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3.2 Theoretical Transportation Energy

3.2.1 Moving around in the Earth-Moon system

The Earth is 81 TIMES as massive as the Moon, and asteroids have a trivial mass compared to the Moon.

To get from the surface of the Earth or the Moon into orbit around Earth (where space products providing valuable space services will reside) requires energy in two forms:

  1. Energy to rise above the surface, i.e., "potential energy"; and
  2. Energy to stay up there without falling back down, that is, acquiring the speed to go into a circular orbit, i.e., "kinetic energy". In a circular orbit, gravity is countered by the centrifugal force constantly.

Notably, when the Space Shuttle goes into low Earth orbit about 500 kilometers up, only about 7% of the theoretical energy required goes into lifting it to that height (potential energy). About 93% of the energy goes into accelerating the Space Shuttle to a speed where it goes into a circular orbit (kinetic energy).

The total amount of energy (kinetic plus potential) required is often expressed in terms of an analogy -- an "energy well", as pictured here, as if each gravitational body represented a hole in the ground like a water well which a cargo must crawl out of. The bigger the planet, the deeper the equivalent well. In the picture below, the vertical "height" represents the energy required to move from one point to the other, whereby the horizontal length represents the physical distances (to scale).

Note on the graph that the energy required to go into "geostationary earth orbit (GEO)", i.e., "stationary communications satellite orbit", from the Moon is small, compared to coming from Earth. It will later be shown that the energy required to get material from many asteroids near Earth into geosynchronous orbit is even less than from the Moon.

The Space Shuttle can goes to about 500 kilometers, and doesn't have the capability to go significantly higher than that, energy-wise. Communications satellite orbit is at 36,000 kilometers. Roughly half the energy to get to geosynchronous orbit is consumed in just getting to an orbital speed.

When the Space Shuttle carries a communications satellite up, it brings it only above the atmosphere to the 500 kilometer orbit. From there, the satellite is removed from the cargo bay and then launches to geosynchronous orbit 36,000 kilometers up using its own fuel propellant, which mades up most of the cargo in the Shuttle bay, not the satellite. But this is another issue for another place.

What orbital speeds are we talking about? For low Earth orbit, we are looking at a little over 7 kilometers per second (i.e., about 15,000 miles per hour), for the orbital speed. At this speed, the Shuttle orbits the Earth in about one and a half hours.

As a satellite goes higher in orbit where Earth's gravity is weaker, it does not need to go as fast to stay in orbit, and thus one orbit of the Earth takes much longer, e.g., 24 hours for GEO. However, it takes much more energy to lift it up to that orbit.

An orbit used by communications satellites is a high Earth orbit called "geostationary" or "geosynchronous" orbit, where it takes exactly 24 hours for one orbit. Since the Earth rotates once per 24 hours, each satellite stays "stationary" or "synchronized" above one point on Earth. That's why you can point your satellite TV dish to one place and leave it there, rather than having to track the satellite and lose communication if it were to pass over the horizon.

It takes more than 10 times more energy, theoretically, to get into geosynchrous Earth orbit from the surface of the Earth than from the surface of the Moon (that is, a circular orbit). The energy required from asteriods near Earth could be less or more than from the Moon, depending on the particular asteroid's orbital properties. Adding in the heavy vehicle and complexity associated with Earth launch, and launching the fuel for later in the flight, getting materials off of the Moon and especially from asteroids is much easier than from Earth.

To escape Earth orbit altogether takes less than 10% more energy than getting to geostationary orbit. Hence, the energy difference between GEO and other bodies besides Earth is often much less.

(One item often quoted by others it that it takes about 22 times more energy to launch from Earth and "escape" to infinity (without going into orbit) than to likewise launch from the Moon and escape to infinity. That is a simple comparison for laymen to illustrate the point, and differs somewhat from the more detailed comparison given here which accounts for getting into various useful circular orbits.)

It's important to understand that it takes just as much energy to come down as it does to go up -- there's no "free downhill". Coming "downhill" takes just as much energy and fuel in space because there is no friction -- you must spend fuel to lower yourself into a circular orbit. (An exception could be "aerobraking", i.e., using the Earth's atmosphere for friction, but no such vehicle has been operated to date except for return to Earth's surface. Aerobraking is discussed in the vehicles section.) Without aerobraking, if you simply brake and fall down in an elliptical orbit, you'll soon be right back at the top of that elliptical orbit and ready for another cycle. To stay at the bottom of the orbit requires that you circularize your orbit when you arrive there by spending more fuel.

Higher orbits have more potential energy but less kinetic energy. In fact, mathematically, to move from a lower orbit to a higher orbit requires spending two parts potential energy for every one part kinetic energy reduced.

Notably, there's no energy shortcut -- if you skip going into an interim orbit but just shoot from the surface of the Earth to a high orbit, you don't save anything, theoretically. However, in practical terms, there are differences between trajectories to get into a circular high orbit so that you can spend significantly more than the theoretical minimum. In general, haste makes waste, in terms of energy and fuel spent. The theoretically best trajectory from Earth's surface to any Earth orbit is to first get into orbital space, so that one isn't fighting against gravity's pull back down, and then to spiral up slowly, thrusting perpendicular to the line of sight with Earth (i.e., adding purely centrifugal force). However, this is rarely followed due to economic factors other than fuel launched (e.g., time and complexity, and radiation belt damage factors).

On the graph: "Sea Level Earth Orbit (SLEO)" just illustrates the minimum energy required to "stay in outer space" rather than standing (or crashing back) on Earth's surface -- Sea Level Earth Orbit is, say, a purely theoretical orbit just one foot above sea level as if there were no atmosphere or hills to crash into. Energy-wise, Sea Level Orbit represents the 93% kinetic energy to get to Shuttle orbit from Earth's surface, as compared to the 7% to lift up above the atmosphere. The Moon also has a "sea level orbit", or since it has "Mares" instead of "Seas", it has a corresponding "Mare Level Orbit".

The entire graph represents the theoretical minimum amount of energy required. However, the more energy required, the more fuel must be lifted for use later. Thus, the rocket size and complexity increase well out of proportion to the theoretical minimum energy required.

Asteroids have no significant escape velocity or "sea level orbital energy", and can be seen as objects already in orbital space. On the chart, they would be located beyond the dashed line above high Earth orbit, energy-wise. Some near Earth asteroids are just a tiny bit above the the dashed line, though most asteroids are significantly above the line. However, an analysis of retrieving asteroidal materials does not lend itself well to the above analysis, largely due to a concept called a "lunar gravity assist", which saves energy by trading orbital energy with the Moon, as discussed below. > Transportation > Theoretical > Earth-Moon System

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