Dennis Tito’s 500-Day Mission to Mars – the Orbital Mechanics

28 February 2013 by Michael Khan, posted in Uncategorized

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 2018 7 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 days 501 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:

Ecliptic Projection of Trajectory for 500 Day Manned Mission to Mars Launched in Jan. 2018

Credit: Michael Khan/ESA Ecliptic Projection of Trajectory for 500 Day Manned Mission to Mars Launched in Jan. 2018

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.

Sun, Earth, Mars and Venus Distance Profile for 500 Day Manned Mission to Mars, launched in Jan. 2018

Credit: Michael Khan/ESA Sun, Earth, Mars and Venus Distance Profile for 500 Day Manned Mission to Mars, launched in Jan. 2018

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.

Earth Entry Locations Latitude over Local Time, for 500 Day Manned Mars Mission, Launched in Jan. 2018

Credit: Michael Khan/ESA Earth Entry Locations Latitude over Local Time, for 500 Day Manned Mars Mission, Launched in Jan. 2018

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.

Entry Velocity as Function of Latitude and Local Solar Time for Return from 500 day Manned Mission to Mars Launched in Jan. 2018

Credit: Michael Khan/ESA Entry Velocity as Function of Latitude and Local Solar Time for Return from 500 day Manned Mission to Mars Launched in Jan. 2018

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.

18 Responses to “Dennis Tito’s 500-Day Mission to Mars – the Orbital Mechanics”

  1. Tony Mach Reply | Permalink

    What I don't understand is that this a special opportunity in 2018. I read that the next such window would be 2031. But isn't there a Mars launch window every two years (give or take). So what is special about 2018 compared to to say 2020 or 2022?

    • Michael Khan Reply | Permalink

      I didn't check the subsequent opportunities. However, the fact that there is a launch window to Mars every 25-26 months does not mean that there also is a launch window that allows you to go to Mars, perform a close swingby, insert on a fast return back to the Earth, all in around 500 days and with no deep space manoeuvres. I think that therein lies the rub. It sure would be a good idea to check this out in more detail.

    • Jeff Reply | Permalink

      Think about the Solar Max/Min cycle. This is in the middle of Solar Min.

  2. Danniel Qeletti Reply | Permalink

    Well, putting all the Earth-re-entry calculations aside: if we can send human-beings all the way to Mars, I should have thought we'd rather let them also land there and form a Permanent Terran Base on that planet. But, just travelling the entire way, and go back? Sounds like quite a waste.

    • Michael Khan Reply | Permalink

      I am not sure I am the right person to answer this. After all, it wasn't me who thought up that scheme; that was Dennis Tito. I just redid the trajectory calculations, out of personal interest, truth be told.

      However, and irrelevantly, I do have an opinion on this. Several opinions, in fact:

      1.) The whole point of the proposed scheme is to send people to Mars and back at an effort that is orders of magnitude less than that of a landing mission. The upside is that a small spacecraft will suffice, as it doesn't have to take much propellant. For a manned landing mission, you'd be looking at a behemoth spacecraft that is assembled in Earth orbit, with a mass of 750 - 1500 metric tons, most of that beong propellant. Such a craft would include very complex and costly technology to land on Mars, spend months there and lift off again.

      One doesn't need all of that in Tito's scheme, so that saves Giga-oodles of $$$ and years in development time. Of course there then also has to be a drawback, and the drawback is that one can't land and do real Mars science. I think that the Mars science opportunities in this scheme are nil. To put it cynically: the only thing that can be done is to demonstrate crew survivability for a long-term interplanetary mission, provided that the crew does survive. If it doesn't, then at least it will provide some data on how things can go wrong.

      2.) I can only hope that there will be demonstrator flights of this craft, first without, than with a crew, prior to sending it out on a Mars swingby mission. An option would be to perform first a free return trajectory mission to the Moon. That would constitute an end-to-end test of the entire system, from launch to re-entry, albeit with a mission duration of ~1 week. For a more prolonged test, still with the option to return to Earth at relatively short notice, one could do a multiple lunar swingby mission, i.e., one swingby targets at the Moon one month later and so forth, until a final swingby targets back at the Earth.

      When all such tests are satisfactory, a Mars mission can be attempted.

  3. Steve Schaper Reply | Permalink

    Where will Venus be during the flyby of its orbit?

    • Michael Khan Reply | Permalink

      It will be far from the spacecraft. I did not include the Venus position into my trajectory plot, but you can see the distance between Venus and spacecraft in the second diagram. They never approach to less than a mutual distance of 0.7 AU. That's more than 100 million kilometers. No chance of getting some close-up Venus observations, if that was what you were thinking of ...

  4. Andos Reply | Permalink

    I think they referred to the minimum altitude at Mars as 100 miles, i.e. 160 km. Not sure if that impacts your calculations at all.

    • Michael Khan Reply | Permalink

      You're absolutely right, 100 miles it is. Sorry, my bad. I just re-did the calculations assuming the corrected Mars flyby altitude. The launch date shifts by 1 day to 7 January 2018, so in fact I now do have a 501 day mission too. In terms of escape velocity, distances from Sun, Earth etc. and Earth return conditions, no change.

      Thanks for pointing that out.

  5. Ed Davies Reply | Permalink

    It's interesting that the departure from Earth is inwards towards the Sun. Am I right in thinking that a minimum boost would be required if the transfer orbit was tangential to the Earth's orbit and so this orbit must be being optimised for minimum time?

    One might also wonder why the departure isn't made at the point when the transfer orbit crosses the Earth's orbit on the "uphill" leg. Is that just a matter of the phasing of the planets with Mars' very eccentric orbit or is the difference in inclinations of the orbits also important?

    • Michael Khan Reply | Permalink

      You are right in stating that an energy optimal transfer to Mars only would result in (near-)tangential departure and arrival, but that is not the optimization goal underlying the trajectory design in this specific case. Here the aim is to get to Mars, perform a swingby and get back to Earth without a waiting period around Mars, and all that without deep space manoeuvres. Given these constraining parameters, one can't be too picky about energy-optimal transfers; one has to make the best of what one can from the given orbital geometry.

      • Ed Davies Reply | Permalink

        Ah, yes, thanks. It would be a bit of a disappointment for them to swing past Mars into a transfer orbit back towards Earth's then get there and find that Earth is somewhere else.

        I have to admit that I was a bit surprised how little change is visible in the spacecraft's orbit as a result of the Mars encounter.

        • Michael Khan Reply | Permalink

          I just checked. The Mars swingby mainly has an effect on the semi-major axis and thee eccentricity, and therefore on the perihelion and aphelion radii. While the outbound transfer as peri- and aphelion radii of 134 and 214 million km, respectively, these radii are changed to 110 and 207 million km, respectively, on the inbound trajectory. So in fact, the main effect is lowering the perihelion. There also is a minor change in inclination and a shift in the orientation of the orbit, i.e., the line of apsides. This is a bit difficult to see in the diagram, because there you only see part of the two orbits. It would be much more obvious if you could see both orbits super-imposed.

  6. Jan Hattenbach Reply | Permalink

    "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."

    Yes, it is, and I'm missing any ideas to solve this problem. It seem to me it's regarded in many articles as a minor obstacle, with a solution at hand. That is wrong. During a 500 day flight, the chance of a high-energy Solar Particle Event (SPE) hitting the spacecraft (even in solar minimum) may be close to 1, and is impossible to predict over such long timescales. Without any proper radiation shielding (eg. magnetic), there`s a good chance those brave astronauts won't make it home alive, or without serious radiation damage.

    "Normal" manned space-flight never leaves the relatively save area around earth, the fact that the Apollo missions did not face any serious threats by SPEs was just luck:

    "Except for the Apollo missions to the Moon, NASA's manned spaceflight missions have taken place within the cocoon of the Earth's magnetosphere. Between the Apollo 16 and 17 missions, one of the largest solar proton events ever recorded occurred, and it produced radiation levels of sufficient energy for the astronauts outside of the Earth's magnetosphere to absorb lethal doses within 10 hours after the start of the event. It is indeed fortunate that the timing of this event did not coincide with one of the Apollo missions. As NASA ponders the feasibility of sending manned spaceflight missions back to the Moon or to other planets, radiation protection for crew members remains one of the key technological issues which must be resolved."

    Do we have any technology feasible to protect astronauts on long interplanetary missions? I do not think so.

    • Michael Khan Reply | Permalink

      To the best of my knowledge, the solution commonly envisaged for radiation protection is to:

      a.) minimize the background exposure for corpuscular radiation emanating from the Sun by arranging water and fuel tanks (any sizeable layer of hydrogen-rich material offers an efficient protection against these fairly low-energy particles. mostly protons and electrons) around the walls of the habitat such that they consititute a radiation shield and

      b.) provide a "storm shelter" with added shielding for solar flares and the subsequent vastly increased flux of charged particles. The storm shelter doesn't have to be large because the crew will not have to spend more than a few days in it. Its added shielding material does lead to a mass penalty, but that is non-negotiable for extended manned operations.

      In the given case, one might think of using the entry capsule as storm shelter. The crew can take refuge there in the event of a flare, after which they will have some hours of warning before the shower of particles reaches them.

      Of course there also are galactic cosmic rays but there is not much one can do against those unless we are talking about very large space ships ... which here, we certainly are not.

      To me, the radiation issue, though arguably extremely important, is just one of the many things that can go badly wrong. In a bare-bones spacecraft, there by necessity will be little to no redundancy. A micrometeorite or a faulty seal might render the inflatable habitat unusable .... and then what? The ship should undergo extensive end-to-end testing on shorter missions, but I wonder whether there will be time for such prudent precautions.

  7. Mahdi Reply | Permalink

    Why have you shown the orbits of planets circular? Aren't they elliptical ?

    • Michael Khan Reply | Permalink

      The orbits of the planets are displayed as they come out of the ephemeris files that are commonly used for astrodynamics computations. I think that if you look a bit more closely you will see that the orbits of Mars and mercury are in fact quite visibly elliptical.

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