AST101H1 Final: clear and detailed study guide for preparation for the final~

Planetary motion.

A planet or asteroid the sun in an elliptical path. The diagram shows two points of interest: point P, the perihelion, where the planet is nearest to the Sun, and the far point, or aphelion, at point A. At these two points (and only these two points), the velocity v of the planet is perpendicular to the corresponding "radius" vector , from the Sun to the planet. An arbitrary point Q is also shown.

Suppose the asteroid's speed at aphelion is , and its distance from the sun there is (AU is the "astronomical unit", commonly used in planetary astronomy).

a) Determine the planet's speed at perihelion.

b) Determine the planet's distance from the Sun (in AU) at perihelion.

Assume that the Sun is orders of magnitude more massive than the asteroid. This means the Sun does not accelerate significantly in response to the planet's gravity and can be assumed to remain at rest.

Derive a symbolic formula, but don't try too hard to simplify it. Look up the values and conversion factors you need in order to obtain a numerical answer.

Recall the universal gravity formulas:

Force           

potential energy     

Consider the Sun-asteroid system to be isolated and apply conservation of energy.

Which, if any, of the following statements is/are true?

1)Our galaxy, The Milky Way, is a member of The Local Group, whichis one of several groups of galaxies located in the VirgoSupercluster.
2)Most astrophysicists believe that our Solar System formed from animmense cloud of gas and dust about 4-1/2 million years ago.
3)Planets are believed to have formed by a process known asaccretion.
4)Two key elements in the Condensation Theory of PlanetaryFormation are 5)Conservation of Angular Momentum and CondensationNuclei.
6)The name of the second largest object in the Universe is TheSouthern Wall.
7)In our Solar System, the four jovian planets, Jupiter, Saturn,Uranus, and Neptune, are separated from the four terrestrialplanets, Mercury, Venus, Earth, and Mars, by the Kuiper Belt.
8)Our star, The Sun, is located on the Orion Arm, about 26,000light-years from the center of the Andromeda Galaxy.
9)It takes a photon of light about 4-1/5 years to travel from ourSolar System to the second closest star to Earth, ProximaCentauri.
10)The full range of human knowledge about our Universe spans about40 or 41 orders of magnitude on a spatial scale and about 13.7billion years on a temporal scale.
11)It takes a photon of light about 5-1/2 hours to travel from theSun to the orbit of the former planet Pluto.

4) According to the ancient Greeks, the Earth was the center ofthe universe and the sun, moon, stars, and planets all went aroundthe Earth. In the 1543 Copernicus proposed the heliocentric theoryof the universe in which the Earth was just another planet orbitingthe Sun and only the moon orbited the Earth.

a) What is the speed at which the Moon goes around the Earth?
b) How does the Moon's orbital acceleration compare to theacceleration of objects near the surface of the Earth?
c) What is the magnitude of the force that the Earth's gravityexerts on the Moon to keep it in orbit?
d) According to Newton's third law, all forces occur in pairs. Whatis the reaction to the Earth's gravity on the moon? Explain.