Work, Energy, and Celestial Mechanics Flashcards
Work
Force x Displacement
Work Energy Theorem
Work = Change in E[k]
Change in E[k]
1/2mv[2]^2 - 1/2mv[1]^2
Conservation of Energy
Energy at start is equal throughout
Simple Harmonic Motion
If spring is stretched/compressed, the sum of the forces = k x change in x.
Elastic Energy
1/2kx^2
Motion of an Orbiting Body
v^2 / r = GM / r^2
Aristotle
Geocentric model, planets attached to circular epicycle which rotates while attached to crystal spheres which the celestial bodies are attached to.
Ptolemy
Found that Aristotle’s models didn’t really explain, thus made epicycle system more complex.
Copernicus
Introduced heliocentric model, explained retrograde motion simply.
Tycho Brahe
Made very detailed and accurate records of star and planet locations, First to discover a supernova and document a comet.
Johannes Kepler
Tried matching Brahe’s data to Copernicus’s model but didn’t match. Suggested elliptical orbits.
Kepler’s First Law
Each planet moves around the sun in an elliptical orbit with the sun at one foci.
Kepler’s Second Law
The straight line joining a planet and the sun sweeps out over equal areas in equal time intervals
Kepler’s Third Law
r^3 is proportional to T^2; r^3 = (Cs)(T^2)
Calculate C using Newton’s Laws
C = GM / 4π^2
Eg for Orbiting objects
- GMm / r
Escape Speed
Minimum speed needed to project a mass (m) from a body (M) and just escape the gravitational pull.
Escape Energy
Energy needed to escape gravitational field.
E = GMm / r
Binding Energy
Amount of additional Ek that would be required to escape the gravitational field.
