Youtube edgar here and welcome to artifexian here you will learn everything
You ever wanted to know about worldbuilding and then some
An orbit is the gravitationally curved path of an object around a point in space
Like a planet orbiting the centre of a star system.
Kepler's first law of planetary motion tells us that all orbits are ellipses
With the centre of mass at one of the two foci
Ok so ellipse two foci a star at one of
Them and a planet looks about right to me
Kepler's second law of planetary motion basically tells us that a planets
Orbital velocity varies with distance.
So it moves fast when
Close to the star and slow when further away.
Like so and finally here's Kepler's third law
In mathematical form its P^2/A^3.
(P) is the orbital period
aka the time it takes for a planet to complete one orbit around its star
And (A) is the semi-major axis of the orbit.
In essence, the time required to orbit a star is proportional
To the distance of a planet from the star.
Got it cool let's talk orbital elements.
In classical or
Keplerian celestial mechanics we will need to know 6 orbital elements
To fully describe any specific orbit.
They are size, shape, pitch, yaw, roll and plot.
Number 1 Size
Notice there are two points in the orbit.
Here and here.
We call these points apses.
Periapsis here; the closest a planet
Will get to its star.
Apoapsis here; the greatest distance between the two bodies
Add up the distance between the two apses and the centre of the system
Then divide by 2 and you have your semi-major axis (a).
The semi-major axis is basically the average separation
Between the star and the planet.
So when we say “the earth orbits at 1 AU”
We are referring to the semi-major axis.
Orbital parameter no.1 Know thy semi-major axis.
2.
Shape
The shape of an orbit is down to the eccentricity.
Remember eccentricities (e) is a measure of how much an orbit deviates
From a perfect circle.
0 is a perfect circle and 1 is a parabola.
Now, Kepler just told us an orbit is an ellipse so the orbital eccentricity
Must be greater than 0 and less than 1.
Low eccentricities give circular-ish orbits
The higher the e value the more elliptical the orbit becomes
Orbital parameter no 2.
Know thy eccentricity
3.
Pitch
To explain let's set up an xyz axis with our star at the origin.
The blue plane, our reference plane, runs through the equator of our star
Aka The equatorial plane.
Notice that the orbital plane in red intersects
The blue plane here forming a line of intersection upon which are two points.
We call these points the ascending and descending nodes.
Why?
Because the planet as it orbits counterclockwise will cross the
Equatorial plane rising here and a descending here like so.
Seen edge on we can pitch the orbit about the x axis like so
The degree of pitch is known as the (i) the inclination.
Values range from 0-180 degrees.
Just as a pilot can alter the pitch
of his plane so to we can alter the inclination of our orbit
Orbital Parameter no.3 Know they orbital inclination.
4.
Yaw
Speaking of angles let's set up a arbitrary reference point in this direction say.
For earth this reference frame points towards the vernal equinox
But it could point anywhere really its just a construct
There to help the construct of various angles and define the orbit
Notice the angle that is formed between our reference frame and the ascending node
Imagine we increase or decrease that angle.
Seen top down it would look like this
What we are doing is rotating the orbit about the y axis
Or in terms of aircraft adjusting its yaw
So what do astronomers call this angle
Wait for it “longitude of the ascending node”
Testament to the fact that we should never let astronomers name things
Now despite the unwieldy name it indicates the yaw of an orbit as measured
In degrees in the equatorial plane form the reference line to the ascending node.
Oh and its denoted by the greek letter omega and can go from 0 – 360 degrees
Orbital parameter no.
4 Know thy “Longitude of the Ascending node”.
5.
Roll
Ready for another terrible terrible name
Try this on for size the “Argument of periapsis”
Again another silly name for something simple enough to understand.
Simply draw a line in the orbital plane connecting the periapsis
The closest the planet comes to the star, and centre of the star.
Now again in the orbital plane measure the angle between this line
And the ascending node and boom you're done.
Just make sure the angle is measure counterclockwise and denoted with small omega.
This determines the location of the periapsis which indicates
The degree of rotation about the z axis.
Seen front on
We can increase or decrease the angle like so.
Values can range from 0 – 360 degrees.
Again the aircraft analogy may be useful here.
Orbital parameter no.
5 Know thy argument of periapsis.
Now you might be asking why am I bothering with all of this
Well two reasons one a stat sheet like this will make for some badass canon
And two if you're a developing a game like kerbal space program
Or universe sandbox you NEED to know these orbital elements
In order to render any orbit in 3d space.
We'll look at the numbers behind these parameters in the next few videos
When we construct orbits for our dwarf planets, gas giants and terrestrial planets
And trust me the figures are WAY easier to grasp than their explanations.
That said I'll leave you with
No.6 Plot
This is the position of your planet in its orbit with reference to the periapsis
Simply draw a line counterclockwise in the orbital plane
From the periapsis to your planet.
The angle in degrees indicates your planets position
So this guy looks like he's at about 150 degrees.
Again the range goes from 0 – 360 degrees and it denoted by the letter nu or theta.
Could be useful if you're plotting an intercept course
For your scifi setting for example.
It's simple concept really I wonder what simple name astronomers
Have come up with describe this.
Oh ye ye that's just great “true anomaly” why astronomers why?
See you next time guys
Guys if you like what you see here on artifexian
Click the links in the description to find me on facebook and twitter
And if you're interested hit like and subscribe
For more awesome science based worldbuilding.
Thank you all so much for watching.
Edgar out.