We can now combine these two results to find out pr how massive the nebula can b

Question

We can now combine these two results to find out pr how massive the nebula can be and still be consistent with our simple model. The contribution to the accel- eration of gravity at the point from the proto-Sun is about 10-5 m s2, and this must be larger than the acceleration due to the nebula, Equation (4.16). This condition leads to the requirement that be much less than about 104 kg m2. This is not a very severe striction, if were equal to this value the total mass of the nebula, assuming that it extended out to about 30 AU, would be of the order of 1 Mo Exercise: Confirm the numerical estimates above. ste Se arg re- Shu Thus for the model to be consistent, we simply re- quire that the total mass of the nebula be substantially smaller than the mass of the proto-Sun. Observations of disks around other protostars suggest disk masses of the order of 0.02 Mo, consistent with our model; this disk mass would correspond to a surface mass density of a few hundred kg m2. St Exercise: Estimate the (volume) mass density and the number density of H2 molecules at mid-plane in th 1 AU, assuming T 103 K there. total nebula mass 0.02 Mo, and uniform surface mass density (r) out to 30 AU e nebula at Y =

Explanation / Answer

(a) Mass of nebula with radius of 30AU and surface density of 104kg/m2

=4.(22/7).(30X1.496X108)2. 104=2.53X1024kg which is less than one solar mass

(b) At T=103K , number density of Hydrogen is 0.1/cm3

Or number density= (1X105/m3)

and mass density= 0.1008gm/cm3

Or mass density=1.008X102kg/m3

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