Once a satellite is launched into space, depending on its mission, it soon settles into an orbit around a body, like a planet or the moon and continues on its orbit. This is not a smooth ride however; the satellite receives numerous gravitational tugs to from other gravitational sources, which need to be corrected for to keep the satellite in the preferred orbit. There are however special points around objects, like the earth where a satellite in orbit can remain stable with relatively little corrections. These special spots are called Lagrange points, locations in space where the gravitational forces of two large celestial bodies (like the Sun and Earth) and the centripetal force of a smaller object (like a satellite) balance out. They're like gravitational parking spots where a spacecraft can hover with minimal energy. The Sun-Earth system has five Lagrange points - L1 to L5.
Reaching the Lagrange point however does not automatically guarantee stability. This is where station-keeping comes in – the art of using thrusters to make tiny adjustments and keep the spacecraft exactly where it needs to be. Researchers from Space Applications Centre, ISRO, Ahmedabad and Indian Institute of Technology (IIT) Kharagpur, have been looking into the best ways for station-keeping for spacecraft in halo orbits around the Sun-Earth L1 point.
Did you Know? Typically, two large objects exert an uneven gravitational pull at any given location, which usually disrupts the orbit of anything present there. However, at Lagrange points, the gravitational forces from these two large bodies, along with the centrifugal force, achieve a perfect equilibrium. |
Halo orbits are can be thought of as the three-dimensional paths that loop around a Lagrange point, kind of like a halo around a saint's head. These orbits are naturally unstable, meaning even a slight push can send a spacecraft drifting. Station keeping allows researchers to constantly monitor and correct for any instability. However, since this is the classical three-body problem with the sun, earth and the satellite all interacting, finding solutions to this complex problem can be quite a challenge.
Two main strategies used for station keeping are: the target point approach (TPA) and the linear quadratic regulator (LQR) method. The TPA works by planning a series of minor course corrections that aim to guide the spacecraft through specific target points along its intended path. The researchers used a technique called a genetic algorithm (GA) to figure out the best timing for these corrections, or manoeuvre intervals, to save as much fuel as possible. They tested this with different numbers of future target points, anywhere from two to five.
On the other hand, the LQR method is a more systematic approach. It uses math to figure out the best way to apply thrust to minimise errors and keep the spacecraft on its path, essentially trying to find the most efficient way to correct any deviation. The method is akin to a intelligent autopilot that constantly calculates the perfect adjustments.
In their new study, the team compared the performance of the two models to provide ideal solutions for our space mission. The study, involved creating simulated halo orbits with different sizes and then introducing realistic errors or nudges to their starting positions. For small disturbances, the TPA method, especially using two or five target points, was more fuel-efficient. It used less fuel to get the spacecraft back on track.
However, as the initial errors got bigger the TPA methods started to struggle. The 2-TPA, for example, became less efficient and required more fuel. Interestingly, the 5-TPA, which wasn't as good with small errors, actually became the most efficient when dealing with large disturbances, outperforming the other TPA methods. The LQR method, while generally using more fuel, proved to be more robust and better at handling these larger errors, keeping the spacecraft's path more stable.
The study suggests that for missions where a little drift is acceptable, the TPA can save a lot of fuel. But for missions that require extremely precise positioning, the LQR method might be a better, albeit more fuel-hungry, choice. The researchers also transformed their data into a frame that's easier for real-world missions to use, making their findings more practical.
Knowing which station-keeping strategy works best under different conditions can help engineers design missions that are more fuel-efficient and last longer. The detailed analysis helps mission planners make informed decisions, ensuring that our spacecraft can continue their important work, whether it's observing distant stars or monitoring our own Sun, without running out of precious fuel.
This article was written with the help of generative AI and edited by an editor at Research Matters.