We therefore estimate that Mercury was formed from material within an annulus of 0.38±0.17 AU => 0.33 - 0.83 x 1013 cm.o The surchallenge density of an annulus,= mass / location,wright here area = router2 rinner2 = <(0.83 x 1013)2 - (0.33 x 1013)2> = 1.82 x 1026 cm2 o Surconfront density of disk near Mercury is therefore: 1160x1026 / 1.82 x 1026 = 637 g cm-20.33x1013 cm0.83x1013 cmPY4A01 Solar System Science Nebular surface thickness profile o For Venus at 0.72 AU, Mercury is at 0.38 AU and also Planet is at 1 AU => Venus’ annulus exoften tends from (0.72 - 0.38)/2 = 0.17 to (1 - 0.72)/2 = 0.14 o The product that formed Venus was situated in between 0.72 - 0.17 AU and also 0.72 + 0.14 or 0.55-0.86 AU. This is 0.83-1.29 x 1013 cm. o Area is then =2 26 2 router2 inner = 3.06 x 10 cm . => = 13150 x 1026 / 3.06 x1 1026 = 4300 g cm-2.o This is the approximate surface thickness of the disk where Venus created. o For Jupiter at 5.2 AU, the Asteroids are at 3 AU and also Saturn is at 9.6 AU. The annulus therefore arrays from 4 - 7.2 or 6 - 11 x 1013 cm. o As the area = 267 x 1013 cm2 =>= 95200 x 1026 / 267 x 1026 = 356 g cm-2 PY4A01 Solar System Science Minimum mass and densityFrom “Physics and also Chemisattempt of the Solar System” by Lewis PY4A01 Solar System Science Surconfront density of solar nebula o Surface thickness of the drops off as: (r) = o ~ 1.5 and00r-~ 3,300 g cm-3.o Local deficit of mass in asteroid belt.

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Mars is additionally rather deficient in mass. o Inside Mercury’s orlittle, nebula material probably cleared out by falling in on Sun or blvery own out. o Outer edge might be as a result of a finite scale dimension of the original nebular condensation. PY4A01 Solar System Science Surchallenge density of solar nebulao Hayashi (1981) extensively used: (r) = 1700 (r / 1AU)-3/2 g cm-2 o Weidenschilling (1977) created number at best which shows comparable trfinish. o Mars and also asteroids appears to be under-dense.PY4A01 Solar System Science Minimum Mass Extrasolar Nebula o Chuan & Laughlin (2013) offered 1,925 exoplanets observed by Kepler (http://arxiv.org/abs/1211.1673) o Surface thickness close to exoearth is:whereM exoworld = ( Rexoearth / R €Earth )σ exoplanet =2.06M exoworld 2 2πaexoplanetM Earthis ideal fit power-legislation partnership for the Solar System. €o Semimajor axis from Kepler’s laws is:aexoworld = ( P / yr)2 /3AU€ PY4A01 Solar System Science Minimum Mass Extrasolar Nebulao MMEN:# a &−1.6 σ = 620% ( $ 0.2AU " PY4A01 Solar System Science€ Minimum mass estimate o Can likewise estimate minimum mass from M=∫:σ (r)dA =2πRF0RS∫ ∫σ (r)rdrdθwhere RS is the radius of the Sun and also RF is the max distance of Pluto. o Assume that € ( r ) = 3300 ( r / RE )-2, wright here RE = 1 AU. Therefore, M=2πRF0RS∫ ∫= 3300RE2(3300(r /RE )−2 )rdrdθ∫2π 0RFdθ ∫ R r−1drdθ S= 6600πRE2 ln(RF /RS )o Setting RE = 1.49 x 1013 cm, and RS = 6.96 x 1010 cm, and RF = 39 AU = > €M0.02 MSuno Ie about a variable of two of previous estimate. PY4A01 Solar System Science PY4A01 Solar System Science