Spacecraft have different trajectories with different destinations and are launched at different times. How is a spacecraft trajectory designed, and what parameters govern the decision process? Let’s find out about them in this article.

#### Before You Design Spacecraft Trajectory

In the process of designing a journey that a space probe would take, we must first learn about the positions, orbits, speeds of planets and targets of interest. That’s because you apparently need the location of the target to reach it.

However, it is not very simple, as the objects also move around our star as the spacecraft travels towards them. Therefore, you should go for intercepting the object instead of aiming it towards the target like throwing a ball. That’s why the orbits and the speeds, not just the positions and distances, are in the list of parameters.

At first, you may think that it is just as easy as simply estimating the circular trajectory of the target and aiming at it in a straight line using a spacecraft. Nevertheless, this concept is entirely wrong, as interplanetary spacecraft orbit the Sun to save fuel costs. You can still get to a celestial object in our Solar System in orbit around our star, and it conserves fuel costs given that the spacecraft’s velocity never exceeds the escape velocity of the Sun, whereas it must do so if it were to travel in a straight line across the planetary system.

Therefore, substantial knowledge about orbital mechanics and transfer orbits will be needed to design spacecraft trajectories. We’ll explore these in the next section.

#### Transfer Orbits

To get from one planet to another, we need a transfer orbit. It takes the spacecraft on an elliptical trajectory that intersects with the origin’s and destination’s orbit. For instance, if you launch a space probe to Mars, you’ll want to apply acceleration to the spacecraft to distance its aphelion away from the Sun by just the right amount so that it intercepts Mars with the minimum amount of acceleration. Since any change in orbit requires acceleration and fuel, the optimal path is to let it circle the Sun by half an orbit, launching from Earth from one side and arriving at Mars on the opposite side. The same principle is true for other planetary combinations, though the required acceleration will not be the same.

This type of transfer orbit is called the Hohmann transfer orbit and is one of the most common ways to get from one planet to another in modern space missions.

There are other types of transfer orbits, but they mainly adjust the orbits of space probes around our planet. Hohmann transfer orbits and its variants are often still necessary for interplanetary missions.

#### Launch Windows

When you talk about rendezvous with another object, ensure you launch your spacecraft at the right time. For example, imagine that you launch a mission to Mars when Earth and Mars are in opposite directions from the Sun. Mars is also moving like other planets as the spacecraft moves for half a lap around our star. By the time the spacecraft reaches Mars’s orbit, the target is not there anymore, leaving the spacecraft with many laps to circle before it meets the planet by chance, and it cannot achieve its scientific objectives within the span of decades or even centuries.

Therefore, to make sure a spacecraft arrives at a target at the soonest time, you have to wait for the orbital arrangements for what we call the launch window. The time where the space probe can launch is calculated through the alignments of the planets and the orbit that the spacecraft will take. Once it is well-defined, the mission team works on the schedule and waits for an opportunity to launch as they prepare the spacecraft.

However, it is not very simple. For instance, if a rare planetary arrangement occurs only once in a few decades, you may be better off taking more convoluted paths that take longer to reach the target. That way, the mission time will be lengthened, but the waiting time could be shortened by a larger degree, making the spacecraft reach its destination sooner.

#### Gravity Assists

For destinations that require more acceleration for a transfer orbit, the power of a single launch vehicle may be insufficient. Instead, it must accelerate mid-flight with a relatively low fuel quantity. Here’s where gravity assists come in: They exchange angular momentum between the planet and the spacecraft. Its purpose is to naturally accelerate or decelerate a spacecraft, thus putting it into a different orbit from the original one.

Here is also where the trajectory of a spacecraft becomes complicated, especially if the mission requires more than one gravity assist. If there is only one gravity assist in the journey, you could search for a launch window where three objects align optimally. Nonetheless, if there are multiple gravity assists, there are many possibilities of what you could do, so it likely requires an extensive computer search to look for the shortest path with the shortest amount of waiting time to the launch window.

#### Conclusion

Today, we’ve explored how spacecraft trajectory is designed to reach its destination and do science as soon as possible. Even if the trajectory is configured properly, there may still be unexpected errors during launch, resulting in the need for in-flight correction maneuvers. If we’ve missed any crucial parameters we should have included, please leave them in the comments below.