Show that keplerian rotation implies ~ ~ r-1/2. use kepler's third law: p2 ~ ay and assume perfectly circular orbits (i. e. write the rotation speed in terms of p and a) (b) show that a spherically symmetric mass distribution with constant density gives solid body rotation (v = const x r). (set the centripetal force on a star in a circular orbit equal to the gravitational force on that star and substitute for m in terms of the uniform density.)

An  atom  (ours, not carroll's) consists of a positively charged  nucleus, surrounded by one or more negatively charged particles called  electrons. the positive charges equal the negative charges, so the atom has no overall charge; it is electrically neutral. most of an atom's mass is in its nucleus; the mass of an electron is only 1/1836 the mass of the lightest nucleus, that of hydrogen. although the nucleus is heavy, it is quite small compared with the overall size of an atom. the radius of a typical atom is around 0.1 to 0.25 nanometres (nm), whereas the radius of a nucleus is about 10-6  nm.  *  if an atom were enlarged to the size of the earth, its nucleus would be only 200 feet in diameter and could easily rest inside a small football stadium.read more on -

An atom that has fewer electrons that protons is called a positive ion.

Maybe because they hurt or you bleed a lot