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The Scourge of Space Junk, Part 1: Orbital Mechanics

Artist’s impression of the many objects now in Earth orbit

Artist’s impression of the many objects now in Earth orbit.
Image credit: esa

Planet Earth sits at the centre of an orbiting scrapyard. But this is no static pile; it’s a cloud of junk moving at speeds of up to 18,000 mph. International Space Station (ISS) crews live and work in this shooting gallery where even a fleck of paint travelling at high speed has enough momentum to punch a hole through the thin skin of the ISS. The amount of stuff in orbit is growing at a phenomenal rate: whole constellations of satellites in Low-Earth Orbit (LEO) are replacing single units in geostationary orbit. Tiny CubeSats are being deployed practically on a daily basis, and when a dead and out-of-control satellite collides with something else, thousands of potentially deadly fragments fly in all directions.

Clearing the Junk

Before 1957, the only object known to be in orbit around the Earth was the Moon. In fact, there were, indeed are, many rocks (asteroids) moving around silently and largely invisible until recently. The launch of Sputnik in 1957 saw the first artificial satellite in an elliptical orbit 134 miles up at its lowest point. At that low height, it encountered wisps of atmosphere and the speed loss due to friction effects eventually led to it heading back to Earth and ‘burning-up’ a year later. A lot of junk has been destroyed by natural orbital decay over the years, but much of it in higher orbits will remain a hazard for decades, even centuries. There are a number of options:

  • ‘Destroy’ the object using a missile and warhead fired from another spacecraft or from the surface. This is the worst possible way of doing it – only in the movies does an explosive device ‘vaporise’ a target completely. In fact, it just creates a bigger problem with many more hard-to-detect bits of wreckage heading off in random directions.
  • At the satellite’s design stage incorporate an end-of-life mechanism – not explosive self-destruct – such as retro rockets to slow it down and force a de-orbit.
  • Use an orbiting trash-collector robot that will apply a non-destructive force to the satellite to cause a de-orbit. See Part 2 for some of the ideas under development.
  • Move the defunct satellite into a higher ‘graveyard’ orbit. This method of disposal is used already when the object is too big to be certain of burn-up before it hits the ground, or it has something nasty on-board, like a nuclear power source. When the Soviet spy-satellite Kosmos 954 failed and made an uncontrolled re-entry in 1978, it scattered radioactive debris all over the Canadian tundra. By a miracle, no-one was killed or injured.

 

A 2.9-tonne pallet of dead batteries ejected from the ISS

A 2.9-tonne pallet of dead batteries ejected from the ISS as I wrote this article. Hopefully, it will burn-up in a few years, if nothing collides with it.                                                                   Image credit: NASA

Orbital Mechanics

Once you start thinking about the ways by which this existing cosmic scrapyard might be cleaned up, it becomes clear that an understanding of the forces that created it in the first place is required before coming up with a method of dismantling it. Sir Isaac Newton, inspired by the work of Kepler and Galileo, published his laws of motion in the book Philosophiæ Naturalis Principia Mathematica in 1687. Until recently, these simple laws or formulae have been used to describe the motion of everything from atoms to planets. At the atomic and sub-atomic end of the scale, they don’t work so well and have been superseded by the theories of Quantum Mechanics based on probability, not certainty. But in the world of satellite orbits and planetary motion, they work just fine!

Newton’s Laws of Motion

  1. “Every object remains at rest or in uniform motion in a straight line unless compelled to change its state by the action of an external force”.
  2. “The rate of change of momentum of a body over time is directly proportional to the force applied, and occurs in the same direction as the applied force”. This is usually presented in the form of an equation: Force = Mass x Acceleration (F = ma)
  3. “When body A exerts a force on body B, body B will exert an equal, but opposite force on body A”. Or as I learned in school: For every action, there is an equal and opposite reaction.

 

These laws apply to any object in motion anywhere, on the surface of a planet or in the depths of Space. However, Newton went further and defined the force of attraction between two bodies, the force we know as Gravity: "The force of gravity between two bodies is directly proportional to the product of their two masses and inversely proportional to the square of the distance between them".

Forces of gravity equation

Newton’s Laws work so much ‘better’ in Space

I’ll elaborate on that statement as it’s technically not true. Perhaps I should say that it is a whole lot simpler to create a flight plan for a spacecraft journey over millions of miles than it is for, say, thousands of miles in an aircraft on Earth. Now the movements of both aircraft and spacecraft are governed by Newton’s laws, but because the aircraft is operating in an atmosphere it is subject to four basic forces during its journey: Thrust, Drag, Lift and Weight. The first three are affected by prevailing atmospheric conditions (weather) which can be unpredictable. Even the mass varies during a journey as fuel is used continuously and gravity varies with altitude, albeit predictably. The First Law suggests that all you need to do to get a body moving and continue to move in the same direction forever is to give it a sharp kick. That would be true in the absence of frictional forces due to the air (i.e. in a vacuum) and of course, gravitational forces (literally universally present to some degree).

Now let’s look at the forces encountered while moving through Space. With no atmosphere, all those unpredictable forces disappear. That leaves the thrust of the rocket engine (when it’s running) and the combined effects of gravity from any nearby stars, planets or moons. And that’s about it. The rocket engine, whether driven with chemical, electrical or nuclear energy, is ideal for use in Space as it offers a near-perfect implementation of Newton’s Third Law. They were originally invented for use in the Earth’s atmosphere and not long ago many believed that it was the force of the hot gasses emitted, acting against air particles, that drove the rocket upwards. If that were true, Sputnik wouldn’t have made it into orbit and astronauts would have remained the stuff of science fiction.

Mathematics of an Orbit

I’ll leave principles of getting from the surface of the Earth and into a stable orbit for another time. Suffice to say, the rocket does not go up vertically until the required altitude is reached, then stopping and releasing the satellite. If it did, then both rocket and payload would be impacting the ground not far from where they started a short time later. Assuming we deliver the payload in the right way and it begins its orbit, what keeps it there? Firstly, orbits do not have to be circular; planetary orbits around the Sun are mostly elliptical, but artificial satellite orbits are generally made circular for operational convenience with the exception of the important Molnyia orbit. Fig.1a illustrates the variety of sizes and inclinations in use. The LEO orbit at any inclination is the most popular and consequently the most cluttered with non-functional equipment and debris. Note that objects moving in the same general direction as the Earth is rotating are said to be in prograde orbits. Otherwise, they are described as being in a retrograde orbit.

Forces in a circular orbit

The maths (Fig.1b) characterising circular orbits in Space is a special case of the ‘Two-Body Problem’ and is based around a simple equation that balances the gravitational force of the Earth against the centripetal force generated by the satellite as it whirls around with a velocity v. The formula gives the orbital velocity of the satellite that needs to be achieved after launching for an orbit of the required altitude A. The higher the altitude, the slower the velocity. So, for a LEO of 150 miles (242 km) the orbital velocity needs to be about 17,000 mph (27,359 kph). A single orbit then takes about 90 minutes. The calculation can be reversed to find the altitude necessary for an orbital period of 24 hours: Geostationary orbit: 22,236 miles (35,786 km) at v = 7,000 mph (11,300 kph).

All this orbital mechanics stuff is important when it comes to designing de-orbiting robots that need to find and approach the target. It’s not like driving a car on the surface: precise engine ‘burns’ need to be performed to bring about a change in orbit or indeed to ‘catch-up’ with the target once the robot has arrived in the same orbit. It’s all about changing position in Space by using thrusters to make a precise change in velocity: the ‘delta-V’ (ΔV), not by turning a steering wheel. Some of that junk will have suffered a collision and been pushed into a higher, perhaps elliptical orbit with a different inclination making tracking and acquisition even more difficult.

Nothing is ‘weightless’

A key takeaway from this discussion is that an object in Earth orbit is not ‘weightless’ and it’s certainly not experiencing ‘zero-gravity’. The ISS and the astronauts within it may feel as if Earth’s gravity has disappeared, but it’s still there, albeit reduced by altitude, and constantly trying to pull them down. What keeps them up is that balancing centripetal force produced by the station’s orbital velocity of 15,500 mph. If you whirl a solid ball on the end of a piece of string around your head, it’s centripetal force that keeps the ball in the air and the string taut. The astronauts feel weightless because they too are held in this balance of forces. From Newton’s gravity law it might be assumed that the astronauts with their small mass might experience different forces from that of the ISS itself with its larger mass. Take a look at the equation in Fig.1b again. The mass of the orbiting body mS appears on both sides so it just cancels out, making the orbit of an object independent of its own mass. That’s lucky!

In Part 2

I’ll take a look at some of the proposed solutions to the orbiting junk problem. Readers may recall that I’m involved in a project to send a couple of hundred tiny Sprite satellites into orbit. Should they make it into LEO, it will be at a low altitude and they should burn-up a few weeks later.

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Engineer, PhD, lecturer, freelance technical writer, blogger & tweeter interested in robots, AI, planetary explorers and all things electronic. STEM ambassador. Designed, built and programmed my first microcomputer in 1976. Still learning, still building, still coding today.
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