Orbits For Earth-like Planets

Youtube! Edgar here. And welcome to Artifexian.
Here you will learn everything you ever wanted to know about world building…and then some! Let’s put those habitable, earth-like, terrestrial
planets we’ve been building into orbit. 1. Semi-major axis Remember, the semi-major axis of an orbit,
(a), is the average separation between a planet and its star. Seeing as we are building a
habitable planet, its semi-major axis must fall within the star’s habitable zone. Why?
Because life as we know it! So, here’s our star. It has a mass of 0.75
solar masses. It’s 0.37 times as luminous as our own sun and, importantly, its habitable
zone extends from 0.57 AU out to 0.83 AU. Unsure where I’m getting these figures from.
No worries. Click the links on screen for a guide to constructing stars. Anyways, all we need to do now is pick a semi-major
axis that falls within this habitable zone. Any figure will do, but bear in mind that
temperature is a function of distance. I’ll go with a middle-of-the-road 0.69 AU. 2. Eccentricity Habitable worlds will need to orbit on nearly
circular paths. Thus, a safe eccentricity range here is anything greater than 0 and
less than or equal to 0.2. I’ll go with an orbital eccentricity of
0.03. Check this out! The black ellipse here represents our orbit and the green circles
represent the inner and outer boundaries of our habitable zone. The whole point of setting
a low eccentricity value is to ensure that our planet receives even-ish heating throughout
its year and is at all times inside the habitable zone. Contrast this…with this! Here I’ve ramped
up the eccentricity to 0.75. Now our planet is spending most of its time outside of the
habitable zone…which ain’t great. To make matters worse, the closer a planet is to its
star, the faster it travels. So summers here will be extremely short and extremely hot.
And winters here will be incredibly cold and will last for a long, long time. Not very
life friendly. As an interesting aside, there is some data
to suggest that the more planets there are in a system, the less the average eccentricity
of those planets will be. This relationship is governed by 0.584*N^-1.2
where N is the number of planets in a system. As long as there are 2 more planets this relationship
holds. So, say I want our planet to be in a five
planet system. The average orbital eccentricity of all the planets should about 0.085. Not
a hard and fast rule by any means; just a cool creative restraint to bare in mind. 3. Periapisis and Apoapsis: The periapsis, the closest our planet will
get to its star, will be given, as always, by a(1-e) which, in this case turns out to
be 0.6693 AU. The most distant point in our planet’s orbit,
aka the apoapsis, is given by a(1+e). Again, in this case, we get 0.7107 AU. With the extremes of our orbit plotted, we
need to quickly double check to see if both apses still fall within our habitable zone.
Thankfully, they do and we are good to proceed. 4. Orbital period: Like before, a year on our planet will, thanks
to Kepler, be given by sqrt(a^3/M). The numbers here tell us that our planet’s year will
be about 2/3 the length of an earth year. Or in other words, 241.73 earth days. 5. Orbital Velocity: The speed at which our planet orbits will
be given by
the sqrt(m/r). So this guy’s orbital velocity is about 1.04 times that of earths, i.e.,
31.05 km/s. Which makes sense: close in planets orbit faster than distant planets. 6. Inclination: Earth’s orbit lies in the ecliptic plane.
In fact, Earth’s orbit defines the ecliptic plane and, as such, Earth has an orbital inclination
of 0 degrees with respect to the ecliptic plane. We use the ecliptic as our primary
reference plane when describing the position of other bodies in our system. A fictional system will be no different. Set
the orbital inclination of your system’s main habited planet to 0 degrees and measure
the position of other planets in your system with respect to this plane. Be careful though, planetary systems are relatively
flat. That is, planets will never orbit far from the ecliptic plane. In our system, the
average orbital inclination of the planets, with respect to the ecliptic plane, is about
2 degrees. The general idea is to keep planets on low orbits, saving the highly inclined
orbits for the oddball asteroids and kuiper belt objects. Now, we could set an inclination of 180 degrees
– it would still fall within the ecliptic plane. The problem here is that orbits greater
than 90 degrees are retrograde, i.e., the planet will orbit in the opposite direction
to the star’s spin. Retrograde orbits are difficult to set up
and maintain and will likely require outside influences to make them stable. Such is the
case with HAT-P-7b, a gas giant on a retrograde orbit around a star about 1000 light years
away in the constellation Cygnus. This star has a companion, which in turn has
a distant gas giant orbiting it. It is the gravitational interference from the companion
and its planet that is thought be responsible for the upkeep of HAT-P-7b’s backwards orbit. All things considered, I’ll give our planet
a prograde orbit and an inclination of, you guessed it, 0 degrees. 7. Longitude of the Ascending Node and Argument
of Periapsis Quick re-cap! The Longitude of the Ascending
Node is a measure of the orientation of an orbit about its Y axis. And the Argument of
Periapsis is the orbit’s orientation about the Z axis. If an orbit is in anyway inclined,
both parameters can have values between 0 and 360 degrees – as was the case in previous
videos. Now, non-inclined orbits are different. By
definition, a orbit with 0 degrees of inclination will have a 0 degree longitude of the ascending
node and an undefined argument of periapsis. Why? Well…it’s complicated. Short answer
is that it is a consequence of the fact that the orbital plane lies exactly in the reference
plane. But don’t loose to much sleep over this; just set the values at 0 and undefined.
Head into your favorite orbital simulator. Input the numbers and…boom! One habitable
earth-like orbit. Done! Now, I am nothing if not a completionist,
so here’s the rest of our system. Pretty cool, eh? Stats in the doobly-doo. Good morning, Interweb. So this is my fifth
video on world building planetary orbits. If you found this video useful, check out
the rest of the orbit videos, by either clicking on my face or the (i) in the top right hand
corner of your screen. If there’s any questions, please leave a comment and I’ll try my best
to sort you out. As always, click the links on screen for more
artifexian content. Like! And if you think I earned it…hit subscribe. Thank you all so much for watching Edgar out!


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