Quirks & Quarks·Analysis

The Artemis mission to the moon is being guided by Kepler, Newton and Einstein

Bob McDonald's blog: Mathematical laws of motion and gravity that go back hundreds of years underpin our ability to guide spacecraft to distant destinations.

Bob McDonald's blog: Our understanding of fundamental laws of gravity and motion make these missions possible

A spacecraft in a black sky above a blue planet
Illustration of NASA's Orion capsule being boosted out of Earth orbit. (NASA)

NASA's Orion capsule is a triumph of technology and engineering. But its complicated, figure-eight path as it travels from the Earth out beyond the moon and back owes everything to some fundamental laws discovered starting hundreds of years ago.

The machines might be modern, but the ideas came from Johannes Kepler, Isaac Newton and Albert Einstein. 

In some ways spacecraft are like projectiles fired from a cannon. They get all their energy at the beginning of the flight, then mostly coast freely for the rest of the journey, with a trajectory determined by the laws of physics. Thanks to deep thinkers from the past, these laws have been laid down with such accuracy that we are able to shoot rockets at a moving target more than 300,000 km away with a cannonball that takes three days to get there.

From the very first moment the Space Launch System rocket engines ignite, Isaac Newton's third law of motion, comes into play. The action of hot gasses expanding from a rocket nozzle, causes an equal and opposite reaction that lifts the gigantic machine upwards and sideways (downrange, in rocket terminology), faster and faster, and out of the Earth's atmosphere.

An illustration showing a spacecraft orbiting the Earth and moon.
During the Artemis I mission, the Orion capsule will follow a complex figure-eight orbit to approach the moon and return to Earth. (NASA)

The sideways motion is critical. The rocket has to reach, not just the right height, but the right speed, relative to the Earth's surface, to stay in orbit before it cuts its engines. At that point it's free falling, as gravity pulls it toward the planet's surface, and its precise speed makes sure it misses.

Another way to think about it, is that it's circling around the walls of the Earth's gravity well. Albert Einstein pictured space as a flexible membrane that could be stretched and curved by mass, like the surface of a trampoline. Picture a bowling ball in the centre of the trampoline creating a cone shaped depression with the spacecraft as a baseball rolling around it following the curve. That curve in spacetime is what we perceive as gravity.

After one orbit around the Earth, Newton was called on again as Orion's rocket engine was fired to give the spacecraft the extra velocity it needed to climb up out of the gravity well and head out toward the moon. The outbound journey is a curved path because both the Earth and moon are orbiting in the sun's gravity well, which extends all the way out to the edge of the solar system. 

Artist's impression of the Earth's gravity well. (NASA)

Calculating trajectories that will take into account all these factors, and find a path that will take Orion into orbit around the moon, is a daunting mathematical task. Fortunately, working out all the geometric complexities is possible in part because of principles Johannes Kepler figured out 400 years ago. Kepler's laws were derived to explain the elliptical paths of planets going around the sun, and calculate the speeds objects travel at different parts of their orbits. 

As the spacecraft leaves the gravity well of the Earth, it falls into a second, smaller well created by the moon. When it arrives at the moon, the rocket engine is fired again to slow the spacecraft down just enough so it will be captured by the moon's gravity well and go into a precise orbit there.

The changing gravitational forces that guide the spacecraft from the Earth to the moon and back were also calculated by Newton, who found that gravity depends on the mass of an object and how close you are to it. The moon is smaller than the Earth, so it exerts less gravitational pull.

Circa 1615, Johannes Kepler is the German astronomer who worked out the laws of planetary orbits. (Hulton Archive/Getty Images)

All of these factors had to be taken into account by the scientists and engineers who fly spacecraft to get it safely to the moon and back again.

We tend to focus on the technological marvels of rockets and space capsules, and the brave astronauts. But if it wasn't for the basic science governing the laws of motion that brilliant minds started to reveal centuries ago, we would not be able to reach other worlds at all.

Basic science is often underrated, or even criticized for pursuing obscure subjects such as black holes, that don't seem to have practical applications here on Earth. But those studies could lead to future inventions we haven't even imagined. Who knows where a better understanding of extreme gravity could take us?

There is also the less practical, more philosophical notion of the benefit of knowledge just for the sake of understanding our universe. 

WATCH: NASA Video describing the Artemis I mission to the moon


Bob McDonald is the host of CBC Radio's award-winning weekly science program, Quirks & Quarks. He is also a science commentator for CBC News Network and CBC-TV's The National. He has received 12 honorary degrees and is an Officer of the Order of Canada.