Being Smart Will Get You A Rendezvous With Mars, Here’s How
Do you know how Voyager-2 could visit all four gas giants of our Solar System, and then escape the gravitational pull of the Sun forever? Before its launch on August 20, 1977, NASA scientists analyzed all planets, and could take advantage of a 175-year planetary alignment. Using gravitational assist manoeuvres, Voyager-2 has exceeded the Solar System’s escape velocity, and is now travelling at 15.341 km/s (55,230 km/h) relative to the Sun. With that speed, one could travel from New York to Los Angeles in just 4 minutes 22 seconds. (You would probably get there and back by the time you finish reading this article.)
But how could NASA people know when to launch? And how do they know when should we launch our spacecraft to Mars? Can’t we just go every day, and go where Mars is?
Well, we could, but it would take a lot of energy, and in some cases, it’s just impossible. In this article, I want to dive deeper into Launch Periods & Windows, and hopefully, by the end, you will understand these concepts, as well as synodic periods, payload fraction, mass ratio, the Oberth effect, Hohmann transfer orbits, Porkchop plots, and a few other things.
I hope your mind is open and you are ready to digest some knowledge.
What’s the difference between Launch Periods and Windows?
Launch Periods are just a collection of days in the calendar, during which a particular mission must be launched. Launch Windows, on the other hand, are the exact time intervals on a given day in the launch period.
Don’t worry, most people confuse this, but if you want to use correct terminology among smart people, you better get this right. I have a very easy way to remember this, and I’m going to share my secret with you now. Just think about how long women’s periods are. It takes days, right? Usually a week. There are also calendars to track one’s periods, so it’s surely not hours. It’s the same in space exploration, so it’s easy to remember. Periods for the calendar, windows for the hours. Easy.
So, what’s the use of these launch opportunities? We need them to be able to rendezvous with another spacecraft, planet, or other point in outer space. And no, not to rendezvous with people from the other gender. That’s for a different topic.
We also need to be extremely careful with timing (just like women’s periods…) because orbital overlap is needed for mission success. When planning our space endeavours, we need to shoot where our target will be, not where it is now. It’s very similar to how a quarterback throws a forward pass. They aim for where the receiver will be, not where he is. Launch windows can be just a second long, called an instantaneous window, or they can spread throughout the entire day. If the window happens to be close to midnight, it can stretch over two calendar days as well, from 11 pm to 1 am, for example.
There’s a saying that “Man plans, god laughs”, and I find this fascinating. In Hungarian (my native language) it translates a little differently, but the meaning is the same. We have plans, and something usually screws them over. Then, we feel bad, because we feel like our future was stolen from us.
In spaceflight, there can be a ginormous number of reasons to delay a launch, and potentially miss the window, or the whole period. Usually bad weather, or technical malfunction with the rocket or secondary equipment. As a result, the mission is postponed to the next launch window or period. For example, ESA’s Rosetta mission was originally intented to launch in January 2003, and rendezvous with comet 46P/Wirtanen in 2011, but after an Ariane 5 rocket’s failure, the mission was grounded, and the opportunity was missed. Five months later in May, a new target was identified called comet 67P/Churyumov–Gerasimenko, and after launching in February 2004, Rosetta completed the rendezvous in 2014.
How do we know when to launch to Mars?
There are many factors we need to consider, but with current launch vehicles, the most prominent are energy and travel time. We need to identify the lowest-energy Hohmann transfer orbit: an elliptical orbit used to travel between two circular orbits. Such an orbit requires the least amount of energy, in our case: fuel. The less energy we need, the more payload we can carry with a fully loaded rocket.
The closer the target is, the less delta-v we need. The distance between Earth and Mars ranges from 58 to over 400 million kilometers, as the chart below shows us. For the most efficient way to travel, we need to launch around the time of oppositions, and we definitely should avoid conjunctions, as they need more fuel, which means much lower payload mass.
I notice a pattern here. And whenever I see a pattern, my mind wants to identify it. A synodic period is an observable characteristic of two bodies (in this case, Earth and Mars), which orbit a third body (The Sun) in different orbits. The time between conjunctions is the synodic period.
If Earth’s and Mars’ orbital periods are P₁ and P₂ respectively, so P₁ < P₂, their synodic period is calculated by the following equation:
Earth’s orbital period is 1 year (365.26 days), and Mars’ is 1.881 years (686.98 Earth days). If we solve the equation for Psyn, we get 2.135 years, meaning Earth and Mars are in opposition every 780 days. That’s why we launch our Martian missions every 26 months or so.
In 2018, the window was between April and May, and we launched the InSight mission. The next opportunity will be between July and September 2020, hopefully launching Rosalind Franklin and Mars 2020 among other missions. That doesn’t mean we can’t launch at other times, but these are the most effective periods. To visualize this, engineers use porkchop plots.
What is a porkchop plot?
Also known as a pork-chop plot, is a chart that shows contours of equal characteristic energy (C3) against combinations of launch date and arrival date for a particular interplanetary flight.
This chart represents curves of constant C3, called porkchop curves. These curves tell us when the launch opportunity is, that’s compatible with the capabilities of a particular spacecraft. Here, the blue curves represent lower required delta-v, whereas the red ones represent higher required delta-v.
Lambert’s problem or theorem was first solved in 1761 by Johann Heinrich Lambert, and it identifies the orbital elements of the solution. Departure date, arrival date and length of flight.
If we take a fully loaded spacecraft, let’s take Falcon Heavy (FH) for example, it has specific payload capabilities it can carry to specific destinations. Reaching LEO (low-earth orbit) takes the least delta-v, so FH can carry it’s most payload to that destination (63.8 tonnes). As we need to increase delta-v to get to GTO (geostationary transfer orbit), the payload decreases (only 26.7 tonnes). Mars needs even more delta-v, decreasing the payload capability further (16.8 tonnes). But that’s calculated for the most effective orbit. As we take a less optimal launch period or window (going toward the red porkchop curves), the payload capability decreases, making the same rocket less effective.
Characterizing the efficiency of a rocket
In aerospace engineering, understanding vehicle effectiveness is critical. This is done by calculating the payload fraction, which equals payload mass divided by takeoff mass. For commercial airlines, this is a useful metric, as the number is around 25–55%, the bigger the payload fraction, the further an aircraft can fly, as it is more effective.
For spacecraft, however, this number stays below 1%, so a much better way to measure rocket efficiency is mass ratio. It’s very simple, let me show you:
Mass ratio = wet mass/dry mass = (vehicle + contents + propellant / vehicle + contents). Lower mass ratio means less propellant needed for a given goal, meaning a more efficient design. On the other hand, higher mass ratio can mean higher absolute delta-v, thus a more powerful rocket. Engineers need to carefully balance power and efficiency when designing rockets. You can have a ridiculously effective rocket, but if it can only bring 1 liter of milk to the ISS, it’s of no use. On the other hand, if you want to bring 10 tonnes of supplies, launching it atop of Saturn V is probably an overkill.
Typical multistage rockets have a mass ratio between 8 and 20: Space Shuttle: 15.4, BFR (2017): 18.7, Saturn V: 23.1. (Unfortunately, I haven’t found reliable data to Falcon rockets or the Starship. If you have these numbers, please comment below with a source, so I can update the article. Thanks!)
After identifying our launch period and window, as well as the rocket for our needs, we need to know the orbits we want to use to get to Mars. And this is where the Oberth effect comes into view.
What is the Oberth effect?
The Oberth effect is a phenomena that happens during powered flyby. As the rocket is falling into a gravitational well, accelerating at maximum speed is much more effective than any other acceleration, which means a more effective manoeuvre. This is what engineers used to give Voyager-2 so much momentum that it has left the heliosphere by now.
For us, we don’t want to visit other stars just yet, it’s enough if we can get to Mars. To do that, first we need to get to LEO. Then, depending on the impulse period, we need to get to the Hohmann transfer orbit to Mars in one, or multiple impulses. Using more impulses is more effective (slowly increasing the apogee, by firing the engines at the perigee), but takes more time.
Once we’re on the way to Mars, we may need to do TCMs (Trajectory Correction Manoeuvres) to make sure we don’t miss. InSight had planned six of these. But for most of the time, it’s just a chill drifting in space. Except you don’t have a fabulous view on Earth, you’re weightless, so you constantly lose muscle mass, bone density, and movement coordination; and you’re constantly being bombarded with powerful ionizing radiation. I’m going to write more on these topics later on, but it doesn’t seem like a trip to Hawaii. Nor like an escape plan for rich people, after they screw up our planet. But I’m gonna leave this topic for a different day.
As we approach Mars, we need to slow down to reach Mars orbit. Again, using the Oberth effect, the best way to do this is as close to Mars as possible. After getting into Mars orbit, we can start our landing sequence, starting with a de-orbit manoeuvre, aerobraking, and landing.
Congratulations, you’ve landed on Mars!
We’ve covered a lot of ground today, let me summarize briefly. We identified our optimal time to launch, we figured out how to choose our rocket, and we learned what path we need to take to get there. Wow, what a ride!
But our trip doesn’t stop here, heck, it’s just starting. I’m writing many more articles on Medium about Mars-related topics in the coming days. Don’t miss out, just tap Follow Marstronauts below or on the side (mobile and desktop, respectively).
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Thanks so much for taking your time, I hope it was worthwhile. Here are some links to check my account Marstronauts on social media, in case you’d like to keep in touch. :)
