Chapter 5.3, Problem 2E

Planetary Velocity The following table gives the mean velocity of planets in their orbits versus their mean distance from the sun. Note that $1\text{ AU}$ (astronomical unit) is the mean distance from Earth to the sun, abut $93$ million miles.

Planet	$d=distance$ (AU)	$v=velocity$ (km/sec)
Mercury	0.39	47.4
Venus	0.72	35.0
Earth	1.00	29.8
Mars	1.52	24.1
Jupiter	5.20	13.1
Saturn	9.58	9.7
Uranus	19.20	6.8
Neptune	30.05	5.4

Astronomers tell us that it is reasonable to model these data with a power function.

a	Use power regression to express velocity as a power function of distance from the sun.
b	Plot the data along with the regression equation.
c	An asteroid orbits at a mean distance of $3\text{ AU}$ from the sun. According to the power model you found in part a, what is the mean orbital velocity of the asteroid?