# How long would it take to travel to Eris?

1. Jul 30, 2015

### Karl Coryat

A friend of mine is doing a science-fiction project involving the dwarf planet Eris and wants to employ scientific accuracy. He would like to know, given the orbits, when approximately would be a good time to leave Earth to travel to Eris (using our best current space-travel technology), anytime within the next 1,000 years, and when the craft would arrive there. The craft would not be flying by but would be decelerating so as to orbit Eris -- which I imagine would necessitate coming to a nearly complete stop in Eris' rest frame.

Not to be too demanding, but he'd also love to know how the leave-and-arrive dates would be different if the craft could go twice as fast as our current best technology allows.

I realize these are difficult questions, but Physics Forums members have always been extremely helpful in the past, so I offered to post the problem here. Perhaps someone knows of a calculation applet or something. Thank for any help you can provide!

2. Jul 30, 2015

### DaveC426913

Eris' orbit varies between 40AU (inside Pluto's orbit) and 97 AU. It is currently almost at aphelion, so nearing 97 AU.

New Horizons, our fastest craft, took 9 years to get to Pluto, so if your craft could make 31,000mph, it would take 18 years to fly by. Probably a few years longer to arrive with no residual velocity.

It takes 560 years for Eris to orbit, so in 18 years it will barely have moved (esp. since its nearing aphelion). For the purpose of launch window, Eris is essentially a stationary target.

And it doesn't help that, with an orbital inclination of almost 45 degrees. it'll spend almost all its time nowhere near our orbital plane or any other SS bodies.

They might want to wait until late in the 23rd century (2015 + (560/2)) when Eris will be approaching perihelion, and be only as far away as Pluto.

All that being said, the next two centuries (esp. in a world where planning a trip to Eris is actually viable), our craft speed will surely increase MUCH more than 2X, which will likely render all of the aforesaid moot.

Last edited: Jul 30, 2015
3. Jul 30, 2015

### ohwilleke

The other factor to consider is what kind of craft would be used to make the trip. Several hundred years in the future, something more impressive than chemical rocket engines, such as some form of nuclear propulsion (or heck, even anti-matter), might be available, allowing for shorter travel times and greater payload to fuel ratios due to the greater energy density involved than chemical rockets.

The maximum viable speed limit with arbitrarily powerful engines and no fuel constraints that could be imposed by the passengers in reasonable comfort for a sustained period would be not much more than 1 G of acceleration (9.8 m/s^2), so, if the vehicle could accelerate at 1 G for the first 20 AU and the deccelerate for the second 20 AU, that would pretty much be the fastest possible manned trip anyone could take. At that rate, the entire trip would take about 11 days to Eris from Earth and 11 days back.

Without doing the engineering calculations, my numerical intuition is that the fuel to move a ship at full 1 G continuously for 11 days (assuming the new fuel was available on Eris), even with the energy density of hydrogen bombs, would require fuel to be a prohibitively large share of the total mass of the ship, unless extra fuel could be strategically placed along the way moving at the right velocity to allow for refueling en route. So the actual trip would take longer. But, there is no good reason that a manned spacecraft several hundred years in the future shouldn't be able to travel faster than New Horizons, at least. The calculations ought to be possible to do on the back of a napkin, but I don't have the brainpower left today to do those as well this evening.

4. Jul 30, 2015

### DaveC426913

Sure, but you acknowledge that you are describing a fantasy craft. As you say, any real craft is limited by fuel and/or reaction mass. A ship that can expend fuel and reaction mass at such a rate as to produce constant 1G acceleration to the edge of the solar system is well beyond the OP's specs.

5. Jul 30, 2015

### ohwilleke

Absolutely. If it were morning, I'd do the fuel and reaction mass calculations myself. The main point was to establish an absolute maximum practical speed (which is much slower than any relativistic speed), and then to note that while this is realistically impossible, that it certainly isn't impossible to make the trip in much less than 9 years with improved propulsion technologies that are 1970s technology on paper even if they've never actually been built. The energy density of the fuel used to propel the ship with successive nuclear explosions sketched out in the late 1960s would be roughly 1,000,000 times as great as rocket fuel. If you could use something along that line to get even twelve times the average velocity of New Horizon (which was built for fuel efficiency and not speed since it was unmanned and had only a basic science R&D sized budget), you could make the trip in nine months, instead of 9 years, which is starting to sound realistic for both the passenger and the engineering limitations of the technology, and due to the previously 1 G trip time calculation, we know that this wouldn't impose undue physical stress on the passengers.

One could rotate the craft on the axis of travel to get manageable gravity in between the bursts of acceleration to get to cruising speed and to slow down to land on Eris afterwards.

6. Jul 31, 2015

### Chronos

Using current technology, 15 years looks reasonable, if not optimistic.

7. Jul 31, 2015

### DaveC426913

The OP has said nothing about the mission. Long stay? Short stay? Many people? Few? The reason I ask is because this would affect the mass of the craft, as required by fuel, equipment, supplies and people, which would affect fuel consumption and thus how much fuel needs to be factored in.

8. Jul 31, 2015

### DHF

Another thing to consider for the story is budget. As pointed out, Our current space missions are limited more by money then technology. given the right resources, you can achieve some fantastic figures even with current technology. One of the reasons we did a flyby of Pluto and didn't park in orbit is because it would have required a craft of enormous size to include enough engines and fuel to decelerate. I saw one mockup in Kerbel and the ship was larger then the Empire State Building. So make sure your friend's protagonists are well funded :)

9. Jul 31, 2015

### Karl Coryat

Thank you very much for the help! I know very little of the plot of the story, but I'm sure this will help. If he wants a little more accuracy, I figure it would be easy enough to calculate the tangential velocity at the perihelion and get a linear approximation of the actual travel distance.

10. Jul 31, 2015

### Upsilon

11. Jul 31, 2015

### DHF

Yeah that is probably a project for the next generation.

12. Jul 31, 2015

### Janus

Staff Emeritus
That depends. New Horizons used Jupiter for a sling shot boost, so the majority of its trip was spent with that extra speed. If your craft left Earth at twice the speed New Horizons did, it would also arrive at Jupiter moving faster, this would decrease the angle of deflection of the craft by Jupiter. The less the angle of deflection, the less velocity gain. So your craft wouldn't leave Jupiter with twice the velocity that New Horizons did.
That can be taken care of by performing a broken plane maneuver when the craft crosses the line of nodes. Though granted, this would require extra fuel.
Roughly 2259. Eris' Mean anomaly is 204 degrees which puts it on this side of aphelion and 243.5 years away from perihelion.

13. Jul 31, 2015

### DaveC426913

If it starts off faster, but doesn't gain as much in the boost, that does not necessarily result in a longer total journey.

What I was getting at was that that wouldn't have any chance at boosts. So, yes, it would have to make up for it with fuel. Another reason why the mission engineers might wait for a better window.

That's nearish what I figured. A screenshot from a sim in 2013 showed Eris nearing perihelion. So it would be about 2275 when nearing aphelion. And there'd be a window of quite a few decades to play with, depending on other factors such as velocity matching etc.

14. Jul 31, 2015

### Janus

Staff Emeritus
I wasn't implying that it would take longer, just that leaving Earth with twice the velocity doesn't mean you can't count on the trip as taking half as long. For instance, let's say ship A arrives at Jupiter moving at 10 kps, picks up 4 hps and leaves at 14 kps. Ship B arrives moving at 20 kps but only gains 2 kps and leaves at 22 kps. 22 is only 1.57 times greater than 14, so B traverse the rest of the trip in ~0.64 the time as A not 1/2 the time.