SpaceProf.xyz || Nibbles in Space: 000A16

How do you move around in space?

November 2020 || 000A16

3 - 4 minute read

Title image is an artist’s impression of the joint ESA & JAXA BepiColombo spacecraft in cruise configuration with the ion thrusters firing. Image Credit: ESA/ATG medialab

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The ability to move from one orbit to another is pretty important for a lot of things we might want to do in space. At its simplest, a spacecraft can change its orbit by changing its velocity. And, perhaps surprisingly, to go higher you need to go slower.

On Earth, to increase the speed of a rowing boat the oar applies a pressure to the water that causes the oar and boat to move.

In space, there is nothing much to push against. So, the main way of changing the velocity of a spacecraft is to take part of the mass of the spacecraft, and eject it. The force required to do so creates an equal and opposite force on the spacecraft, meaning the spacecraft changes velocity. This is the basic principal of function of a rocket, and is what happens when you let the air escape from a balloon, and the balloon flies across the room.

Generally speaking, rockets can be categorised as either chemical or electric propulsion, which broadly corresponds to a high- or low-thrust. Electric systems take longer to change the spacecraft velocity, but tend to require less mass be ejected from the spacecraft.

The simplest and most common approximation to changing orbit using chemical propulsion is termed a Hohmann transfer, after Walter Hohmann. Typically, this provides the minimum required change in velocity between two orbits. A Hohmann transfer is an arc, or intermediate orbit, connecting the two orbits with the start and end of the arc tangential to each orbit. It requires the spacecraft’s rockets to fire twice, once at either end of the arc to enter the intermediate orbit, and to leave it and enter the target orbit.

This basic principal can be applied to large or small transfers, and can even help with the rendezvous and docking of spacecraft.

The use of low-thrust, electric propulsion to change orbit altitude is often approximated with continuous thrust, rather than the impulses assumed for chemical propulsion. This creates a very different type of orbit transfer, approximated as a spiral, and taking several orbit revolutions to complete the transfer.

To change an orbit in in three-dimensions, that is to change the plane in which the spacecraft orbits, requires an out of plane force, and anything but small plane changes require a lot of energy, which can make such manoeuvres prohibitive.

The motion of a spacecraft around Earth can be approximated as a curve, or specifically a conic section. Such an approximation is termed Keplerian motion, after the description provided by Johannes Kepler’s laws of planetary motion.

Whilst this is a good approximation, it’s just that. An approximation. And, at times, due to the external forces acting on a spacecraft it can be a poor approximation. These forces acting on a spacecraft’s motion are termed perturbing forces.

As the word perturb suggests, perturbing forces generally cause a spacecraft to stray from its desired path. But, they can also be used to help maintain a desired path, or to change an orbit.

Up to an altitude of, at least, 1000km the Earth’s atmosphere will cause a drag force on a spacecraft, this will cause its orbit to lose energy, and the spacecraft to lose altitude, slowly spiralling towards Earth. Generally, this is undesirable, but it can be used to help remove a spacecraft from orbit at the end of its life.

Similar to an orbit not being a perfect ellipse, the Earth is not a perfect sphere. The Earth’s true shape is complex, but it’s typical to approximate the Earth as having a bulge around the centre. In-fact, the Earth’s diameter is almost 43km more at the equator than between the poles.

Visualisation of the Earth's shape from ESA's GOCE mission. Image credit: ESA

Without any perturbing force on the spacecraft, the orbit plane will stay stationary with the Earth rotating underneath it. This means as the Earth itself moves around the Sun, the relative geometry of the orbit to the Sun varies over a year. For an orbit passing over the poles, it might start off edge-on the Sun, and three months later it would be face-on, because the Earth has moved one quarter of the way around the Sun.

The Earth’s equatorial bulge however means that for an orbit passing over the poles, the Earth’s gravity isn’t directed towards the centre of the Earth. Instead, it’s slightly out of the orbit plane, towards the equator. This perturbs the spacecrafts motion and although it doesn’t affect the spacecraft’s altitude, it can be used to change the orbit plane, causing it to rotate with respect to the Earth rather than staying stationary.

It turns out, this rotation with respect to the Earth can be used to make the orbit plane appear stationary with respect to the Sun without the need for propulsion. So, as the Earth rotates around the Sun, the orbit plane also rotates at just under on degree per day to maintain a constant alignment. This is termed a Sun-synchronous orbit, it is used in Earth observation missions to maintain consistent illumination of the ground throughout the year. It can also be used to avoid the spacecraft ever entering the Earth’s shadow, and so working with the space environment, rather than against it, allows spacecraft to do things that would otherwise be far more difficult.

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