Rendezvous in space

The images of the recent docking of a Dragon spacecraft with the International Space Station were impressive.

The spacecraft gently lined up, moved in slowly and docked. It all looked so graceful and simple. In fact, keeping a rendezvous in space is anything but simple, and not intuitive.

Imagine you are on a spacecraft on its way to the International Space Station (ISS). You are, say 2,000 kilometres behind the space station, lined up in the same orbit. Since you are moving at the same speed as the space station, you will never catch up with it, so you fire the engine for a few seconds.

Your spacecraft accelerates, you see the distance to your destination start to drop, and then you notice something funny. You are moving up into a higher orbit, and slowing down, and the space station is getting further and further away.

This is actually what would happen. Why?

When we try to move a stationary object or change the direction of a moving object, it resists. We call this resistance to change inertia. A curving path, like a spacecraft orbit, is a continuous change in direction. The resistance to this changing direction manifests itself as an outward force, often called centrifugal force.

This force increases with speed and tightness of the curve. A spacecraft moving in orbit is following a balance between gravity pulling down, and centrifugal force pushing out.

For every height above the ground, there is a specific velocity that meets this balance. When we fired our engines, we accelerated the spacecraft, breaking that balance. The centrifugal force then exceeded the pull of gravity, and we moved outward, into a higher orbit.

Climbing against gravity takes energy, which slows the spacecraft down, just like throwing a ball in the air.

The trick is to drop into a lower orbit, by slowing down. As you drop, you speed up. Orbital speeds increase as you get lower, and because lower orbits are also smaller, you overtake objects in higher orbits.

As you overtake the space station, you use the engine to speed up, which makes you rise and slow down, and rendezvous with the space station. Now, it is a matter of docking, using precision sensors and thrusters.

This procedure would work, but it is wasteful. It is better to design the mission from launch to rendezvous, calculating the path of the spacecraft so that the launch process delivers our spacecraft close to the rendezvous point.

Since the actual docking consists of something with a mass of tonnes having a slow-speed collision with something else with an even larger mass, this has to be carefully managed.

It has to be slow and the meeting face on. This is easiest if the docking assembly is at the front of the spacecraft. Having the docking device in front means the astronauts can see directly exactly what is going on, to deal with problems if they arise.

Secondly, that docking assembly, which often includes an airlock, is fairly heavy. So for stability and structural strength reasons it is best located on the centreline of the spacecraft. Since the engine at the rear needs to be on the centreline, the docking assembly has to be on the nose.

The fact that these space-docking procedures are now standard is due to technological improvements over years. In the development leading up to the Apollo space missions, things were more uncertain, and in at least one case, the docked vehicles went into a wild tumble that was only brought under control by prompt action of an astronaut.

Since the Apollo Moon missions depended on multiple docking operations, they had to be as safe and as well understood as possible. That they go so smoothly these days does not mean we should take them for granted.

• After dark, Saturn and Jupiter lie close together, low in the southwest
• Mars lies fairly high in the southeast.
• Venus lies low in the dawn glow.
• The Moon reaches Last Quarter on Dec. 7. 

This article is written by or on behalf of an outsourced columnist and does not necessarily reflect the views of Castanet.