What Revolves Around What
1. Geocentric System - Earth is in the center
A step up for flat earthers
2. Heliocentric System or Copernican Model - Sun is in the center
First published by Nicolaus Copernicus (1473-1543) in 1543
Galileo Galilei (1564-1642) provided evidence
Copernicus died right after publishing, so Galileo got blamed for heresy
3. Copernicus thought the planets orbited in circles
Johannes Kepler (1571-1630) fixed that
Kepler's Three Laws of Planetary Motion (1609-1619)
1. The Law of Ellipses
Planets revolve in elliptical orbits around the Sun, which is one of the two foci
The point in the orbit where a planet is closest to the Sun is called perihelion
The point in the orbit where a planet is farthest from the Sun is called aphelion
2. The Law of Equal Areas
Imagine an ellipse representing a planetary orbit and a focus representing the Sun
Pick any two points on the ellipse and draw lines from them to the Sun
Color in one of the two sectors you've just created; this has an area
Imagine a second sector created in a similar fashion with an equal area
A planet travels the elliptical edge of either shape in equal amounts of time
3. The Law of Equal Areas Explored
Here's a helpful graphic from NASA
Assume those two areas are equal
The planet travels along the red edge in the same time as the yellow edge
In other words, planets travel faster when they are closer to the Sun
But the areas don't actually look equal; the yellow one looks bigger
So Kepler is more dramatic than NASA
3. The Law of Harmonies
The squares of the orbital periods of planets are directly proportional
to the cubes of the semi-major axes of their orbits
An orbital period is just the amount of time it takes to orbit
The semi-major axis of an orbit, informally speaking, is just the "longest radius"
So this just means that planets closer to the Sun orbit faster than those farther
But a lot faster, because exponents are involved
4. The Law of Harmonies Explored
One astronomical unit (AU) is the semi-major axis for the Earth's orbit
(That happens to be 149, 597, 870,700 m)
Here are the AUs for the other planets in our Solar System:
Mercury - 0.39 AU
Venus - 0.72 AU
Earth - 1.00 AU
Mars - 1.52 AU
Jupiter - 5.20 AU
Saturn - 9.54 AU
Uranus - 19.22 AU
Neptune 30.06 AU
If we square the orbital period of the Earth (365 Earth days)
And divide it by the number of AUs cubed (1),
Our constant is derived from Earth days and AUs is 133,225
That means the orbital period of Mercury in Earth days should be
square root [(133,225(.39)(.39)(.39)] = 89
That's pretty close to what the internet said :)
Here are the years, measured in Earth days, of the planets
Mercury year - 88 Earth days
Venus year - 225 Earth days
Earth year - 365 Earth days
Mars year - 687 Earth days
Jupiter year - 4,333 Earth days
Saturn year - 10,759 Earth days
Uranus year - 30,687 Earth days
Neptune year - 60,190 Earth days
Ellipse Eccentricities
1. How squished a circle gets to become an ellipse is quantified by "eccentricity"
2. An ellipse with an eccentricity of 1 is a line
An ellipse with an eccentricity of 0 is a circle
3. The Earth is an "oblate spheroid" and not a perfect sphere
As are the Sun and the Moon; all three bulge at the equators
4. The eccentricity of a cross section of the Earth, cutting from pole to pole, is .0818
The Earth's equatorial radius, or semi-major axis, is about 6,378 km
Its polar radius, or semi-minor axis, is about 6,357 km
The next time you walk through the earth, go through the poles to save yourself 21 km
5. The eccentricity of the Earth's orbit, on the other hand, is .0167
Perihelion is at .983 AU
Aphelion is at 1.017 AU
6. The orbit of the Earth is (much) more circular than the Earth itself
The Earth's Revolution
1. The Earth's revolution around the Sun is perpetuated by the Sun's gravity
2. The diameter of the Sun (1,392,000 km) is about 109 times that of the Earth
3. Let's define a bird's eye view as the perspective from above the N Pole of the Sun
From a bird's-eye view, the Earth's revolution travels in a counterclockwise direction
4. Each revolution takes about 365.25 days
5. The Earth revolves at a speed of about 108,000 km/h
We can check that - (149,597,870*2π)/(365*24) = 107,300 km/h
And that's slower because we made the orbit bigger by using the semi-major axis
6. The Sun's planets all revolve in an "ecliptic plane"
In other words, all the planetary orbits exist in one plane
The Earth's Rotation
1. The Earth rotates on an axis
2. The top of the axis is the N Pole and the bottom is the S Pole
The great circle in the middle is the equator
We can double the semi-minor axis and multiply by π to see how big it is
So the equator is about 40,075 km
3. Everything north of the equator is the northern hemisphere
Everything south of the equator is the southern hemisphere
4. From a side view, the axis is about 22.1-23.5° from the ecliptic plane
The north side of the axis is pointed towards the star Polaris, the north star
5. From a bird's-eye view, the Earth rotates in a counterclockwise direction
(But we knew this already because the Sun rises in the east and sets in the west)
6. Each rotation takes 23 hours, 56 minutes, and 4 seconds
We can divide 40,075km/24h
At the equator, the Earth is rotating at about 1,670 km/h
Solar Calendar
1. The summer solstice in the northern hemisphere is the longest day/shortest night
This is the winter solstice in the southern hemisphere
It is June 20 or 21 (first day of summer or winter)
2. The winter solstice in the northern hemisphere is the shortest day/longest night
This is the summer solstice in the southern hemisphere
It is December 21 or 22 (first day of winter or summer)
3. The days that have equal day and night are equinoxes
The northern autumnal equinox is the southern vernal equinox
It is Sep 22-23 (first day of fall or spring)
The northern vernal equinox is the southern autumnal equinox
It is Mar 20-21 (first day of spring or fall)
4. The eccentricity of the Earth's orbit (.0167) does not create seasons
Perihelion, when the Earth is closest to the Sun, occurs around Jan 3
Aphelion, when the Earth is farthest from the Sun, occurs around July 4
5. The difference in distances from the Sun is about 5,000,000 km
We can actually check that
(1.017 - .983), the difference in AUs, times (149, 597, 870 km)
= 5,085,715 km
6. Aphelion occurs when the northern hemisphere is tilted towards the sun
The northern hemisphere is about 40% land
The southern hemisphere is about 20% land
Because land heats faster than water, the Earth as a whole is warmer during aphelion
This is the best science fact in this post
Longitude
1. I don't like longitudes because they're arbitrary
2. All longitude lines are great circles called meridians
3. Longitude 0 is the Prime Meridian
4. It runs through Greenwich, England
5. It has divided the Earth into eastern and western hemispheres since 1884
6. Longitudes run 180° E through 0° to 180° W (which is 180° E)
7. Roughly zigzagging through longitude 180 is the International Date Line
Crossing it moving west adds a day
Crossing it moving east subtracts a day
If Phileas Fogg had traveled west, he would have lost his wager
8. Hours are measured in 15° increments
Every 15° east, the time is one hour later; every 15° west, the time is one hour earlier
Our time zones try their very best to conform, but people always mess stuff like that up
Latitude
1. In contrast with longitudes, I like latitudes very much
2. Latitude 0 is the equator
It is 10,000 km away from the N or S Pole
3. Latitudes run 90° S through 0° to 90° N
That's penguins to Ecuadorian cacao beans to Santa; what's not to like?
4. Latitude 66.5° N, for now, is the Arctic Circle
It is 2,620 km S of the N Pole
From this line and everything northwards, the Sun never sets on the June solstice
Nor doth it rise on the Dec solstice
The further up you go, the more times the Sun never sets
At the N Pole, the Sun never sets for 1/2 the year
5. Latitude 66.5° S, for now, is the Antarctic Circle
It is 2,620 km N of the S Pole
From this line and everything southwards, the Sun never sets on the Dec solstice
Nor doth it rise on the June solstice
The further down you go, the more times the Sun never sets
At the S Pole, the Sun never sets for 1/2 the year
6. Latitude 23.5° N is the Tropic of Cancer
It is 7,400 km S of the N Pole
It is the northernmost latitude where the rays of the Sun strike at 90°
Further north, the rays of the Sun hit the Earth at an angle and are less intense
7. Latitude 23.5° S is the Tropic of Capricorn
It is 7,400 km N of the S Pole
It is the southernmost latitude where the rays of the Sun strike at 90°
Further south, the rays of the Sun hit the Earth at an angle and are less intense
8. The tropics is the band between the Tropic of Cancer and the Tropic of Capricorn
9. A sub-solar point is a point on a planet where the Sun appears to be directly overhead
A zero-shadow day is a day in which the Sun is at a sub-solar point at noon
(The Sun is never at a sub-solar point when it is not the middle of the day)
10. Zero-shadow days are dependent upon latitudes
Areas outside the tropics never have zero-shadow days
At the Tropic of Cancer, a zero-shadow day occurs on the June solstice
At the Tropic of Capricorn, a zero-shadow day occurs on the Dec solstice
At the equator, zero-shadow days occur on the two equinoxes
At other places in the tropics, two zero-shadow days occur some time
For the northern hemisphere, the first is about Apr-May and the second about is Jul-Aug
For the southern hemisphere, the first is about Oct-Nov and the second is about Jan-Feb
Dad Says:
1. Notice that the Earth's axis is at a 23.5° angle
2. Notice that the Arctic Circle is 23.5° latitude S of the N Pole
3. Notice that the Antarctic Circle is 23.5° latitude N of the S Pole
4. Notice that the Tropic of Cancer is 23.5° latitude N of the equator
5. Notice that the Tropic of Capricorn is 23.5° latitude S of the equator
6. I'm going to go row now
7. Thanks, Dad
8. It appears that the poles un-tilted become the Arctic & Antartic Circles whence tilted
Similarly, the equator un-tilted becomes the Tropic of Cancer & Capricorn whence tilted
It may help to look at the graphic below
Connect the left side of the Tropic of Cancer to the right side of the Tropic of Capricorn
This is an upright equator
Similarly, construct upright circles that intersect the N Pole & S Pole
These are areas the size of the Arctic & Antarctic Circles
Earth Summer Solstice
(Same Credit as Above)
Solar Declination
(Same Credit as Above)
The Size of the Moon
1. The diameter of the Moon is 3,474 km
If the Moon's diameter is a unit of 1, then the Earth's is 3.67 and the Sun's is 400
Coincidentally, the Sun is 400 times further away from the Earth than the Moon
They therefore appear to be the same size to us during solar eclipses
2. The Moon is described to have an equatorial bulge
Nobody speaks in terms of a cross section with an eccentricity
They just call the Moon a lemon and get on with their day
But I want to tell you how much of a lemon it is
3. The Moon's equatorial radius, or semi-major axis, is about 1,737.58 km
Its polar radius, or semi-minor axis, is about 1,737.05 km
The formula for ellipse eccentricity is
square root [1 - (semiminor)(semiminor)/(semimajor)(semimajor)]
So the Moon's eccentricity would be about .0247
Compare that to the Earth's eccentricity of .0818
4. While we're at it, the Sun is said to have only a 10 km difference between its diameters
So if the diameter of the Sun is 400 times that of the Moon, it is about 1,389,600 km
It's radius would be 694,800 km
The difference in its semi axes would be 5
Then the Sun's equatorial radius, or semi-major axis, is about 694,802.5 km
Its polar radius, or semi-minor axis, is about 694,797.5 km
Its eccentricity is about .0038
So the Sun is 6.5 times rounder than the Moon, which is 3 times rounder than the Earth
Tidal Locking
1. Imagine connecting the center of the Earth to the center of the Moon
In this case, the same side of the Moon would always face the Earth
This is happens to be true; the Moon always looks the same to us
2. To maintain this, the Moon must rotate around its own axis at the same rate as its orbit
This is a phenomenon called tidal locking
The period for both are 27.3 days
The Moon's Revolution
1. From a bird's-eye view, the Moon orbits the Earth in a counterclockwise direction
2. The eccentricity of the Moon's orbit is .0549
For moons, perihelion is called perigee and aphelion is called apogee
Perigee is 363,300 km
Apogee is 405,500 km
3. From a side view, the Moon's orbital path is tilted about 5.1° from the ecliptic plane
The Moon's Rotation
1. From a side view, the Moon's axis is tilted about 6.7° from the ecliptic plane
This means the Moon's axis is tilted about 1.6° from its own orbital plane
2. To compare, the Earth's axis is 66.5° from the ecliptic plane
So while our axis is nearly perpendicular to our orbital plane, the Moon's is nearly parallel
3. The north side of the Moon's axis is vaguely pointed towards the star Omicron Draconis
Lunar Calendar
1. A new moon is when the moon is between the Sun and the Earth
Its lit side is facing the Sun and its dark side is facing us, so it's not visible
From our perspective, it rises and sets with the Sun
Each following day, the moon rises about 50 mins later than the day before
2. A full moon is when the Earth is between the Sun and the Moon
Its lit side is facing the Sun and its lit side is facing us, so it's entirely visible
From our perspective, it rises at sunset and sets at sunrise
3. Moon Cycle/Synodic Month:
New moon, 0 days old
Waxing crescent, 4 days old
First quarter, 7 days old, half illuminated, rises at noon and sets at midnight
Waxing gibbous, 10 days old
Full moon, 14 days old
Waning gibbous, 18 days old
Third quarter, 22 days old, half illuminated, rises at midnight and sets at noon
Waning crescent, 26 days old
4. The moon takes 27.3 days to orbit the Earth, but because the Earth is in orbit,
the moon must travel another two days to align again with the Sun
5. A synodic month is the time the Moon takes from new moon to new moon, 29.53 days
6. A lunar year is 12 synodic months, which is about 354 days
To align with the solar year, a 13th leap month must be added 7 times every 19 years
The lunar year usually begins on the second new moon after the northern winter solstice
This typically occurs some time between Jan 21 and Feb 20
Eclipses
1. Every new moon, the Moon is between the Sun and Earth
2. But sometimes the orbital path aligns them so well that the Moon obscures the Sun
These are called solar eclipses
They happen during the day
3. There are 3 kinds of solar eclipses:
Total solar eclipse - the Sun is entirely blocked out
Feels like a fleeting nighttime during the day
Partial solar eclipse - the Sun is partially blocked out
The Sun looks like a crescent
Annular solar eclipse - like a total eclipse when the Moon is further from the Earth
The Moon looks like it is surrounded by a ring of fire
4. Opposite this is the phenomenon when the Earth is aligned between the Sun and the Moon
These are called lunar eclipses
They happen during the night
5. There are 3 kinds of lunar eclipses:
Total lunar eclipse - the Moon is in the Earth's darkest shadow
The Mon looks dramatic and red; called a "blood moon"
Partial lunar eclipse - the Moon is in some of the Earth's shadow
The Moon looks like a black circle has been erased from its side
Penumbral lunar eclipse - the Moon passes through the fainter part of the Earth's shadow
Nothing to write home about; the Moon simply looks dimmer
6. Solar eclipses only happen on new moons
Lunar eclipses only happen on full moons
7. Total solar eclipses happen every 18 months, but their paths are very narrow
A specific location only experiences a total solar eclipse once every 330-540 years
8. Total lunar eclipses happen every 2.5 - 3 years
From any specific location, a total lunar eclipse is visible about every 2.5 years
This is great news because blood moons are exceptionally beautiful
For the continental US, our next one is 26 Jun 2029
Mark those calendars
Blood Moon
(Same Credit as Above)
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