Suppose that a spiral galaxy is located at the center of a spherically symmetric dark matter halo

(a) if the orbital speed of a star in this galaxy, v, is constant at any radius, how does the mass density rho(r) within the halo vary with radius r?

(b) suppose the rotation curve is fitted by a single relation v x r, answer the same question as in part (a).

(c) if the total mass interior to any radius r is a constant, m(r) m, as if it is dominated by a central point mass, find out how the orbital speed v of a stair varies with raditus r.

There is a theory that indicates that dinosaurs became extinct when about 65 million years ago, a large asteroid hit the earth surface. dust caused by this collision blocked the sunlight reaching the earth's surface and many forms of life became extinct due to the cold. fearing this threat, how large the radius of an asteroid should you be looking for if the dangerous asteroid size is approximately the same as the one that killed the dinosaurs? available data suggests that about 18% of that asteroid's mass ended up as a dust spread evenly over earth after eventually settling out of the upper atmosphere. about 0.0180 g/cm^2 of dust, which is chemically different than the earth's rock, covered the earth's surface. typical asteroids have a density of about 1.9 g/cm^3. now that we know the size of the asteroid, how much energy was released during impact, assuming all of it was just the kinetic energy of the asteroid right before the impact?

You charge a parallel-plate capacitor, remove it from the battery, and prevent the wires connected to the plates from touching each other. when you increase the plate separation, what happens to the following quantities?

How does the entropy of steam compare to the entropy of ice?