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
2a. 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
2b. The Law of Equal Areas Explored
Here's a helpful graphic from NASA
If the red and yellow areas are equal, a planet travels along those edges in the same time
In other words, planets travel faster when they're closer to the Sun
But the areas don't actually look equal; the yellow one looks bigger
So Kepler is more dramatic than NASA
3a. 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"
This law means that planets closer to the Sun orbit faster than those farther
But a lot faster, because exponents are involved
3b. The Law of Harmonies Explored
One astronomical unit (AU) is the average distance from the Earth to the Sun
That happens to be 149,597,870,700 m; I’ll use 149,587,871 km
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
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
Ellipse Eccentricity
1. The formula for ellipse eccentricity is
square root [1 - (semiminor)^2/(semimajor)^2]
2. The Earth is an "oblate spheroid" and not a perfect sphere
As are the Sun and the Moon; all three bulge at the equators
3. 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 Earth's eccentricity is about
square root [1 - (6,357)^2/(6,378)^2] = .081
The next time you walk through the Earth, go through the poles to save yourself 21 km
Orbital Eccentricity
1. The formula for orbital eccentricity, which accounts for more than static shape, is
(aphelion - perihelion)/(aphelion + perihelion)
Its calculated from "energy and angular momentum"
I don't know why, and I don't know what that means; I'm no astronomer
2. Earth perihelion is at .983 AU and aphelion is at 1.017 AU
The eccentricity for the Earth's orbit is about
(1.017 - .983)/(1.017 + .983) = .017
We really can't compare that to .081, because they're calculated differently
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 as a whole revolves at a speed of about
(149,597,871*2*π)/(365*24) = 107,300 km/h
6. The Sun's planets all revolve in an "ecliptic plane"
In other words, all the planetary orbits exist in one plane
But upsettingly, this is only almost true and not actually true
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, which is about
(6,378*2*π) = 40,074 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 tilted about 66.5° from the ecliptic plane
The equator is tilted about 23.5° from the ecliptic plane
5. The north side of the axis is pointed towards the star Polaris, the north star
6. 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)
7. Each rotation takes about 23 hours, 56 minutes, and 4 seconds
8. At the equator, the Earth is rotating at about
40,074/24 = 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 (.017) 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
(1.017 - .983)*(149,597,871) = 5,086,327 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 the 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 that stuff 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 around 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 all 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. If the Earth were not tilted, the Sun would hit the equator at 90° at all times
Its rays would be tangential at the poles
We find these points very interesting, so we sought them out with the tilt of the Earth
As the Earth orbits, these points have a range
We created imaginary lines to be boundaries for the ranges
9. It may help to see the graphic below to compare tilting and un-tilting
The solstices are the extremes, so they depict the boundaries for the ranges
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 at Winter Solstice
Earth at Summer Solstice
(Same Credit as Above)
Solar Declination
(Same Credit as Above)
The Moon
1. The diameter of the Moon is about 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 farther away from the Earth than the Moon
The Sun and Moon therefore appear to be similar in size to us during solar eclipses
2. The Moon is described to have an equatorial bulge
Nobody speaks of this in terms of 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 1,738 km
Its polar radius, or semi-minor axis, is about 1,736 km
So the Moon's eccentricity would be about
square root [1 - (1,736)^2/(1,738)^2] = .048
4. Compare that to the Earth's eccentricity of .081
While we're at it, the Sun is said to have only a 10 km difference between its axes
So if the diameter of the Sun is 400 times that of the Moon, it is about 1,389,600 km
Its radius would be 694,800 km
The difference in its semi axes would be 5
So 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
The Sun's eccentricity is about
square root [1 - (69,797.5)^2/(694,802.5)^2] = .0038
We did a lot of rounding, and you aren't supposed to quantify things like this
But perhaps the Sun is 13 times as round as the Moon and 21 times as round as 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 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 periods for both are 27.3 days
3. But our tidal locking isn't entirely perfect
The Moon doesn't appear fixed; it wobbles on us - a phenomenon called libration
Instead of seeing 50% of the Moon's surface, we see 59% over the course of an orbit
There are lots of reasons for this; it is an extremely complicated situation
One big reason is that the Sun pulls on the Moon with twice the force the Earth does
4. In addition to all of this, the Moon appears larger when it's closer
For moons, perihelion is called perigee and aphelion is called apogee
Perigee is usually about 363,300 km and apogee is usually about 405,500 km
The Moon's Revolution
1. From a bird's-eye view, the Moon orbits the Earth in a counterclockwise direction
2. The distance from the Earth to the Moon is about 384,400 km
3. If perigee = 363,300 and apogee = 405,500 km, then
The eccentricity of the Moon's orbit is about
(405,500 - 363,300)/(405,500 + 363,300) = .055
We can compare that to the eccentricity of the Earth's orbit, which is about .017
So the Earth's orbit is over 3 times as round as the Moon's
4. From a side view, the Moon's orbital path is tilted about 5.1° from the ecliptic plane
5. The angle of the Moon's orbit does not point to a specific star
The Moon's Rotation
1. From a side view, the Moon's axis is tilted about 88.4° from the ecliptic plane
Its equator is tilted about 1.6° from the ecliptic plane
2. From a side view, the Moon's axis is tilted 83.3° from its own orbital plane
Its equator is tilted about 6.7° from its own orbital plane
3. The north side of the Moon's axis is vaguely pointed towards the star Omicron Draconis
4. Because of its small axial tilt, the Moon has minimal seasonal changes
Its exosphere doesn't trap the Sun's energy, so the temperatures are extreme
The temperatures at the Moon's equator range from -208° to 250° C
In craters near the Moon's poles, permanent shadows make for temps below -246° C
5. Those angles were hard to imagine; here's a very helpful graphic from Wiki
The Moon's Orbit
(Same Credit as Above)
Moon Speeds
1. At the Moon's equator, the Moon is rotating at about
(1,738*2*π)/(27.3*24) = 16.7 km/h
At the Earth's equator, the Earth is rotating 100 times as fast, about 1,670 km/h
2. The Earth rotates once a day and the Moon rotates once every 27.3 days
So the Earth as a whole rotates 27.3 times as fast as the Moon as a whole
3. The Moon as a whole revolves around the Earth at a speed of about
(384,400*2*π)/(27.3*24) = 3,686 km/h
(384,400*2*π)/(27.3*24) = 3,686 km/h
The Earth as a whole revolves around the Sun about 29 times as fast,
(149,597,871*2*π)/(365*24) = 107,300 km/h
5. The Moon is gravitationally bound to the Earth
Therefore, its speed relative to the Sun is the same as the Earth's
6. We can also calculate how fast the Moon is moving in its spirograph path
This would be [(Earth's orbit) + (365/27.3)(Moon orbits)]/(365*24), which is about
[(149,597,871*2*π) + (365/27.3)(384,400*2*π)]/(8760), which is about
[939,951,145 + (13.37)(2,415,256)]/(8760) = 110,986 km/h
That's a little over a third of the speed of light, which is very roughly 300,000 km/h
Mercury is the fastest planet in our solar system, traveling at about 172,000 km/h
Lunar Calendar
1. The Moon takes about 27.3 days to orbit the Earth
Because the Earth is moving, the Moon must travel further to align with the Sun
A synodic month is the time the Moon takes from new moon to new moon, 29.53 days
2. 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
3. A new moon is when the Moon is between the Sun and the Earth in its orbit
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
4. A full moon is when the Earth is between the Sun and the Moon in its orbit
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
5. The Moon's orbital path is considered "pretty close" to the ecliptic plane
Because of this, we think of the Moon as following the Sun's trajectory
New moon - highest at the June solstice and lowest at the Dec solstice
First quarter moon - highest at the Mar equinox and lowest at the Sep equinox
Full moon - highest at the Dec solstice and lowest at the June solstice
Third quarter moon - highest at the Sep equinox and lowest at the Mar equinox
Synodic Month
1. Waxing - illuminated part is growing
Waning - illuminated part is shrinking
Crescent - less than a semi-circle
Gibbous - more than a semi-circle
Quarter moons - half illuminated
2. New moon, 0 days old
Rises at sunrise, sets at sunset (6-18)
Waxing crescent, 4 days old
Rises in the morning, sets in the evening (9-21)
First quarter, 7 days old
Rises around noon, sets around midnight (12-0)
Waxing gibbous, 10 days old
Rises in the afternoon, sets after midnight (15-3)
Full moon, 14 days old
Rises at sunset, sets at sunrise (18-6)
Waning gibbous, 18 days old
Rises in the evening, sets in the morning (21-9)
Third quarter, 22 days old
Rises around midnight, sets around noon (12-12)
Waning crescent, 26 days old
Rises after midnight, sets in the afternoon (3-15)
Moon & Hemispheres
1. The moon appears similar in both the northern and southern hemispheres
2. However, the perspectives are upside down from one another
3. Up to 90% of the population lives in the northern hemisphere
4. So for up to 90% of the population, an evening crescent is not oriented like a C!
For us, that's a morning crescent only; our evening crescent is backwards
5. Notice that the graphic above favors the northern hemisphere
6. The following graphic shows both
From left to right:
Wax Cresc, 1st Quarter, Wax Gib, Full Moon, Wan Gib, 3rd Quarter, Wan Cresc
Eclipses
1. Every new moon, the Moon is between the Sun and Earth
2. Usually, its 5.1° orbital tilt keeps it too high or low from aligning with the Sun and the Earth
But sometimes, the Moon lines up precisely enough 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 therefore looks like a crescent
Annular solar eclipse - like a total eclipse when the Moon is farther from the Earth
The Moon appears surrounded by a ring of Sun
4. Sometimes, the Moon lines up with the Sun and the Earth but on the opposite side
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 Moon 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
Know Your Moons
1. A full moon, as you know, is a moon that is fully lit up from our perspective
2. A blood moon, as you know, is a full moon that is positioned in the Earth's darkest shadow
The only light that reaches the Moon comes from the edges of the Earth's atmosphere
The air molecules from the Earth's atmosphere scatter out most of the blue light
3. A supermoon is a full moon that looks large
This is because it is closest to us in its orbit
Astronomers call it a "perigean full moon"
4. A blue moon is defined as many things
Least frequently, it means a full or partial moon appearing blue
This happens rarely and unpredictably from forest fire or volcano emissions
Calendrical blue moons are full moons on the 13 leap months of the lunar calendar
They happen 7 times every 19 years, so about once every 2.5 years
Since 1937, blue moons have been defined as the second full moon of the month
I don't know why
5. A harvest moon is the full moon that occurs closest to the Autumnal equinox
This was named before farmers had electricity and moonlight was important
Transits
1. Mercury and Venus are also causing eclipse-like things; these are called transits
Because they're so small/far away, they appear as tiny black dots
They cause no change in daylight and require solar filters to see
2. Here are some diameters:
Moon - 3,474 km
Sun - 1,390,000 km
Mercury - 4,880 km
Venus - 12,104 km
Earth - 12,756 km
Mars - 6,792 km
Jupiter - 142,984 km
Saturn - 120,536 km
Uranus - 51,118 km
Neptune - 49,528 km
3. The distance between Earth and Venus is 38,000,000 km at its closest
The distance between Earth and Mars is 55,000,000 km at its closest
4. Therefore, we aren't creating any meaningful eclipses
Mars was our only hope, but we're too far away
You probably already knew that by instinct alone, so this was a bad way to end this post
Solar Eclipse
Types of Solar Eclipses
(Same Credit as Above)
Lunar Eclipse
(Same Credit as Above)
Blood Moon
(Same Credit as Above)
