How our spacecraft use physics to navigate the universe

Who has never planned a pleasant family trip and ended up encountering unexpected problems that turned the trip into an adventure worthy of an American comedy? To avoid setbacks, many people plan the best route in advance, choosing strategic stops to fill up the tank and empty their balloons. Even so, they are surprised by the uncertainties of chance that destroy any planning. Now, just imagine how our scientists plan the itinerary of a space trip. A trip of millions of kilometers through the void of space, carrying limited fuel, with no refueling station.

Traveling through space, reaching other planets and exploring the Universe is an old dream of humanity. It was only in the second half of the 20th century that we were able to begin to realize this dream, but this was only possible thanks to the brilliant minds of Johannes Kepler and Isaac Newton. From the distant 17th century, they gave us the maps and tools to plan and carry out our space travels. Kepler described the cosmic dance of the planets around the Sun, with his fundamental laws of celestial mechanics. Newton, with universal gravitation, revealed the invisible force that governs this dance.

Newton even proposed an imaginary experiment that showed that it would be possible to put an object into Earth's orbit. He imagined a cannon launching projectiles from the top of a mountain. If the projectile's speed is low, it will fall back to Earth. But if we launch it with enough speed, it could enter orbit, falling forever without ever touching the ground. Two centuries later, this idea became reality with the launch of Sputnik, the first artificial satellite to orbit our planet.

However, the Soviets did not use a cannon to do this. Instead, they used a rocket, powered by Newton's third law: the law of action and reaction. When rockets expel gases at high speed, they generate a counterforce that propels them upwards, overcoming gravity.

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However, putting an object into Earth's orbit is just the first step, and certainly the most complicated. To complete this stage of the journey, the rocket consumes hundreds of tons of fuel. And it leaves our spacecraft up there with a minimum amount of propellant to continue its journey. And that is why, from then on, it will travel much of the journey to its final destination “in a rut”.

At the top of a hill, a car has potential energy due to Earth's gravity. This potential energy can be converted into kinetic energy if it rolls down the hill slowly. And to travel through space, our spacecraft use this potential energy, but not from Earth's gravity, but from the Sun. So, from the moment it frees itself from Earth's gravitational influence, it is as if it were at the top of a hill 150 million kilometers high. But for this hill to take us to our planned destination, we need a transfer orbit.

Kepler, in his first postulate, described planetary orbits as ellipses with the Sun at one of their foci. Imagine that we are going to send a spacecraft to Mars. The transfer orbit between the two worlds would be an ellipse that is tangent to the orbits of Earth and Mars and has the Sun at one of its foci. From Kepler's third law, we can calculate the time it would take for the spacecraft to reach the destination orbit. For Mars, this time is 8 and a half months. Now, we just need to plan the launch of our spacecraft so that it occurs 8 and a half months before Mars passes through the opposite side of the transfer orbit.

This ideal launch moment is called the “window of opportunity.” In the case of Mars, this window lasts about two weeks and occurs every 26 months. And to reach the transfer orbit, the spacecraft must fire its engines at just the right moment to free itself from Earth’s gravity and accelerate until it reaches the right speed that will take it to its final destination. From then on, it’s all business as usual. Our cosmic traveler will be subject to the laws that govern planetary motion and will only need to fire its engines again at the end of the journey to leave the transfer orbit and enter the orbit of the destination object.

This strategy, called the “Hohmann Transfer Orbit,” was proposed by Walter Hohmann in 1925, and is the most economical way to travel between two worlds. There are also some variations, such as the bi-elliptical transfer, used to achieve very eccentric orbits or to minimize fuel consumption in more complex space missions.

Low-thrust orbital transfer, as the name suggests, uses low-power thrusters that operate for long periods of time. This strategy generally results in longer journeys, but with good fuel economy. Now, to reach more distant worlds, there is a maneuver that provides us with a form of refueling where our ships can get additional energy to go further. It is called “Gravity Assist”.

During a gravity assist, a spacecraft “surfs” on a planet’s gravitational field. Depending on how close it approaches the planet, this can give it extra speed to reach more distant objects and even leave the Solar System. It may seem like a magical violation of the law of conservation of energy, but the physics behind this maneuver is quite elegant. The spacecraft actually “steals” some of the planet’s kinetic energy, which, because it is much more massive, won’t even feel the loss.

The gravitational assist maneuver was proposed at the beginning of the 20th century by Yuri Kondratyuk, a visionary Russian engineer and mathematician who, before we sent any object into space, conceived the navigation strategies that are the basis for interplanetary travel. Among other things, Kondratyuk established the foundations of the orbital rendezvous maneuver, which made it possible to put man on the Moon. In addition, of course, to gravitational assists, the main source of additional energy for our most important space missions.

So, the next time you follow a spacecraft on its journey through the cosmos, remember that behind every maneuver, every trajectory adjustment, there is a team of brilliant scientists and engineers using the laws of physics to guide these spacecraft in their exploration of the universe. The same laws that Kepler and Newton unraveled centuries ago, today allow us to navigate this immense cosmic ocean.