Phys 260: University Physics III
Prof. Anca Constantin
Due date: 9/18/12 at the start of sophistication.
Please make use of a diﬀerent document to show your calculations plus your answers. Trouble 1:
The distribution of stars inside the Galaxy's hard drive (fyi: Galaxy = Milky Way; galaxy = some other galaxy ) can be estimated by an exponential function. If celebrities dominate the mass distribution of the disk, we can after that say that the mass circulation of the disk follows a great exponential function, like this:
Σ(r) = Σ0 e−r/h, in which h is just a scaling aspect, a constant. Making use of this function, obtain an discursive expression to get how the orbital (circular) speed of the celebrities dependence on the space to the centre of the galaxy, i. elizabeth., Vc sama dengan Vc (r) (which is named the rotation curve in the galaxy) should look like (ignore the stick and resplandor of the Galaxy for this calculation). Remember that for any disk of material, the mass interior to a radius ur is given by simply (integral above rings of thickness dr):
M (r) =
a) After you worked out the mass of the hard disk drive of the Galaxy enclosed by a circle of radius l, your appearance for the rotation shape at that l, should appearance something like: Vc (r) sama dengan f (Σ0, h, r). I did not refer to universal constants (e. g., G) from this function, they must be there someplace.
b. Now, with the next notation one particular pc = 3 × 1013 kilometres (a very helpful step-ladder in astronomy), and understanding that 1kpc = ciento tres pc, and if Σ0 = 780 Msun /pc2 and h = 3. 5 kpc, plot what the rotation curve with the galaxy will need to look like via r = 0 to r = 30 kpc. (Hint: if it looks ﬂat, you screwed. )
c. You probably know currently that the discovered rotation curve is ﬂat (see ﬁgure on the top right-hand side corner for some real info for two galaxies, not The Galaxy this time); by r = 30 kpc, the rounded velocity is still ∼ 230 km/s. Precisely what is the mass needed to give this spherical velocity? Simply how much disk mass is there inside r sama dengan 30 kpc? So how...
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