Pearson Orbit

What is the Pearson Orbit?

Well – it’s not an official orbit, nor an official term. I can only say that it’s an endearing dedication to the man that led us to find its uniqueness among the infinite number of existing orbits around our planet.

Little did we know that, when pursuing research about the Space Elevator for my Graduate Research Project at Embry-Riddle Aeronautical University,  we would come to discover something unique.

Here’s a basic explanation of how this was discovered and why it’s important.

If you would like the read the full text of the Graduate Research Project, here it is.

Let’s start with some of the basics:

1. The rotation of the Earth:

For the sake of simplicity, let’s say that the Earth makes a complete, full rotation every 24 hours (it doesn’t? – look up Sidereal Day). If you were standing on the equator, in that 24 hour time period, you would travel roughly 24,000 miles in relation to space. I know you didn’t actually walk anywhere, but here’s another way to think of it: if you stood on the equator and walked due East or West, 24,000 miles later, you would be right back where you started. The circumference of the Earth is approximately 24,000 miles. Using simple math, we can say that, at the equator, the earth rotates at a speed of 24,000 miles per 24 hours or 1,000 miles per hour.

2. Newtons Law of Gravitational Force:

Again, for the sake of simplicity, we must note that two bodies are always attracted to each other. The strength of the attraction depends on their individuals masses and how for apart they are. This is important to understand when trying to keep an object in orbit.

3. Orbits:

As you travel further from the mass that you are orbiting, you require less velocity to maintain an orbit. The key here is to understand that the requirements to maintain a circular orbit change.

4. Escape Velocity:

This is the amount of velocity required for one mass to leave the sphere of influence of another mass. This also changes with the distance between the two masses.

5. Space Elevator travel

The Space Elevator is a system in which a cable is tethered to the Earth, preferably close to the equator, and is long enough to stretch out into space where centrifugal force keeps it taught. With this cable in place, an elevator will “climb” the cable to a desired altitude.

The rotation of the cable in space, being tethered to the Earth and pulled directly outward, keeps the entire system rotating with the rotation of the Earth, which is every 24 hours. As an elevator climbs out, the elevator is traveling a larger circle around the Earth, but is maintaining the same time to travel this distance. When compared to free objects in space that maintain a circular orbit, we see that an elevator has less velocity than is required to maintain a circular orbit up until it reaches the Clarke Orbit, or what is known as Geosynchronous Orbit (GEO).

Here’s where things get interesting, and I’m almost done telling my story, so hang in there. As the elevator passes beyond GEO, it is still rotating around the Earth approximately every 24 hours, but now it has more velocity than that which is required to maintain a circular orbit. If the elevator were to disconnect, it would enter an eccentric, or oval, orbit around the Earth. However, there is a point at which the excess velocity is too much to maintain an orbit around the Earth, and releasing at this point, or beyond, sends you off to orbit around some other mass.

It is the point, located at 46,750 km, that I am calling the Pearson Orbit. It’s the altitude at which, if you release from the cable, you are no longer hanging out around the Earth. May God then be with you. Legendary science fiction writer Arthur Clarke has GEO named after him (Clarke Orbit – 35,768 km). In his honor, I am dedicating the orbit located at an altitude of 46,750 km from the surface of the Earth to Major General Jeremiah Pearson III.

Godspeed Jed – you will be missed. Your knowledge, wisdom, sense of humor, and love of Johnny Cash music will be shared with future generations.

Jason Coe