In Plan two, the Hermes bug out occurs, and the team leaves Mars early, resulting in a slightly longer 236 day return to Earth. This plan includes a long deceleration period, to facilitate Earth re-entry and landing procedures.
In Plan Three (Purnell), they return to constant acceleration, in preparation for a slingshot around Earth and subsequent return to Mars. Yet the return time from Mars to Earth still says 236 days.
How can this be? They are accelerating at rate which makes them go 2mm per second faster, every second that they travel. If I’m getting this right, (And I’m probably not) they should be traveling 1,720,000 miles per day faster by the time they arrive at Earth.
Not only that, but each second of acceleration shortens the distance they have to travel to catch up with Earth, so there is a double (well, maybe secondary) effect for the acceleration.
I sent a note to Andy Weir about this through Facebook, and he responded:
I just can’t see how. Even if Plan two arrives at 12:01am on day 236 and Plan Three arrives at 11:59pm, it still seems like too little time has been gained.
You’d have to overlay the original and modified trajectories to verify, but I believe the modified trajectory carves a wider turn (to be expected since it isn’t decelerating) and so covers more distance. That it intercepts on the same day as the original return trajectory is a little coincidental (I think) but it can’t be all that far off either way; the Earth and Mars orbital speed relative to a Sun-fixed coordinate system is 29.8 and 24.1 km/s so the aggregate sped of the probe is always going to be somewhere in between for direct trajectories (except during the swing-by maneuver, as it will pick up speed during the approach to Earth but lose it again as it falls away). I was originally thinking they were adopting one of the identified cycler trajectories (periodic transfers between Earth and Mars that occur at low but not minimal energy trajectories) but this doesn’t look like any of the cycler trajectories I remember offhand.
If you pause two screens at :49 and 1:11, you’ll see that the return circles are nearly identical. The Plan 3 circle looks, if anything, slightly tighter than the Plan 2, and that Plan 2 nonetheless appears to intercept Earth slightly earlier than Plan 3 (gap between intercept point and Earths origination point is slightly wider than in the Plan 3 intercept.)
I can’t really tell by looking at the videos; I’d need to read the ephemerides of both trajectories to see what is going on. But if the Hermes in the modified trajectory is going faster (on average) but intercepts the Earth on the same day then it has to have covered more distance. Reliaze that the function of the swing-by maneuver isn’t really to pick up speed but to make a radical modification in trajectory by transferring momentum between the planet and the spacecraft, and that objects naturally speed up as they fall in closer to the sun per Kepler’s second law, notwithstanding the thrust that Hermes is making while decelerating.
Here is an article discussing, among other things, the Rich Purnell maneuver. Unfortunately they don’t actually reference the trajectory parameters except incidentially, but it does have some interesting discussion.
I just realized I’ve been kind of stupid. The solar orbital speed when leaving Mars is 24.1 km second; at Earth intercept for the original trajectory it would be 29.8 km/s, so Hermes would actually have to accelerate (thrust somewhere along) their trajectory in order to have a zero net velocity intercept with Earth for the original trajectory, while in the modified trajectory you’d want to maximize the velocity difference by not accelerating in order to get the most effect from the swing-by maneuver. I’d still need to look at the ephemerides for each trajectory to understand exactly what change is made, but that would seem to match what they are doing.
Does it mention anywhere the rate of the deceleration?
Thanks, Stranger!
This does illuminatesomewhat, in that it says the acceleration resumed on sol 192. I thought I remembered it as sol 90-ish. So that’s only 50 days of difference, less than half what I was thinking.
Still 50 days at 2mms/second acceleration, means by the time they reached Earth they’dbe going 463,851.11 miles per day faster than if they’d stayed steady (is that right?). Then mark that against whatever the deceleration rate was, and move them correspondingly closer to Earth for intercept? It still seems to me they should be gaining enough to slingshot days earlier.
I’m not a rocket scientist. But wouldn’t the original itinerary have been planned to have the shortest overall travel time? In other words, the travel between Earth and Mars and Mars and Earth would have been when the orbits were best synchronized.
If so, why did the Hermes leave Mars orbit early? They had to leave Mars itself because of the sandstorm but they were safe once they left the planet. Wouldn’t their shortest itinerary have been to stay in orbit around Mars for the time they had planned to spend on the surface and then head back towards Earth on the originally scheduled date?
And on a separate issue, wouldn’t it be unusual for everyone to have gone down to Mars? Wouldn’t NASA normally keep at least one person aboard Hermes while it was in orbit in order to deal with any problems that might arise?
Since Hermes uses nuclear electric ion production it may have much larger windows of transit than the traditional pseudo-Hohmann transfers. If so, it makes sense to bring the crew back sooner, thereby limiting exposure to radiation and the probability of getting caught in a coronal mass ejection or solar particle event.
A pilot was kept on board during the Apollo missions for redundancy (in case guidance or propulsion failed on the LM ascent stage near intercept, the CSM pilot could intercept) and because the LM was only designed for a crew of two. This turned out to not be necessary for any of the Apollo missions and post-Apollo profiles generallly consisted of the entire crew landing. In the case of a Mars mission, it would make sense to have the entire crew on the surface to accomplish as much as possible; any observations an astronaut could make from orbit could be as easily made by an uncrewed probe or satellite.
As I noted, I’m no expert. But my understanding is that because of the fact that Earth and Mars are both orbiting the sun and doing so at different speeds, there are times when it’s a very long journey from Mars to Earth and times when it’s a relatively short journey.
So let’s say that the original plan was for the crew to stay on Mars until November 10 and then head back towards Earth on a trajectory that would take 200 days to complete. Then the mission was aborted on October 29. They could start out towards Earth but the quickest trajectory starting on October 29 would take 230 days to reach Earth.
Under those circumstances, the better plan would be to stay in orbit around Mars until November 10, essentially doing nothing but waiting, and then heading back on the original trajectory. By delaying their departure from Mars for twelve days, they’ll arrive at Earth eighteen days sooner.
I’m thinking more along the lines of dealing with minor mechanical problems (which my understanding is have arisen during space missions).
Let’s say the Hermes orbiter has a fuse blow while it’s in orbit. No big deal but it needs to be fixed some time in the near future. If you have somebody on board, it’s not a problem. But if everyone is down on the surface and there’s only one return vehicle, you’d have to abort the entire mission so everyone could return.