To predict when a satellite will pass over a specific location, we need to understand how its orbit is described. For that, we use a standard called TLE, which is based on 6 physical parameters.
TLE (Two-Line Elements)
To figure out when a satellite will fly over us, we can use tools like SatDump, N2YO, or others. All of them rely on TLE (Two Line Elements), which are unique to each object orbiting Earth. NASA and NORAD regularly calculate these values (since orbits change) and publish them on databases like CelesTrak, which power our prediction tools.
Let’s take the TLE of NOAA 19 as an example:
The second line is the one we care about because it’s what determines the object’s orbit. For the curious, these numbers are the foundation of the Orbital Mechanics website.
Inclination
Labeled i, it’s the angle of inclination (in °) of the orbital plane relative to the equatorial plane.
In blue, we have the Earth’s orbital plane, in orange, the satellite’s plane.
There are three types of inclination:
0° ≤ i ≤ 90°: Prograde, where the orbit follows the same rotation direction as Earth (west to east).
90° < i ≤ 180°: Retrograde, where the orbit is reversed (east to west).
i = 90°: Polar orbit, covering all latitudes.
Right Ascension of the Ascending Node
Labeled Ω, it’s the angle between the ascending node and the vernal equinox.
Ascending Node
The ascending node is the point where the satellite crosses the Earth’s orbital plane going "upward." The descending node is the opposite.
Vernal Equinox
The vernal equinox is essentially the ascending node of the Sun’s orbit relative to Earth.
Right Ascension of the Ascending Node
It’s the angle between the ascending node and the vernal equinox.
Okay, I’ll admit, this one’s the hardest to grasp, but check out what happens when we tweak this angle using Orbital Mechanics:
Semi-Major Axis
Labeled a, it represents half the major axis of an ellipse.
Here’s how the orbit changes when we adjust this value:
Eccentricity
Labeled e, it measures the flattening of the ellipse.
For e = 0, the orbit is circular.
For 0 < e < 1, the orbit is elliptical (closed).
For e = 1, the trajectory is parabolic (open).
For e > 1, the trajectory is hyperbolic (open).
Changing e:
Argument of Periapsis
Labeled ω, it’s the angle (in °) between the ascending node and the periapsis (the point in the orbit closest to the central body).
The periapsis is the point in the orbit where the satellite is closest to the body it’s orbiting.
If the body is Earth, we call it perigee and apogee (perihelion and aphelion for the Sun).
Let’s see what happens when we change this value:
True Anomaly
Labeled 𝜈, it’s the angle (in °) between the periapsis and the satellite’s current position.
So, to summarize:
The size and shape of the orbit are determined by the semi-major axis and eccentricity.
The orientation is defined by the inclination, right ascension of the ascending node, and argument of periapsis.
The satellite’s position is given by the true anomaly.
And that’s it, we made it to the end, CONGRATS 😎.
Remember, we often use TLE because they allow us to predict when a satellite will pass over a specific location.
For those who need another visual representation, there’s this awesome video.
