Orbital Mechanics CTLA Earth & Environmental Science
The Earth Spherical body that is flattened near the poles due to centrifugal force (rotation of the Earth) 40,074 KM across at the Equator 40,0007 KM across at the Poles Rotation: spinning of Earth around its axis (~24 hours to complete) Revolution: movement of Earth around the Sun (~365.25 days to complete)
Barycenter The center of mass of two or more celestial bodies that are orbiting one another This is the point around which the bodies orbit Point is based on the masses of the objects and distance between them r1 = distance between body 1 & the barycenter m1 = mass of body 1 m2 = mass of body 2 a = distance between the centers of the two bodies
Barycenter
The Earth Axis: imaginary line that runs through Earth from the North Pole to the South Pole, on which the planet rotates around Earth s axis is tilted an average of 23.5 Nutation: wobbling of the tilt of Earth s axis, which can strengthen or weaken the effects of our seasons Tilt can increase to 24 or decrease to 22.5 Maximum cycle of nutation occurs over an 18 year period, due to the Moon s effects
The Earth Precession: change in the pointed direction of Earth s axis Cycle is completed once every 26,000 years Does not affect intensity of our seasons, but only the time of year they occur Changes the North Pole stars Polaris currently (reaches max on March 24, 2100) Thuban was the N. Pole star around 3000 BC (one-fifth the brightness of Polaris) Alpha Cephei will be the next star, around 5000 AD
The Seasons Equinox: 12 hours of daylight & 12 hours of darkness (Sun is overhead at the Equator) Vernal equinox is currently March 21-22 Autumnal equinox is currently September 21-22 Will be reversed in about 12,000 years due to precession
The Seasons Summer Solstice Occurs June 21-22 Longest day of the year in the N. Hemisphere Sun is directly overhead the Tropic of Cancer (~23.5 N) 24 hours of sunlight for six months at the North Pole Winter Solstice Occurs December 21-22 Shortest day of the year in the N. Hemisphere Sun is directly overhead the Tropic of Capricorn (~23.5 S) Zero hours of sunlight for six months at the North Pole Will be reversed in about 12,000 years due to precession!
What about the Moon? A satellite that orbits the Earth (our only natural satellite) Its gravity is 1 /6th of Earth (too weak to hold an atmosphere for itself) Temperatures reach 134 C in sunlight and -170 C on the dark side of the Moon Its rate of rotation = its rate of revolution also called tidal lock
Phases of the Moon Full Waning Gibbous Last Quarter Half Waning Crescent New Waxing Crescent First Quarter Half Waxing Gibbous
Tidal Effects Both the Moon & the Sun affect Earth s oceans Spring Tide: all three bodies (Earth, Moon, & Sun) are lined up, causing high tides to be higher and low tides to be lower Neap Tide: the bodies are at 90 angles, causing high tides to be lower and low tides to be higher
Eclipses Lunar eclipse occurs when the Moon travels through Earth s shadow Solar eclipse occurs when the Earth travels through the Moon s shadow
What is an ellipse? A geometric shape with 2 focal points (a circle has just 1 focal point) Has two axes (major & minor) Perihelion = when a planet is closest to the Sun Aphelion = when a planet is farthest from the Sun
Kepler s Laws History Tyco Brahe (1546-1601) was a Danish astronomer who found his measurements showed that Mars did not orbit in a perfect circle Johannes Kepler (1571-1630) discovered that the orbit of Mars instead fit an elliptical shape
Kepler s Laws 1st Law: orbital paths are ellipses and the Sun is at one focal point (nothing is at the 2nd point)
Kepler s Laws 2nd Law: the line joining the planets to the Sun sweeps out equal areas in equal times as the planet travels around the ellipse This is due to a planet s changing revolutionary speed during orbit (faster when close to the Sun & slower when farther from the Sun)
Kepler s Laws 3rd Law: the ratio of the square of the revolution time for two planets is equal to the ratio of the cubes of their semi-major axes T 2 = R 3 (where T=time of orbit and R=average distance from the Sun) OR see the equation below Planet T R T 2 R 3