Think of the last time you pulled up to a fast food drive-in window. What cues did you use to judge distances? Why didn’t you hit the curb? Can you describe exactly how to drive your car so that your arm is close enough to the window to grab your food? what would you say? Now try all of that in outer space. Proximity operations refer to the operation of spacecraft in near or close contact with another object. These types of maneuvers may be used for observing another spacecraft, performing an orbital rendezvous to transfer supplies and crew, or performing maintenance on another spacecraft.
Orbits
Parking orbits are orbits that are a temporary stop between a spacecraft and it’s intended destination. These are used to make time for testing onboard systems before launching out to another planet, or to make time for mission planning. Once a spacecraft is ready to move on with it’s mission it needs to transfer to a different orbit.
It is challenging and costly to refuel a spacecraft once it’s in space, so the efficiency of maneuvers is essential for fuel savings. More fuel savings means longer missions. One of the most energy efficient ways to transfer from one orbit to another is called the Hohmann transfer.
To calculate the hohmann transfer orbit between 2 circular orbits you need to find the dimensions of the ellipse that touches both orbits at it’s lowest and highest point. Then you find the velocity differences between the original orbits and the transfer orbits. These results tell you how much you need to speed up to get to the other orbit.
The Direct transfer uses more fuel but takes less time than the Hohmann transfer. It consists of a more aggressive departure and arrival angle. This corresponds with a requirement for greater energy expenditure from the spacecraft.
To visualize how spacecraft operate in the vicinity of each other, imagine a soccer player is standing on a satellite. The player imparts a velocity change to the ball when they kick it. The ball is now moving faster than the player. Here’s where the weird things start. From the point of view of the player, the ball would travel forward and then start rising. Why does this happen?
The ball would not lose energy like on earth because there is no air resistance.. The ball is in a different orbit than the player. Due to the increase in total energy the ball transfers its additional kinetic energy into orbital height. Therefore the ball appears to rise from the perspective of the player. Objects in higher orbits move slower than objects in lower orbits so as the ball rises it slows down. From the perspective of the player, the ball travels forward, rises up, and appears to slow down with the player passing underneath the ball. After one complete orbit, the ball reaches it’s original altitude but it is behind the player.
If the player wanted to pass the ball to another player standing on a different spacecraft in front of him on the same orbit, they would have to kick the ball backward. As the ball moves backward it loses some of its total energy and will fall to a lower orbit. The ball will speed up because lower orbits are faster orbits. By the time it reaches its original altitude, it is ahead of the player that kicked it.
Zero G forward pass image
Zero G backward pass image
The mnemonic to remember when Performing phasing maneuvers is speed-up to slow down, and slow-down to speed up.
Let’s look at an example that shows this counterintuitive behavior. First lets look at two orbiting objects with one object that has an orbit that is 100m higher than the other. From the perspective of the
Frames of Reference
In space to compare relationships between two objects you use a frame of reference. The body Frame is the reference frame that is located at the center of mass of a spacecraft. This reference frame tells you where you would need to look if you were sitting in the spacecraft. The other important reference frame is the Inertial reference frame. This reference frame is used to determine the orbits of spacecraft with respect to the earth. You can define arbitrary reference frames if it suits your problem. For this example, we use a target frame to distinguish between the body frame of one spacecraft and the body frame of the satellite it’s trying to get to.
body frame coordinates
target frame coordinates
inertial frame coordinates
One common body frame coordinate system is the NED system, this stands for North, East, Down. The x-axis is out the front of the vehicle. The y-axis is facing the direction that would be east if the x-axis is facing north. Finally the z-axis is pointing in the down direction in relation to the “north” and “east” axes. With these coordinate system, roll is a rotation around the x-axis, yaw is a rotation around the z-axis, and pitch is a rotation around the y-axis.
Safety
There are many satellites in the sky and it’s vitally important to ensure that none of them collide. A collision will cause catastrophic damage to the spacecraft involved, and the debris field could also endanger other spacecraft.
There are a series of conceptual boundaries called a safety ellipsoid to help prevent collisions. We can’t know the exact position of a spacecraft but we do know the probability that it would reside in a possible location. This probability forms the basis of using safety ellipsoids for avoiding (deconflicting) satellites that would otherwise run the risk of colliding with each other. The specific dimensions of this ellipsoid are chosen to ensure that as long as other spacecraft remain outside of this volume, the probability of collision is less than a defined value.
It’s great to have safety measures involved to prevent accidental collisions, but what if your goal is to connect one spacecraft to another? You need to know how to use orbital dynamics to put your vehicle in the same space at the same time as another. These rendezvous maneuvers are shown with respect to the reference frame of the target spacecraft. As shown below the far rang approach is similar to what was described above, with the soccer player passing the ball. From the reference frame of the target spacecraft, (the ISS) The realtive motion of elliptical orbits make these strange bouncing-ball trajectories.
V-bar
R-bar
Maneuvers
When performing a rendezvous of two spacecraft there is a common reference frame that puts orbits and relative positions and velocities in perspective. This reference frame is the inertial reference frame of the spacecraft that is not maneuvering. There are 3 axes that make up this reference frame, the Velocity vector, the Radial Vector and the Horizontal vector. A V-bar approach is an approach where the chasing spacecraft makes progressively smaller hops along the line determined by the velocity of the orbiting target spacecraft. This happens from either direction but it occurs after basic orbit phasing has been established.
Another common close approach trajectory is the R-Bar approach. This is similar to the v-bar approach except that the spacecraft is moving along the line that points from the center of the earth through the target spacecraft.
Conclusion
As the space above us gets more cluttered, we will need to devise ways to keep spacecraft safe from malfunctioning or defunct satellites. There are various ways to be able to safely de-orbit a satellite or a piece of spacecraft debris. The challenging part is to be able to reach the object in order to move/refuel or attach other devices to it. Along with ongoing human operations in space, the accurate maneuvering of spacecraft in close proximity to each other will be a skill that continues to be essential in our increasingly-connected electronic world.