# Using maths to lower the cost of space travel 🚀 👀

With current advances in technology, exploring our solar system is easier than it has ever been. But these missions are still quite rare since the amount of money needed for space travel remains very high! 💵💵 A mathematical concept called the Arnold diffusion mechanism (I’ll explain this later), however, is being used to reduce the amount of fuel needed for these trips (one of the major costs of space travel 💵) by finding the most efficient routes (those that need the least fuel).

But the most efficient route is in a straight line right?! 🤔 Well this is usually the case on earth but, with the gravitational forces present in space, a straight path isn’t always the best idea. Each planet and their moons 🌓 as well as stars ⭐️ and asteroids ☄️ have gravitational forces surrounding them which pull the rockets without the need to use fuel. By using this, strange looping routes actually become more efficient than straight routes through space. So back to the Arnold diffusion concept – the idea is that if a small amount of force from the engine is applied at the right time and location, then it has a big impact on the movement of the rocket. Maths can be used, therefore, to find the precise times and positions, where a small fire of the engine will be enough to give large distances of space travel.🚀