# How fast is too fast for travel inside the solar system?

I'm looking past the science of fuels and star ship engine details at this point because I'm trying to establish speed limits around our solar system. My initial idea was to use TIME TO DESTINATION as the concept that sets travel speed.

While I picture different speed zones for different areas, one highspeed example is getting from Mars to Jupiter in two weeks. That would require an average speed of 1.5 million kilometers per hour.

3.5 AU = 525 Gm / 14 d = 1'562'500 km/h Roughly half a day of constant 1G acceleration will get you to 1'562'500 km/h by the way, which makes me want to speed up the ship to get more 1G time. However, IRL, the fastest manmade object in space will be a solar satellite that will hit a peak speed in 2025 that doesn't come close to 1.5 Gm/h which makes me doubt my ships should be going so fast.

I'm just having such a hard time envisioning things because the numbers are so wild. I worry about suicide pilots disintegrating entire cities so there's a need for a whole defense array of detectors etc and I worry about ships disintegrating in space by colliding with debris or stray objects that just don't matter at slower speeds.

Making a plot accommodate two weeks of travel time feels like a nightmare task when it should be an opportunity (I guess). So in the end, I'm asking this: What real dangers face a ship traveling even faster than 1.5 Gm/h in our solar system? I'd like to negotiate or navigate those elements with careful writing and planning but cannot envision them.

• Interplanetary spacecraft aren't booking around at ~400 km/s not because of some speed limit imposed by dangers but energy constraints. It would take vast amounts not currently at our disposal. If we could do it we would, 400 km/s is crazy but not crazy.
– BMF
Jan 25 at 23:29
• I can't answer this question - but all I can think of is this: "Excuse me Mr Alien, but do you know how fast you were going? It's clearly signposted that in a Solar System Area, the speed limit is 500,000 Kph. Any reason we were doing nearly 3 times the speed limit? I'd like to see your Licence and registration please and your Craft's certificate of Fitness" Jan 26 at 0:07
• this will be determined more by your tech level than anything else
– John
Jan 26 at 1:37
• Over the speed of light.... Jan 26 at 7:20
• As written, this is unanswerable. You've said that you're trying to establish speed limits, but you haven't said what kind of limits you're talking about. Are you talking about some authority imposing a speed limit, like we have on most roads? If so, then it's a political process and you need to define why they are imposing the speed limit. Are you really asking "how fast can I get my ships to go?" If so, that's a technological limitation which depends on the tech-level in your story, which you haven't defined. Jan 26 at 18:44

If you manage to overcome your colliding-with-dust problem, here's another.

In space, you don't naturally slow down (except by colliding with things). While you're avoiding that, you're sustaining your 400+ km/sec. That is far above solar system escape velocity. If your engines stop working, you will hurtle out into interstellar space. Rescuing you will be quite expensive, and you aren't going fast enough for interstellar travel on any useful timescale.

• HO HO HO! Rescue? From flat space? There is nothing that can possibly be on that ship that is worth chasing it out, matching orbits, turning around , flying home, and landing. ∆v would be exorbitant. Just delete his browser history and forget about him. Jan 27 at 5:56
• @chiggsy Rendez-vous is going to be far cheaper if they're still within heliocentric space than if they're careening at 24x the escape velocity. Jan 28 at 11:08
• Well if traveling around at 400 km/sec has become routine, then rescuing you will be expensive but not prohibitively so. Just send the tow truck out at 500 km/sec. It'd probably be like buying an intercontinental flight. Very costly but you're not gonna leave someone for dead because of it. Jan 29 at 19:31

This speed is 4x10^5 m/s, which means the energy released after collision of a meteoroid with mass 1 kg will be 8x10^10 joules, or 2x10^4 (in kg of TNT).

So, we need to estimate what is a mass of a meteoroid that we are likely to hit on the way. We have some estimates of the number of meteorites that hit Earth, per square meter per second; since our ship moves 10 times faster, we will have roughly 10 times more collisions. Assume that we tolerate a probability of 10^{-5} that our ship will be destroyed, and let the cross-section be 100 m^2. The trip takes about 10^6 seconds. That means that we are concerned for meteorites that hit the Earth at rate 10^{-14} per m^2 s. According to the data, this corresponds to the mass of about 10^{-3} kg. So, the impact we need to withstand is about 20 kg TNT.

If you are willing to spend that much fuel, though, you can just as well spend a bit more and go out of the ecliptic, where (I think) much fewer meteoroids are expected.

As for crushing into cities: if the ship weighs, say, 100 tons, the energy of impact would be be about 4 times the Chelyabinsk meteor, or 1.600 megaton TNT. However, since the Chelyabinsk meteor exploded very high, it did not destroy any cities, only broke some windows.

• 200 kg TNT over a 10^6 second trip is on average 840 Watts of power, spread over 100 m^2. Doesn't sound too troubling.
– BMF
Jan 26 at 0:46
• this is a great point speed limits are not set by how fast the car can go but how fast it can go and still avoid a crash.
– John
Jan 26 at 1:37
• @BMF Except its not spread over the while 10^6 second trip. It plows into you over the course of nanoseconds or less Jan 26 at 3:49
• @CortAmmon If I follow the math right, OP finds the flux density of 1 kg impacts at 10^-14 per m^2 per second, then totals it across the length of the trip to find 10^-3 kg and (an updated) figure of 20 kg TNT kinetic energy. The distribution of particle sizes means you're liable to hit a few sand grains, but mostly dust and hydrogen
– BMF
Jan 26 at 10:45
• @BMF, no, this is not flux density, 10^{-14} is the number of collisions with meteoriods with mass 10^{-3}, per m^2 per second. This will mean that the expected number of collisions with such meteoroid during the trip is of order 10^{-5} , which means that with about that probability, we will hit one such meteoroid. (I don't know which probability we should consider "to risky", 10^{-5} feels about right for regular passenger travel) Jan 26 at 19:14

At your speed (around 434 km/s), a mote of dust weighing a single milligram will have an impact with the same energy as a 20-gram TNT explosive, so unless your ship is capable of tanking hit after hit after hit from military-grade missiles, it definitely won't be able to fly anywhere near the speeds you propose. At a speed of 252'000 km/h (much, much less than your proposed 1'562'500 km/h), the same mote of dust will still hit like half a kilogram of TNT, which will probably still destroy your ship.

Sounds like you need to be able to stop the damage, because otherwise, the damage will definitely stop you before you can get anywhere near as fast as you want.

The issue you refer to is the hypervelocity impact that even small micrometeoroids could have on your ship (or conversely, the hypervelocity impact that your ship would have on people). For the latter, the solution is simple: have the ship's computers prevent the orbital maneuvers required to direct a ship into a planet's surface at speed. Orbital mechanics require some thought going into them, and adding a computer to do it for you has the benefits of a) the pilot not having to do those calculations and b) the ship being able to prevent the use of a starship as a kinetic kill vehicle.

Would a computer still be able to be hijacked and used as a weapon? Of course, but why even use a ship? If you want to destroy something at great distance in the exact same way but for cheaper and without expending human lives, simply attach one of your engines to a giant fuel tank and fire it straight towards your enemy. Whatever engine works for your spaceship will just as well work for kinetic kill vehicles.

As far as preventing damage to your ship, you may be interested in the Whipple shield. This is a real technology that is in use on the ISS that uses spaced armor to disperse the energy of the impact to make it more manageable before the projectile hits the ship. This consists of several relatively-thin plates, not intended to stop or even slow down the micrometeorite that much, but rather to break it up into smaller pieces which individually carry less energy and can be more effectively deflected by regular armor.

In your case, a simple plate of armor won't do - as other answers point out, a micrometeorite encountered by a ship moving at your proposed speeds would have an energy similar to that released by a nuclear bomb. If a regular Whipple shield as displayed on Wikipedia were used, it would probably just get punched through and vaporize the whole ship.

So what if you could just deflect the danger directly instead of fragmenting it? Imagine a large graphene net suspended by poles from your ship, forming a bubble around it (or maybe just a net in front if you're a cheapskate spacefarer). The damage from a micrometeorite at those speeds would certainly not be absorbed at all by the net, but the graphene might deflect the micrometeorite slightly, and if the net is placed sufficiently far in front of the ship and shaped in the correct way (as in an ellipse with the ship between the two foci), it would substantially reduce the probability of the ship getting hit by the projectile. The projectile wouldn't be slowed down in the slightest, but it would be out of the way of your ship, and that's what matters. All you have to do is implement a system that lets you swap out the nets when you arrive at your destination, so that any holes that got punched can be filled to minimize the risk of getting hit by a micrometeorite with enough kinetic energy to destroy a tank.

Safe travels.

• 20 kg of TNT looks impressive, but that mote of dust might just pierce through one side and fly out the other side, depositing very little of that energy on the ship itself. This was a real dilemma in 20th century warfare when ships were heavily armored. If you use a simple shell against a battleship with heavy armor, it won't do damage because it explodes outside the armor without piercing it, so you need armor-piercing shells to defeat the armor. But if you use armor-piercing against a ship with too weak armor, it will fly in one side and fly out the other side, doing next to no damage.
– vsz
Jan 26 at 7:28
• @vsz in space every such hit would be like a penetration below the waterline in the ship analoge. The ship would decompress. Unless ofcourse you fly with a decompressed ship and everyone wears space suits. In that case it would be only fatal for the one unlucky guy whose suit got penetrated together with the ships hull. Jan 26 at 7:38
• @datacube : my point was that it won't necessarily destroy the ship. And historical naval vessels could survive a number of penetrations below the waterline. The spaceship does not depressurize instantly, if the hole is small enough, you can patch it in time. Also, your ship can be compartmentalized, so even if the hole is big enough and pressure drops very quickly, pressure will be only lost in parts of the ship, not in the entire ship. Just like naval vessels which have many watertight compartments, so that one hole below the waterline won't sink the entire ship.
– vsz
Jan 26 at 7:50
• If your capable of reaching those kinds of speeds in the first place your probably using some kind of torch drive at which point weight limitations aren't really a major concern anymore and there's not much stopping you from just applying a thick layer of steel to prevent damage. Jan 26 at 8:18
• "At your speed (around 434 km/s), a mote of dust weighing a single milligram will have an impact with the same energy as a 20-kilogram TNT explosive": Oh no it won't. That is grams of TNT, not kilograms. 1E-6 kg × (434,000 m/s)² / 2 ≈ 94,000 J, which is equivalent to about 22 grams of TNT -- or about 22 food-calories. I would say that a 22 gram bomb is very much less impressive than a 22 kg bomb. Jan 26 at 19:18

Physical limit is 16+ minutes in the earth sphere (orbit) - thats the speed of light. Uranus is 32+ minutes out there - means a ship at the speed of light would cross that sphere in 1h+. Its pretty dangerous to traverse a dense area (material wise) at these speeds. You might not be able to evade and turn your spaceship into a shotgun shell.

I think the best inspiration to take here, is the rules governing the movement of ships. Ships have pretty intricate rules about who has to evade and how to behave on sea and in a harbour (star system). The fast and lightweight have to evade the heavy and inertia rich. At the same time the heavy and inertia rich have to adapt there speeds so they never get into situations they can not prevent a accident. Means you can not go fullspeed with a cargoship in the harbor. Often they can not even manoveur that well alone and need a tug boat.

## Time to CPA

When driving a warship, we constantly talked about Closest Point of Approach (CPA). What is the range at CPA? (1 mile, probably fine. 100 yards, that's a problem!) What is the time to CPA? (An hour, ok a lot is going to change in that time. 5 minutes, that makes them my #1 problem.)

For travel around the Solar System, you set the speed limit based on time and range to CPA. The goal is to ensure everyone is moving at a speed that provides others time to react - whether that's time for others to alter their own ship's course, or time for the orbital defense units to blow them out of the sky.

This is, intrinsically, proposing that max speed is governed by traffic density. If you're at Pluto moving outbound, you probably aren't near any other ships. You have no speed restrictions. If you're at Luna, heading towards Earth, you are in dense traffic and your max speed will be severely restricted.

Probably, you want to keep time to CPA above about 10 minutes to give time for warnings and conversations, with the obvious caveat that to actually dock somewhere your time to CPA has to hit zero, so there's probably some minimum speed at with the CPA restriction goes away so that people can actually land / dock / otherwise arrive at their destination.

• I find this answer fascinating. It's probably the answer for generating ZONES like No Wake zone equals or something once "interplanetary space" is cleared. I used to drive Miami and Washington DC regularly and loved calculating something like CPA imagining the steady deceleration it would define. Thank you for this addition! (I totally get the hitting zero thing too, this is just really nice.) Jan 26 at 19:57

Limiting factors:

a) Speed of light.

b) Pick a maximum tolerable acceleration (e.g. 2g), apply that for half of the journey (e.g. Earth to Jupiter), and measure the instantaneous speed at turnaround.

I'm not confident that I still have the maths, but using the "TIME TO DESTINATION" section at http://www.zitterbug.net/future/future815.html, if we assume a tolerable acceleration of 2g and that Jupiter is of the order of 0.0002 lightyears away, then the maximum speed is of the order of 6E6 m/sec i.e. 6,000 km/sec. This is around 2% of the speed of light, and relativistic effects are beginning to be significant: ship and Earth perceived times differ significantly.

Realistically, for humans taking into account time to eat etc., I think a reasonable maximum within the Solar system is probably 1% of the speed of light, or 3,000 km/sec. However this is an instantaneous speed at turnaround so most of the travel will be at significantly less; OTOH if the destination were substantially more distant the maximum speed might be significantly greater.

And for visitors who might be substantially more hardy (e.g. personae in silico) all bets are off.

• maximum tolerable acceleration is a good way too go, but 2g is probably excessive. While 2g may be fine for a few minutes, you don't want to submit your body to that for extended periods of time. Jan 26 at 19:30
• Depends. I don't have my copy to hand, but IIRC in "Mote in God's Eye" 3g was relatively routine ("but nobody worked") and a fast courier with a young crew in peak physical condition could go higher. A lot boils down to what support is designed into the ship, obviously including things like couches (possibly mobile) but also including nutrition etc. facilities. There's a whole lot here which wasn't specified by OP, who for that matter didn't explicitly say whether the limit should apply only to humans or also to "visitors" who might be substantially more (or less) robust. Jan 26 at 21:40
• The Expanse often had high G travel. While moving at the high G, passengers would lay in crash couches to protect themselves and would have periodic lower- or zero g breaks to recover. Jan 26 at 22:14
• @MichaelRichardson I've just fleshed out my answer with some second-hand maths. One of the most interesting fictional treatments is- IMO- in Vinge's "Deepness in the Sky" where a whole lot of problems were fixed by a combination of relativistic velocities, hibernation, and restorative medicine. Jan 26 at 22:18
• It depends on how healthy your crew is. Heavily screened astronauts or pilots in peak physical shape should be fine at 2G, but general passengers, not so much. Things like arthritis, obesity, poor circulation, various heart conditions, breathing disorders, and seizure disorders could all become deadly by doubling the gravity. Chances are you might see some specialized 2G ships, but after the first few people drop dead from undiagnosed/unreported medical conditions, I don't think they will remain very popular... or legal. Jan 26 at 22:48

## You need Deflector Shields to deal with space dust.

If you want ships that are faster than real world ships, your setting will need some kind of deflector shield technology that will eat up the cost of running into things as part of your fuel budget. The reason I say this is that you can't really go a whole lot faster than modern ships with our current understanding of how to shield against space debris. Even at its modest 17km/sec, if the Voyager 2 probe were to happen across a single 100g grain of dust, it would hit with the kinetic energy of 7kg of TNT. So, if you want to move faster than this, you very quickly get into the realm of things we can not possibly design things to withstand using known material science. But if you can say, "this ship has a 13 gigawatt shield", then you know it can just barely mitigate a 360,000 m/s 100g particle. While we can't make an armor that will protect your ship, we can conceivably create a counter force of energy (using nuclear technology) to stop the threat.

## Why ships would be hard to weaponize

As for weaponized ships, 1 G of acceleration means that ships can peak at VERY high speeds like 359,856 m/s when going to mars or 3,598,560 m/s going to Pluto, but they only reach these speeds when very far away from any planets or populated zones because by the time they get close to thier destination, they should be back down to a near synchronous vector to the destination. Because slowing down takes so long, if a ship were to try to approach a planet without slowing down first, it would be apparent hours, if not days, in advance that something is up, and countermeasures could be taken to intercept the incoming ship. At these speeds, one good missile will turn the attacking ship into a very big and spread out plasma cloud. So, by the time it hits the planet, it would still have a lot of total energy, but be spread out over too large of an area to be a big issue.