Orbital Mechanics & Satellite Communications — Interactive 3D Simulations

March 27, 2026

Some background, references, and value statement

Space is pretty neat. At some point or another, humanity looked up at it, and, after gaining sufficient confidence with the concept of moving things through the air really fast, asked, "So what's a few extra thousand kilometers?"

I'm being facetious. In reality, it's much more complex than that, with a very interesting history that demonstrates the power of compounded understanding over centuries. Perhaps something I'll talk about in a future article. However, to keep the value of this article tight, I'll try to stay within the bounds of this question:

"How do satellites stay in orbit, and how do satellites communicate with the Earth?"

The first, and most obvious question to answer here, is how the heck do satellites stay suspended in a constant orbit without either careening towards the earth or launching out into space? They're pulled toward Earth by gravity with nothing holding them up, and yet the ISS has been in orbit for over twenty years. The answer, unsurprisingly, is physics.

Let's dive into the physics that help explain this.

As an aside, if any of this is interesting to you but only scratches the surface, then check out Satellite Communications, written by Timothy Pratt. This article draws from chapters 1 & 2, but barely scratches the surface.

1. Orbital mechanics

In short, a satellite in orbit is falling. Actually, it's constantly falling. But it's also moving at the same time, sideways, fast enough that by the time it falls, the curvature of the planet has dropped by the same amount. This, in essence, creates a closed loop of constant falling and constant ejection, forming an orbit.

rMF_gravityF_centrifugalv|F_g| = |F_c|Gravity (centripetal)Centrifugal (apparent)Velocity (tangent)drag satellite to rotate

The above diagram shows this competing relationship. Two forces are constantly acting on the satellite: gravity (blue) pulls it inward toward the planet, while the centrifugal force (orange) pushes it outwards. When these forces are equal in magnitude (|F_g| = |F_c|) the satellite neither falls to earth nor escapes to space. The velocity (green) vector is always tangent to the orbit, in other words perpendicular to both forces.

Let's get a bit more sophisticated with our understanding. Below, you'll find a full Newtonian gravity simulation using a Velocity Verlet integrator. Use WASD to fire thrusters to modulate the orbit. Hold Shift for 10x time acceleration. Play around with this for a minute to get an understanding of the forces acting on the satellite, and how the changes in these forces modify the orbit. Note how the orbit shifts from circular to elliptical prior to ever 'escaping' the gravitational pull of the Earth entirely; we will discuss this and how conservation of energy plays into orbits later.

Orbital simulation requires a desktop browser
Alt2200.0km
Speed6.818km/s
v_circ6.819km/s
v_esc9.644km/s
e0.0004
a8567.8km
Period2h 11m
Energy-23.26MJ/kg
F_grav5.43kN
F_cent5.42kN
Time0m 0s
Thrust
Shift — 10× speed

Controls

  • Thruster (bottom-right): W/S for prograde/retrograde thrust, A/D for radial.
  • Telemetry (top-right): eccentricity, semi-major axis, period, energy, forces.
  • Shift: Hold for 10x simulation speed.

Gravity: the only force

In the vacuum of space, a satellite experiences exactly one force, which is gravity. Newton's law of gravitation tells us the force equals G × M × m / r² which is the gravitational constant times the planet's mass times the satellite's mass, divided by the distance squared. The force always points toward the planet.

The satellite's mass effectively cancels out of the trajectory equation. Applying F = ma gives us a = G × M / r². For a point of reference to this math, a 1 kg cubesat and a 420,000 kg space station follow the exact same path if launched with the same velocity. Neat!

MF=1×a = GM/r²1 kgF=3×a = GM/r²100 kgSame orbit, same velocity, same accelerationF = ma → a = F/m = GM/r² (mass cancels)Force (scales with mass)Velocity (identical)Acceleration (identical — mass cancels)

Notice how despite modulating the mass of the satellite, the acceleration arrow remains the same. The force arrow grows with mass because a heavier satellite experiences a stronger gravitational pull. That's mass cancellation as defined by F = ma, meaning that a larger force on a larger mass produces the same acceleration. The orbit depends solely on position and velocity, not mass.

What causes an orbit to be circular vs elliptical

A circular orbit occurs at the circular velocity: v_circ = √(G × M / r). With a faster launch, you get an ellipse with a high apoapsis (point in orbit farthest from the body you orbit). With a slower launch, periapsis (point in orbit closest to the body you orbit) dips closer to the surface.

Earthv = 1.00 v_circv_circCirculare = 0 (perfect circle)r (launch)

At exactly v_circ, the orbit is perfectly circular. Below that, the launch point becomes the apoapsis, and the satellite dips closer to the planet on the opposite side at periapsis, meaning that the orbit will be elliptical with the 'high point' being the place of the launch. Above v_circ, the launch point becomes the periapsis, and the satellite climbs to a higher apoapsis on the far side. Thinking of this in terms of the conservation of energy helps cement understanding. If you don't launch with enough velocity to sustain a circular orbit, the satellite will 'fall' more than 'climb' as it circles, then 'climb' more than it 'falls' until it reaches the beginning of the orbit. This is due to the conservation of energy as the satellite conserves energy towards the apoapsis of the orbit. Inversely, if you launch with too much velocity, that extra energy will contribute to an elliptical orbit in the opposite sense as the satellite 'climbs' to a higher position, converting its extra kinetic energy to potential energy, until the pull of gravity wins and pulls it back towards the original starting point. Both result in an elliptical orbit, just in a different sense.

I think you can imagine the 'failure case' for both of these examples. For below v_circ, you could eventually collide with the body you orbit. For above v_circ, your energy would exceed the escape velocity required to exit orbit and enter space.

Retrograde / Prograde: reshaping orbits

So let's say you launch, and note that your orbit isn't correct. How do you fix it?

Fire prograde at periapsis and you raise the apoapsis. Fire prograde at apoapsis and you raise the periapsis. This concept is known as the Hohmann transfer. A burn (surge of energy) changes the orbit on the opposite side. This is not intuitive, until you think of the orbit in terms of how much energy the satellite possesses. If you surge (burn), you contribute to the kinetic energy of the satellite, which will allow it to 'resist' gravity on its trip to wherever it's headed (whether that be apoapsis or periapsis).

Initial orbitTarget orbitTransfer orbitEarthBurn 1: ProgradeRaises opposite side (apoapsis)+ΔvBurn 2: ProgradeCircularizes at target orbit+Δv1Orbit at initial altitude2Prograde burn → enter transfer ellipse3Prograde burn at apoapsis → circularize at target

The diagram above shows a two-burn Hohmann transfer from a lower circular orbit (green) to a higher one (blue). The first prograde burn at periapsis injects the satellite into an elliptical transfer orbit (amber, dashed). The satellite coasts along this ellipse until it reaches apoapsis on the opposite side, which is now at the altitude of the target orbit. That's step one complete. Next, a second prograde burn circularizes the orbit at the new altitude.

2. Visibility windows and communication bands

Now we understand how a satellite stays in orbit, and how we can modulate said orbit. However, a satellite is only useful if you can communicate with it. Put in a basic sense, we can only talk with a satellite if it's overhead, and the signal quality is sufficient. Earth stations on the surface can only establish a link when the satellite is above the local horizon. What this means specifically is above a minimum elevation angle of 5°; anything below which atmospheric attenuation and ground noise make the link not so great. Each overhead transit is called a pass, and the time the satellite spends above this threshold is the visibility window.

The simulation below shows a single earth station on the surface, with a ray-traced visibility line to the satellite. When the satellite passes through the window, a comm link appears, and the band indicator below shows which frequency band that distance requires (at a basic level; which band you use isn't quite this simple but is beyond the scope of this article).

Frequency bands (IEEE designation, standard in the satcom community):

  • UHF — military / mobile
  • L-band — GPS, Iridium
  • S-band — telemetry, TDRS
  • C-band — classic fixed-satellite service (FSS)
  • X-band — military, Earth observation
  • Ku-band — direct broadcast satellite (DBS), VSAT
  • Ka-band — high-throughput satellites (HTS)

Note how the satellite zips past the earth station quickly. These short visibility windows at a low orbit result in high frequency communication bands, essentially.

Higher altitude: longer windows, different bands

At GPS altitude (~20,200 km, MEO), the satellite moves much more slowly relative to the ground. The visibility window becomes dramatically wider, and now the earth station can track the satellite for a much larger fraction of its orbit. However, the increased slant range pushes communication into Ku-band, requiring more transmit power (also beyond the scope of this article) and larger antenna aperture to close the link budget.

Compare the band indicator with the LEO demo above. The satellite spends its entire pass in the Ku-band range rather than cycling through UHF and L-band. It's all a trade-off. Do you want more frequent communication windows at the expense of link quality, or the inverse? It's also an issue of scale. An LEO constellation can overcome these problems through launching of lots of satellites which effectively cover the full plane at all times (more on this later in this article).

Geostationary orbit: permanent visibility

At 35,786 km, the orbital period of a satellite will match one sidereal day. A geostationary satellite (GEO) appears fixed in the sky relative to the earth station. The visibility window is effectively permanent. This is why your home satellite dishes never need to track and can remain small in size, as they can simply point in a single known vector (which points to the GEO satellite).

Notice the satellite barely moves relative to the earth station. All communication happens in Ka-band due to the ~36,000 km slant range. The benefit of this, however, is permanent coverage of a fixed service area, but ~240 ms round-trip latency and significant free-space path loss. Not a big deal for broadcast, but not fast enough for real-time services.

3. Store-and-forward relay

A single earth station can only see a LEO satellite during each pass. With two earth stations spaced apart, you can relay data: Station A uploads to the satellite on the uplink frequency, the satellite stores the data onboard, and downlinks to Station B on a different frequency during the next pass. This is called store-and-forward architecture, and was used by early systems like Orbcomm.

Note how the satellite alternates visibility between the two earth stations. Data uploaded during one pass can be delivered during the next, and vice versa. The gap between contacts, called the blackout period, is when no communication is possible. The uplink and downlink use different frequencies to avoid self-interference.

A satellite transponder enables real-time two-way communication between earth stations. Unlike store-and-forward, a bent-pipe transponder receives the uplink signal, frequency-translates it, amplifies it, and retransmits on the downlink — all in real time with no onboard processing or storage.

For a full-duplex link between two earth stations, the satellite handles four frequency translations: Station A transmits on the uplink (f1), the satellite retransmits on the downlink to Station B (f3). Simultaneously, Station B transmits on a second uplink frequency (f2), and the satellite retransmits on a second downlink (f4) to Station A. This was how early satellite telephony circuits operated, where each direction of the conversation used its own uplink/downlink pair through the transponder.

5. Satellite constellation

Following up on their previous mention, let's discuss satellite constellations. Real satellite networks solve blackout with multiple satellites. For instance, a three-satellite constellation in the same orbital plane ensures at least one satellite is always visible from most locations. Below, three satellites are equally spaced (~120 degrees apart) at 2,200 km altitude with a similar network of earth stations.

With enough satellites and earth stations, you can achieve continuous coverage, even in lower orbit. This is the principle behind GPS (24+ satellites in MEO), Iridium (66 satellites in 6 orbital planes), and Starlink (thousands of satellites in LEO).

6. Direct broadcast satellite (DBS)

As a reminder, at exactly 35,786 km altitude where the orbital period matches Earth's rotation, geostationary orbit (GEO) is achieved. This is how the broadcasting-satellite service (BSS) works, which you probably know commercially as direct broadcast satellite (DBS) or direct-to-home (DTH).

One uplink earth station transmits programming to the satellite, which will then rebroadcast to all receiving earth stations within its coverage footprint simultaneously. f1 in this case is the uplink; think of this as whatever information is being broadcast, like television. The downlinks, f3 and f4, would in reality be potentially hundreds of thousands of receivers which are all receiving the transmitted broadcast.

Another use of geostationary satellites is as a real-time relay between two earth stations on different continents. In the early days, this meant no submarine cable or terrestrial link required to talk with someone across the ocean. This is referred to as a single-hop satellite link where Station A on one continent transmits on the uplink, the GEO satellite's bent-pipe transponder frequency-translates and amplifies the signal, and retransmits on the downlink to Station B on another continent.

This architecture was the foundation of international satellite telephony (Intelsat, established 1964) and remains critical for maritime, aviation, and remote-area communications.

Because the satellite is geostationary, the link is permanent, and both earth stations maintain continuous visibility. The satellite's footprint covers roughly one-third of Earth's surface, enabling intercontinental connectivity through a single relay hop. Pretty insane to think someone thought of this!

8. GSO orbits

As stated by Timothy Pratt, a perfectly geostationary orbit has three primary characteristics:

  1. The orbit must be exactly circular, meaning it has an eccentricity of exactly zero.
  2. The orbit must be at the correct altitude — that is, it must have the correct orbital period to match the Earth's sidereal rotation.
  3. Its plane of orbit must lie over the equator.

Any deviation in orbit eccentricity or inclination with respect to the equatorial plane will instead result in a geosynchronous orbit (GSO). A GSO satellite appears to "wobble" at a consistent mean angle as seen from an observer on the ground.

In the above demo, the amber dashed line tracks the observer's line-of-sight to the satellite. The orange trace shows the satellite's path over time, and you'll notice the oscillation back and forth rather than staying fixed. This wobble means the ground station's antenna must track the satellite rather than point at a single fixed position, unlike a true geostationary orbit where the dish never moves.

What a ride! The whole picture

From a single satellite following Newton's laws, to earth station visibility windows, to store-and-forward relay, to bent-pipe transponder links, to constellations, to GEO broadcast and intercontinental relay; each layer builds on the one before it. The constant across all is the physics. Gravity shapes the orbit, the orbit determines visibility, and the link architecture determines how reliably data flows.

And that is the foundation everything in satellite communications builds on. Again, if you want to learn more, I highly encourage you to read up on Satellite Communications by Timothy Pratt. It's the definitive work on the subject, and has all of the depth you could want on the subject.


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