Introduction Investigating the rotation curve for the Milky Way requires an understanding of the way stars move inside the Galaxy, and a recognition of the existence of Dark matter. Universal gravitation dictates the way that stars will move in orbit around the Galaxy. The forces a star or other object experiences is due to the enclosed mass up to where the star is. This force is what sustains the orbit around the disk, i.e. the centripetal acceleration on the object. The force this creates causes an angular velocity by changing the direction of the velocity vector while sustaining its magnitude. At constant radii, an enclosed mass can be attributed to observed velocities. This will facilitate making distinctions between observed and calculated rotation curves. Since the enclosed mass is the only thing that can change the velocity of a star any observed differences in velocity can be …show more content…
When looking at our own Galaxy or the universe writ large Dark matter isn’t picked up by instruments since it has no luminosity. The composition of Dark matter isn’t entirely known, as there aren’t any ways to probe it through conventional measures.
Newtonian Understanding
In beginning the derivation of an analytical expression for the rotation curve of the Milky Way a few assumptions. Stars in the Milky Way exhibits perfect circular motion Mass density is only a function of r
The first assumption allows for simpler calculations later. By taking advantage of Newton’s third law, an object in a central field will experience a centripetal acceleration that points a direction opposite that of the central field; in this case, the central field is gravity. Since starts are staying at functionally the radius through their orbit around the Milky Way we can assume the net force along the radial direction is zero.
F_net 〖=F_cent+ F〗_grav=0
F_cent= -F_g m_* a_cent=m_* a_grav m_* (V_c^2)/r=(m_* M(r))/r^2 G
(V_c^2)/r=M(r)/r^2