Gravitation

Question 1

Kepler’s First

Answer 1

Law of Orbits. All orbits are elliptical, with the central mass at one focus and the orbiting object on the radius. a^2 = b^2 + c^2, or semimajor length, semiminor length, foci distance from center. Eccentricity equals c/a, at 0 for a circle.

Distance from each foci added together is always 2a.

Question 2

Kepler’s 2nd.

Answer 2

Law of Areas: the area a line between a foci and an orbiting object is the same if time period is constant. Angular momentum is constant. Closer means faster tangential speed.

Question 3

Kepler’s Third

Answer 3

Law of Periods. Describes the relationship between period and semimajor axis length. Relates universal gravity to centripetal (angular) acceleration, then substituting in period. T^2 = (4pi^2/GM)a^3. Everything in parenthesis is usually constant!

Question 4

Universal Gravitation

Answer 4

Force of Gravity = -GmM/r^2. R is the distance between c of m, m is small mass, M is big mass. G is constant 6.67*10^-11 Nm^2/kg^2

Question 5

Escape Velocity

Answer 5

Velocity to launch something off earth forever. Angular independent - conservation. Found by mechanical nergy being 0 at infinitely far away for minimum v.

v^2 = 2GM/r .

Question 6

Binding Energy

Answer 6

Energy to completely move object from planet. Equivalent to positive U.

Question 7

Shell Theorem:

Answer 7

Any spherically symmetric object affects outside objects as if a point mass. Inside a spherically symmetrical shell, net gravitational force is 0. (Gravity acts, just cancels itself out. Energy is bottomed out at well!)