Dennis Tito’s 500-Day Mission to Mars – the Orbital Mechanics
You'll all have heard of Dennis Tito's idea about sending a manned mission to Mars that would take 500 days (well, 501, actually). Launched in January 2018, a small manned spacecraft would fly to Mars, skim past the red planet and use its gravity to send it on an Earth return trajectory.
This is without any doubt a bold concept, one that is fraught with perils and technical challenges. I can't claim to know the answers to all questions that arise. One thing I do know about is celestial mechanics. So what I did is to apply my knowledge to recalculate the trajectory both ways (out- and inbound), based on the information I have. I know that launch shall take place in January 2018, that the minimum altitude at Mars flyby shall be 100
km miles (=162 km, which means the spacecraft will actually be dipping into the tenuous upper atmosphere, albeit briefly), that the transfers shall be free of deep space manoeuvres (so no large propulsion stage is required once Earth escape is achieved) and that the total duration shall be around 500 days. That is sufficient information to get started.
I will spare you the details on the mathematical process. The main thing is that I immediately found a solution that should be very close to what Dennis Tito's mission concept is based on. Small wonder; it is a rather straightforward math problem. The salient results I obtained are as follows:
- Launch date:
8 January 20187 January 2018
- Hyperbolic escape velocity 6.2 km/s (rather high but feasible for a large launch vehicle even with a manned spacecraft)
- Mars swing-by date: 21 August 2018 (Earth-Mars transfer duration 226 days)
- Earth arrival date: 22 May 2019 (Mars-Earth transfer duration 275 days)
- Total mission duration
500 days501 days
- Hyperbolic Earth arrival velocity 8.9 km/s. That definitely is high and will make the design and choice of materials for the heat shield of the entry capsule non-trivial to a high degree
- No delta-v manoeuvres required either on the out- or the inbound arc, other than small trajectory corrections for targeting
So that's it, in a nutshell. Now let's look at the obtained results in a bit more detail. First, I plot the trajectories as seen from looking down from over the north pole of the ecliptic (the plane in which the Earth revolves around the Sun). The outbound trajectory (Earth to Mars) is shown in red, the inbound trajectory (Mars to Earth) in purple:
Next, the distances from the Sun, the Earth, Mars and Venus. You can see that the maximum distance from the Earth is around 1 astronomical unit (AU). this means that radio signals from the Earth will take 8 minutes to reach the spacecraft and it will take another 8 minutes for a reply to reach the Earth. So the crew will have to operate autonomously. That's the essence of it. You can also see that while the maximum distance from the Sun is 1.4 AU, at the time of the Mars encounter, the minimum Sun distance is less than 0.75 AU, on the way back.
That's not so good, but it's typical for this class of fast Mars missions. In essence it means that they will have to design the spacecraft such that it will work at both half and double the power and heat received from the Sun compared to the conditions we have at the Earth. That is a challenge for sure, but it can be done. The low minimum solar range also has implications for the radiation loads, solar corpuscular radiation probably constituting the single most important threat to the crew.
Next, the entry conditions. I don't know how what atmospheric entry conditions they plan to baseline. Too steep, the heat flux and g-loads go off-scale. Too shallow, integrated heat load gets too large, the landing accuracy suffers or you might start having to worry about not achieving capture and instead skipping back out of the atmosphere, which would be a major disaster for the crew. I assumed an entry angle range between -11 and -13 degrees, which is likely a bit steep. It doesn't make a big difference for the sake of this analysis, so let's just stick with this assumption for now.
The diagram below shows on the horizontal axis the local solar time and on the vertical axis the geographical latitude of the entry locations. It also shows the sub-solar point at the date of Earth arrival (at 12 h local solar time, obviously, and the terminator), the direction from which the spacecraft will approach the Earth and the locations in which it enters the atmosphere. Now, there are several things that are not good here. Firstly, the spacecraft will approach the Earth almost directly from the Sun, which will may impede communications and interfere with orbit determination. Then, entry and landing will in all instances take place on the night side of the Earth, with prograde landing (landing in the same direction as the Earth rotates around its axis, so the actual entry velocity is reduced a bit) taking place in the early evening, just after sunset and touchdown taking place a bit further into the night, due to the distance travelled between entry and landing. Neither issue necessarily constitutes a show stopper, but they certainly don't make life easier for the mission designers.
OK, one more diagram and we're through for today, I promise. This one's the velocity als function of entry latitude.For prograde entry you have to look at the left end of the graph, where the lower values are. The lowest possible entry velocity is a bit above 13.8 km/s, if entry takes place near the equator. If the range of possible entry locations shall include also moderate latitudes, the velocity rises to 13.9 km/s. This is a fundamental input parameter for the heat shield design. By the way, this diagram also shows that for retrograde entry, you'd have to design the system to cope with over 14.6 km/s, which one certainly would not want to do if it's not strictly necessary.
We could now start to look at the Mars swing-by in some more detail, but I think I will do that in a later post.