When is the right time to launch a spacecraft from Earth to Mars?
Timing is important here: Earth and Mars are constantly moving,
and the distance between the two planets is constantly changing.
Earth takes about
365 days to make a full orbit around the sun.
Mars, meanwhile moves more slowly. It takes about
687 days for the Red Planet to make its own full orbit.
And because of these different paces, sometimes the two planets are closer together, and sometimes the two planets are further apart.
And every once in a while Earth and Mars line up
such that the Sun and Mars are on directly opposite sides of the Earth.
And around that time — a time known as opposition—  the Earth and Mars are about as close together as they'll ever be.
But how often does opposition happen?
Well, knowing how long each planet takes to complete its own orbit,
we can do some math to estimate how many Earth days it would take for the Earth with the
365-day orbit to complete one full orbit and then catch back up to Mars with the
687-day orbit.
Solving the equation tells us that it takes a little over two years — or about every 26 months or so —
for Earth and mars to line up again.
It might seem like that would be the best time to launch a spacecraft.
After all, the distances between the two planets is as small as it can be,
so that should make for a time-efficient and fuel-efficient journey.
But it's not quite that simple, and we quickly run into some problems.
The first is that Mars is moving. If we were to launch a spacecraft
traveling in a straight line from Earth out to Mars during opposition,
by the time the spacecraft made it to Mars's orbit, Mars would have long passed, as it continues its own orbit around the Sun.
And furthermore, it's not just the Earth and Mars orbiting around the Sun.
The spacecraft is orbiting too. It's orbiting the Sun while on Earth since Earth itself is orbiting the Sun.
And after the spacecraft is launched, the spacecraft is then following its own orbit around the sun, too.
So, in order to get to Mars, we need to think not about traveling in a straight line,
but instead about adjusting the spacecraft's orbit. It begins on Earth's orbit, and we want to move it into Mars's orbit.
And it turns out that the most energy efficient way to do this is something called the Hohmann transfer orbit,
In which the spacecraft starts on Earth's orbit,
and we add just enough energy to move our spacecraft onto a so-called "transfer orbit"
that ends up bringing the spacecraft to Mars's orbit, by the time the spacecraft has traveled
180 degrees around the Sun.
The distance the spacecraft travels is therefore going to be a longer distance
than the direct path between Earth and Mars during opposition.
But the goal here is energy efficiency.
Rocket fuel is heavy and rocket fuel is expensive, so maximizing energy efficiency with the Hohmann transfer orbit
makes for a practical and comparatively affordable journey to the Red Planet.
Using this strategy, this means that when the spacecraft launches, it starts on Earth on one side of the Sun,
gains energy to enter a transfer orbit, and then needs to intercept Mars just at the moment that the spacecraft reaches
precisely the opposite side of the Sun.
And from there,
we can work backwards to figure out just where Earth and Mars need to be relative to each other
when the spacecraft is first launched.
We still need to wait for just the right alignment of the planets, which happens only once every 26 months,
during a narrow period of time known as the launch window
when the planets are in the right positions to make this kind of journey possible.
And if we miss a launch window,
we'll generally then need to wait another 26 months until the planets return to the right relative positions once again
before we can begin another launch.
And then, if we want to make a round trip and return to Earth after we're done on Mars,
the whole process repeats again in reverse.
We can't just leave Mars whenever we want since, if we follow the Hohmann transfer orbit back to Earth's orbit,
It's likely that the Earth won't be at the right place in its orbit when we return.
So we have to wait for a different launch window, waiting to start the return journey
so that by the end of our journey, Earth is there waiting for us.
Actually planning a trip to Mars is even more complicated, though.
Our model has been assuming that Earth and Mars make perfectly circular orbits,
but that's not entirely true. The orbits of Earth and Mars aren't perfect circles,
they're actually elliptical, or oval-shaped. And Mars's orbit is more elliptical than Earth's orbit, which is closer to a full circle.
And, as a result,
the planets aren't always traveling at constant speeds. And to complicate matters even further,
Earth and Mars don't even orbit on precisely the same plane.
Mars's orbit has an inclination almost two degrees offset from that of Earth.
All of these factors make traveling to Mars a task that requires an incredible amount of planning and precision.
But with our knowledge of planetary motion, we can and have made the journey happen with today's technology
when the launch window is right, once every 26 months.
