Final answer:
In terms of energy, low Earth orbit (LEO) is considered 'halfway to the edge of the universe' because the kinetic energy needed to maintain orbit is much greater than the energy required to reach the altitude of LEO. Once in orbit, additional energy requirements are relatively smaller to travel further into space, and hence reaching LEO can be seen as a significant step towards interplanetary or interstellar travel.
Step-by-step explanation:
The statement "In terms of energy, low Earth orbit is halfway to the edge of the universe" is a surprising but mathematically factual way of looking at the energy required to reach space. To enter low Earth orbit (LEO), a satellite must fight against Earth's gravity to reach an altitude of about 600 km. However, the challenge does not end there; the satellite also requires a significant amount of kinetic energy to maintain its orbit. In fact, the energy required to accelerate the satellite to orbital velocity is significantly greater than that needed simply to lift it to that altitude.
When considering the energy balance for a satellite in orbit, it is known that for circular orbits, the kinetic energy (KE) is half the magnitude of the potential energy (PE), but with opposite sign. In essence, KE = 1/2 |PE|, and the total energy of the orbiting satellite, i.e., the sum of KE and PE, is negative. This negative total energy indicates a bound orbit. The concept is that a satellite with zero or positive total energy would have enough energy to break free from Earth's gravity (become unbound) and travel into deep space.
As we go further out into space, towards geostationary orbit (about 36,000 km) and the Moon (about 385,000 km), the additional energy needed increases. However, once a satellite reaches a stable orbit around Earth, it no longer needs to constantly fight against gravity. Therefore, the greatest portion of energy expenditure is spent on achieving orbital velocity. It is in this sense that it is said once you have reached LEO, you have expended a large share of the energy necessary to travel much farther into space, thereby being 'halfway to the edge of the universe'.