earth moon and planets exam 1

kepler’s first law

a planet moves on an ellipse with the sun at one focus

perihelion distance: a(1-e)

aphelion distance: a(1+e)

kepler’s second law

describes how the speed of the planet changes as it moves through its elliptical trajectory (aka the law of equal areas)

also states that the planet moves fastest when it is closest to the sun at perihelion and slowest when it is furthest from the sun at aphelion

kepler’s third law

for any two planets orbiting the sun, the square of the ratio of their orbital periods is equal to the cube of the ratio of semi-major axes

(p_2/p_1)² = (a_2/a_1)³

describe the apparent motion of the stars as seen from the north pole. where are the ncp, scp, and celestial equator? which stars are always above the horizon, which stars are always below the horizon, and which stars rise and set?

ncp is directly overhead at zenith

scp is directly underfoot at nadir

celestial equator is on the horizon

stars make a counterclockwise motion around ncp; clockwise motion around scp

stars north of the celestial equator are always above the horizon

stars south of the celestial equator are always below the horizon

no stars rise or set

describe the apparent motion of the sun and how it changes through the year as seen from the north pole

the sun makes counterclockwise circles around the ncp (and clockwise around the scp) once per day. the elevation of the sun above the horizon varies with the season

motion of the sun during vernal equinox

the sun is on the horizon and circles the horizon once per day. the sun slowly spirals higher and higher in the sky until it reaches its maximum elevation of 23.5 degrees above the horizon (summer solstice)

motion of the sun on summer solstice

the sun circles the sky at an elevation of 23.5 degrees above the horizon. past the summer solstice the sun circles lower and lower each day until the autumnal equinox

motion of the sun on autumnal equinox

the sun circles below the horizon

motion of the sun on winter solstice

the sun spirals up and appears again on the horizon on the vernal equinox

*an observer on the north pole will see the sun above the horizon for the summer half of the year and below the horizon for the winter the other half

new moon movement

rises: 6am

transits: noon

sets: 6pm

waxing crescent movement

rises: 9am

transits: 3pm

sets: 9pm

first quarter movement

rises: noon

transits: 6pm

sets: midnight

waxing gibbous movement

rises: 3pm

transits: 9pm

sets: 3am

full moon movement

rises: 6pm

transits: midnight

sets: 6am

waning gibbous movement

rises: 9pm

transits: 3am

sets: 9am

third quarter movement

rises: midnight

transits: 6am

sets: noon

waning crescent movement

rises: 3am

transits: 9am

sets: 3pm

describe the phases of the moon you can see from the north pole near the vernal equinox

new → waxing crescent → first quarter → waxing gibbous → full

describe the phases of the moon you can see from the north pole around the winter solstice

first quarter → waxing gibbous → full → waning gibbous → third quarter

what phase of the moon is required for a solar eclipse to occur

new moon

what phase of the moon is required for a lunar eclipse to occur

full moon

what is required for an eclipse

the correct phase, the moon crossing the ecliptic, requiring that the sun be at a lunar node at the correct phase

why don’t we have a solar eclipse and lunar eclipse every cycle of lunar phases

a new moon with the moon far from the ecliptic; the moon’s shadow will miss the earth; if you have a full moon with the moon far from the ecliptic, the moon will pass north or south of the earth’s shadow

explain why solar and lunar eclipses come in pairs

an eclipse season in a 38 day period when the sun is close enough to a lunar node for an eclipse to occur at the correct phase; the length of the cycle of lunar phases is 29.5 days - shorter than an eclipse season - there must be a new moon and a full moon every eclipse season

describe the physical motion of the earth that is produced by the precession of equinoxes

precession of the equinoxes is produced by the motion of the earth’s axis of rotation. the earth’s axis sweeps out the surface of a cone. the axis of the cone is perpendicular to the earth’s orbital plane. the opening angle of the cone is a 23.5 degree axis tilt. the sense of motion is left handed

describe the motion of the ncp due to precession of the equinoxes

the ncp is the projection of the perpendicular to the earth’s orbital plane on the sky. the ncp moves in a circle around the nep. the radius of the circle is 23.5 degrees. the motion is counterclockwise. it takes the ncp one precession period of 26k years to make one complete circle

describe the motion of the solstices and equinoxes due to precession of the equinoxes

the solstices and equinoxes move east to west along the ecliptic. they take one period of 26k years to go 260 degrees around the ecliptic

describe the seasons experienced by the inhabitants of the equator of your planet

two cold “winters” near the solstices when it gets very little sunlight and two hot “summers” near the equinoxes when it gets a lot of sunlight. an observer on the equator will see the sun stationary on the horizon due north and on the summer solstice see the sun stationary on the horizon due south. on the winter solstice since the sun is on the horizon all day you don’t get much sun and it is cold outside

describe the apparent motion of the sun from an observer at the equator of your planet with a 90 degree tilt

an observer on the equator will see the sun rise due east, transit at zenith, and set due west on the equinoxes. this is what the sun does for observers on the equator of earth. earth’s equator is warm because it gets lots of sun so it is warm near the equinoxes

describe the cycle of phases of the moon seen by inhabitants of the planet with a 90 degree axis tilt

a full cycle of phases is possible at the equinoxes

moves away from equinox: the new and full phases are no longer possible. the new phase becomes minimum crescent and full phase becomes maximum gibbous

solstice: minimum crescent and maximum gibbous both approach quarter phase. moon is always quarter phase at solstices

equi nox: minimum crescent approaches new phase and maximum gibbous approaches full

describe conditions for full moon and summer solstice

we get a full moon if the moon, earth, and sun are lined up with the earth in the middle. we get summer solstice if the earth’s rotational axis is tilted towards the sun and winter solstice if the earth’s rotation is tilted away from the sun

why is the elevation of the full moon near midnight different in the two seasons

winter solstice: the sun is 23.5 degrees south of the celestial equator, so it transits the meridian low in the southern sky at noon

the full moon is 23.5 degrees north of the celestial equator near the winter solstice, it transits the meridian high in the southern sky at midnight

describe the lunar phases as seen at the north pole around the vernal equinox

new → first quarter → full is visible bc the moon is north of the celestial equator and therefore above the horizon

full → third → new is not visible because the moon is south of the celestial equator and below the horizon

describe the lunar phases as seen at the north pole around the summer solstice

third quarter → new → first quarter is visible bc the moon is above the horizon (north of celestial equator)

first quarter → full → third quarter is below the horizon and not visible

describe the lunar phases as seen at the north pole around the autumnal equinox

full → third → new is visible bc moon is above the horizon

new → first quarter → full is not visible bc moon is below the horizon

describe the lunar phases as seen at the north pole around the winter solstice

first quarter → full → third quarter is visible

north celestial pole

the point on the celestial sphere defined by the projection of the earth’s axis of rotation on the sky due north

south celestial pole

the point on the celestial sphere defined by the projection of the earth’s axis of rotation onto the sky due south

celestial equator

the great circle on the celestial sphere defined by the projection of the earth’s equitorial plane onto the sky

ecliptic

the great circle on the celestial sphere defined by the projection of the earth’s orbital plane onto the sky. also the path of the sun through the stars as seen by observers on earth. the sun moves against the background stars throughout the year due to the orbit of the earth around the sun

horizon

the great circle on the celestial sphere defined by the projection of the plane tangent to the surface of the earth at the location of the observer onto the sky. this separates the half of the sky visible to an observer (above the horizon) from the half of the sky not visible to an observer (below the horizon)

equator

an observer sees the ncp on the horizon due north and the scp on the horizon due south. the celestial equator intersects the horizon due east, crosses the meridian at zenith, and intersects the horizon due west. no stars are always above or below the horizon. all stars rise and set. stars make clockwise circles around the scp and counterclockwise circles around the ncp

tropical years

the period of repetition of the seasons. the time it takes the sun to go from vernal equinox to the next vernal equinox. length is 365 days

sidereal years

the amount of time it takes for the earth to make one complete 360 degree orbit around the sun. this is the period of repetition of the earth’s position relative to the sun as measured with respect to the distant “fixed” stars

describe the motion of the moon’s ascending and descending nodes on the ecliptic

on opposite ends of the ecliptic. a point on the celestial sphere defined by projecting the line of nodes onto the sky. the gravitational influence of the sun on the moon’s orbit causes the moon’s line of nodes to precess clockwise around the ecliptic if viewed from looking down from the north. this causes them to move east to west around the ecliptic

during a solar eclipse, does the moon pass in front of the sun from east to west or west to east and why

from west to east. the sun and moon both move west to east along the ecliptic and the moon moves faster than the sun, so the moon catches up to the sun and passes it west to east every new moon. if a solar eclipse occurs at new moon, the moon will cover the western limb of the sun first and pass in front of it from west to east

describe what is meant by the inclination of the moon’s orbit. what is the line of nodes of the moon’s orbit? what are the moon’s ascending and descending nodes?

the inclination of the moon’s orbit is the angle between the ecliptic plane and the moon’s orbital plane. the angle is 5 degrees. the line of nodes is the line of intersection between the ecliptic plane and the moon’s orbital plane. the ascending node is the point where the moon crosses the ecliptic south to north and the descending node is the point where the moon crosses the ecliptic north to south.