What near-future propulsion system(s) could be employed by my spaceships?

Question

In a near future setting I am working on, humans have built space-habitats and have established colonies on celestial objects such as Luna. Their spaceships cannot go faster-than-light and have their fair share of other issues - yet are still the primary means of transport across the Solar System and are the result of constant improvement since the first space shuttle.

The void between these specks of life is populated by small-scale entrepreneurs, shipping cargo from a to b in trips that are measured in months to years. That is, thanks to cryogenics, for them only a few days pass, maybe a week.

They basically take on a cargo, plot the course and then wake up sporadically for maintenance, course-corrections, and so forth.

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In a previous question I have been asking about plausible technological constraints that would favour text-interfaces over graphical ones. In this question, I want to focus on another aspect of my spaceships, namely their propulsion systems.

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With some obvious exceptions, such as the cryo-sleep, I want most of the tech in this world to be current-day or plausible near-future extrapolations. E.g. the propulsion systems.

These ships traverse the voids of the Solar System on a regular basis. An excerpt from the schedule of a busy pilot might look like this (chronological order):

...
Deimos-Station        drop H2O cargo
                      pick up 20 ounces REDACTED (bribe T-Sony)
Hephaestus-Station    deliver REDACTED (payment for that Luna incident)
                      mixtape for Suul
                      pick up cheap and glittering stuff
SOL5-92-Jup92         drop off glitter stuff
                      visit Maja
...

¹

In order to get a feeling for the times involved in traveling these distances, I need hard numbers for things such as constant-/max-acceleration, fuel consumption, etc. of the propulsion system(s) in use by these spaceships.

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Q: What near-future propulsion system(s) could be employed by my spaceships?

I am looking for answers with current-day technologies or plausible extrapolations of current-day technology.

An answer needs to address the following things:

• complexity of the whole system: The easier it is to repair/replace, the better
• achievable max-(constant-)acceleration: The smoother the better
• fuel consumption rates: Graphs would be amazing
• fuel efficiency: Space is a premium, the less fuel needed, the better
• fuel type: Being able to refuel between trips is great, having to replace whole sections of my engine after each trip is not

_{¹Station/staellites/asteroids (MINORS) are named after the convention STAR ORDER - ORDER_OF_MINOR - MINOR_DESIGNATION}

Answer 1

Ion propulsion would be the best solution for your near future propulsion system. It is already in use and newer more powerful versions are being constructed now such as the X3.

Although ion propulsion would probably be the best solution a detailed answer is difficult because there are a number of variables that must be considered as related by the rocket equation:

Δv = Ve ln(Mi/Mf)

Where
Δv = the change in velocity required
Ve = the exhaust velocity of the rocket exhaust
Mi = the initial mass of the vehicle with propellant
Mf = the final mass of the vehicle without propellant

The real problem is the multiplicity of assumptions that must be made in order to arrive at an answer. In addition to the variables above the time taken for the journey and the destination are also key parameters.

Assuming the Mi/Mf ratio is 10 (90% propellant 10% rocket and payload) and the exhaust velocity is 20km/s ref (the lower end of the stated 20-50km/s)

Δv = ve ln(mi/mf) becomes 20000*In(10) = 46km/s

This should be sufficient for your requirements. see the delta V links below for examples of the required delta V for different destinations. A greater exhaust velocity or mass ratio would produce even more delta V but at the expense of pushing ever further into uncharted performance territory or ever smaller payload capacity.

One big issue with ion propulsion is the vast amount of electricity required. In the inner solar system this might be provided by large solar arrays, but in the out solar system nuclear electric propulsion would be required. Range of ion drive rockets using different electrical sources

Delta V Links
Planetary transfer delta V
Near earth delta V
Delta V and time requirements*
*Note delta V of roughly 10km/s to get into orbit from earth included

Concerning the other requirements

Complexity
The ion drive is complex but has virtually no moving parts except the propellant and examples have been run for extended periods without problems. Inner solar system solar array also no moving parts so relatively simple. Outer solar system requires nuclear electric propulsion which would be more complex but should be a sealed unit.

Acceleration
Ion engine acceleration is very low but is continuous for months and is smooth. Conventional chemical rockets tend to have high acceleration and short (minutes) burn times

Fuel consumption and efficiency
Ion engines are much more fuel efficient than conventional chemical rockets by an order of magnitude due to their high exhaust velocity. But a lot for fuel will still be needed. I have assumed 90% propellant and 10% rocket/payload above but the calculation can be made for any mass ratio you wish by plugging in different numbers into the rocket equation above.

Fuel type
Most current ion propulsion engines use Xenon as a propellant but other propellants are possible and some have been tried. For your refuel requirement Xenon would not be ideal as it may not be readily available at the destination for refuelling.

I suggest Diamondoids such as Adamantane or Diamantane would be more suitable. These are relatively cheap on earth being found in oil in very small quantities and could probably be produced at the destination sites with some suitable chemical engineering provided that a source of carbon, hydrogen and energy were available. They have been examined as potential fuels for ion engines along with various others as can be seen here.

Conclusion
The suggested ion drive rocket could meet your needs and is a realistic projection of current technology. But a lot of further research would be required especially in the development of the ion engines themselves, the fuels used and the large space based reactors required for outer solar system operation.

There are various other current, future and speculative propulsion systems listed here that may be of interest also including ion drives.

General references
http://www.braeunig.us/space/ http://www.projectrho.com/public_html/rocket/mission.php#id--Hohmann_Transfer_Orbits http://ccar.colorado.edu/asen5050/projects/projects_2001/stephens/termpapera.html

Remember it’s not rocket science (no wait…)

Answer 2

This answer is a hard-science expansion of this answer. Please read that other answer to get a description of the system I am proposing, as well as justification of its technical feasibility. That post also has lots of reference links for various design decisions. I will summarize the system here and numerically address the questions posed.

System summary

The power source is a pebble bed fission reactor. The fuel source is uranium nitride pellets coated in a pyrolitic carbon moderator. These fuel pellets are held in molybdenum 'pins' in a geometry that will make them supercritical if a neutron reflector is placed outside the reactor. Heat exchange is done directly with the working fluid to save mass.

The working fluid is helium, which is passed through the reactor core. Electrical power is generated through a Brayton-cycle turbine similar to a marine gas turbine used on ships, except replacing the combustion chamber with the reactor core. The helium is compressed by a compressor coupled to the gas generating turbine into the core, and then allowed to expand over the gas generating and power turbines. Exhaust will still be at ~700 K, and will then be run over various auxiliary systems to utilize this extra energy. The exhausted gas will then have its remaining energy bled off into space through heat exchangers and then fed back into the compressor. The rotational power generated by the power turbine is then coupled to an electrical dynamo to generate power for the vessel.

The main propulsion system is a magnetoplasmadynamic Lorentz Force Accelerator (LFA) arcjet thruster. Lithium fuel is ionized and fed into an acceleration chamber, where a combination of magnetic and electrical fields are applied. The induced current in the plasma, once the input power is in the MW range, will help maintain the magnetic field in the plasma while will then induce an electric current in a tungsten-barium cathode.

System Specifications

The reactor must produce 300 MW of heat energy. This is possible from a pebble bed reactor, the Chinese are building a pair of production 250 MW pebble bed reactors at Shidao Bay. From this thermal energy, gas generating turbines produce an output of 100 MWe at 33% efficiency. This is equivalent to the power output of 4 GE LM2500 marine gas turbines, which is the same energy source as an Arleigh Burke-class destroyer. The LM2500 has efficiency of about 40%, but we are losing efficiency due to the reactor core being cooler than a typical combustion chamber (our core is ~1750 K compared to ~2250 K in a marine gas turbine). The overall system mass estimate for the power generation portion is 0.4 kg/KWe (based on a NASA estimate), or 40,000 kg.

The size of the MPD thruster is much more conjectural, as no thruster of nearly the size required has been built. I have estimated the characteristics from the information available at the EPPD laboratory at Princeton. This design calls for a single 7.5 kN thruster at a fuel usage rate of 0.5 kg/s with an ISP of 15 km/s. There is an available high ISP mode where thrust drops to 1 kN at 0.01 kg/s with and ISP of 100 km/s. The mass of the thruster unit is 10,000 kg. I honestly do not have an good basis for this estimate, but it is needed to proceed.

Reactor Safety

The pebble bed fission power system is inherently safe. There are several avenues for a nuclear accident, the two most significant being an overpower casualty (Chernobyl) and a loss of coolant casualty (Three Mile Island, Fukushima).

An overpower casualty is not physically possible for a pebble bed reactor. The fuel source will use low-enriched Uranium, enough to achieve critical mass, but low enough that there are significant interactions between U-238 and neutrons in the core. As temperature of the fuel pellets increases, U-238 is affected by doppler broadening, causing it to absorb more neutrons. This lowers the number of neutrons available to cause fissions in U-235,thereby lowering the reaction rate and reducing power input. Therefore, the core is naturally moderated at an upper temperature controlled by the U-235/U-238 ratio, which will be engineered at 1750 K. At temperatures below this, with the reflectors (to be discussed later) in place, the temperature will increase to 1750 K. As fluid flow over the core is increased and heat removal increases, the reaction rate will increase to keep temperature stable, and this power output is naturally controlled by demand. At temperatures above 1750 K, power output will decrease due to U-238 absorption until temperate settles back at 1750 K. Therefore, there is no human or computer based control of the reactor. Once started it simply outputs energy at the rate heat is removed from the core, moderating itself at 1750 K. This effect is trustworty; computer modeling in Strydom, 2004 indicates that the uncertainty band during a loss of forced cooling casualty will amount to less than 100 C even for a reactor shutting down from full power.

As an aside, we should discuss the way that the reactor is started and stopped. In the core's state as built, it is sub-critical. The core will be undergoing fission at a very low rate, but too many neutrons will be lost passing out of the core for a chain reaction to occur. This is changed by surrounding the core with beryllium reflectors. Once these reflectors are positioned in place, they reflect neutrons back into the core, as well as helping to moderate the high energy neutrons produced by fission. As a result the core will be super-critical and increase temperature until the upper limit described in the last paragraph. By removing the beryllium reflectors, the core can be shut down.

A loss of coolant casualty is the most dangerous remaining one. However, and simplest strategy for this risk is to ignore it. On Earth, reactor casualties are costly because they leave radiation that no one wants to deal with. In space, probably no one cares. Sure, you lose the ship, but people shipped plenty of things in the Age of Sail while the risks of losing the ship were great. Transportation in space has more in common with the Age of Sail, what with month long travel times and low cargo capacities, than it does with modern shipping.

System complexity

As described above, there is no requirement for control systems for the reactor itself, only the activation of one safety system in case of emergency (removing the reflector for shutdown). The emergency heat removal system will be self activating.

The Brayton cycle gas generators will be designed to operate continuously for the duration of a mission. Already, ships at sea using marine gas turbines operate for 1 year + without the turbine enclosure or electrical generator enclosure being opened. The conditions at sea are far more challenging than space, what with salt and water both present. Long term maintenance can be performed at a (space)port between missions. Furthermore, the advantage of operating multiple turbine units in parallel is that the thruster will still be able to fire (if at a reduced power level) if turbine are offline, even when only one turbine is operational.

The MPD thruster is, again, the least developed part of this plan and the most conjectural, so I cannot make any statements about its reliability. However, it does have the advantage of no moving parts; power is generated and transferred through the movement of gas, current, and electromagnetic fields.

Power and Fuel Efficiency

Given the above specifics, we can calculate some burn times and travel times. Here is a list of delta-v needed for various Hohmann transfers.

Tsiolkovsky's rocket equation is solved for fuel mass, $m_f$, by $$m_f = m_0\left(\exp{\left(\frac{\Delta v}{v_e}\right)}-1\right).$$

Our parameters are $m_0$ (mass without fuel) is 50,000 kg plus cargo size; and, $v_e$ is either 15,000 m/s or 100,000 m/s depending on operating mode of the thruster.

The burn time can then be calculated by dividing fuel expended by mass flow rate. The mass flow rates are given as 0.5 kg/s or 0.01 kg/s, depending on the operating mode of the thruster.

Below is a table for required fuel mass and burn times for various configurations. A 3.0 delta-V will get you to Mars or Venus, 8.8 delta-V to Jupiter, and 12.3 anywhere in the Kuiper belt:

Cargo (tons) deltaV (km/s) V_e(km/s) Fuel(tons)  Burn(days)
     1000        3.0         15         232          5
     1000        3.0        100          32         37
     1000        8.8         15         838         19
     1000        8.8        100          97        112
     1000       12.3         15        1334         31
     1000       12.3        100         137        159
    10000        3.0         15        2225         52
    10000        3.0        100         306        354
    10000        8.8         15        8020        186
    10000        8.8        100         924       1070
    10000       12.3         15       12769        296
    10000       12.3        100        1315       1522
   100000        3.0        100        3047       3527
   100000        8.8        100        9203      10652
   100000       12.3        100       13095      15156

A few things to note. The optimal burn profile (how long to burn thrusters in which mode) is still an open question. I posted a question about that using similar numbers to this answer, but didn't get a great answer. I might take a stab at that question again later. The reason you have to calculate the optimal burn profile is that fuel has a cost. If you are moving 100,000 tons of raw lithium from Mars orbit to Earth orbit, not only does your burn take 10 years, but you also burn 13,000 tons of refined lithium doing it! That makes it seriously questionable whether moving bulk cargoes is going to be profitable in your solar system. Also note that the above calculations use a 100% fuel burn; you aught to leave at least something in reserve, which cuts further into your fuel efficiency.

I didn't post the scores for using the 15 km/s mode with cargos of 100,000 tons, because the fuel usage is ridiculous. As it is, those numbers are in tons of lithium fuel. Keep in mind world lithium reserves are estimated at about 34 million tons, so you can see how you'd burn through that quickly.

A big open question with this process is the availability of lithium for fuel. If it can be mined in commercial quantities from space rocks, then that sort of operation would be the equivalent of petro-states here on Earth. It may be possible to use alterative propellants, though there would likely be a loss in efficiency. Neon, Argon and Xenon are not very common, either, but hydrazine is another possible propellant. It could be that hydrazine refining in the orbit of the gas giants is the oil refining of your near-future solar system.

Conclusion

Here is a system for space propulsion that provides a reasonable ability to traverse the solar system using technology mostly already demonstrated today. The big exception is scaling up the magnetohydrodynamic propulsion system to kN power levels.

Most burns that you might imagine for a sublight space opera set in the solar system are feasible. Cargo capacity is relatively low, with the 100,000 tankers (roughly the size of large container ships today) being probably unfeasible for fuel cost reasons. Taking 1000 tons of cargo from Earth to the Kuiper Belt isn't that inefficient; you must burn 14% of your cargo mass in fuel, and the burn takes half a year, but what is half a year compared to the decade or more it will take to coast there?

Meanwhile, a quick hop to mars could be done in relatively fast time. If you skip a Hohmann transfer orbit and try something else, you could burn more fuel to get somewhere faster. For example, a max burn from Earth orbit with 1000 tons of cargo and 1000 tons of fuel in the high thrust mode can get you to Mars orbit in a matter of days. Of course, the problem is you have to stop. The point I'm trying to make is that for the lower delta-V transfers at lower distances, this spaceship is powerful enough to ignore Hohmann transfers and attempt some other orbital transfer that requires more energy. Now what that transfer might be sounds like the subject of a future post :)

Answer 3

Consider Beam Powered Propulsion to possibly eliminate the need for fuel entirely. https://en.m.wikipedia.org/wiki/Beam-powered_propulsion

The power needed to provide thrust to your ship wouldn't be generated on the ship but instead in oribit of the various settlements and beamed at the ship using lasers or masers. The ship would then convert the beam energy to thrust by use of a sail. Because no fuel is needed acceleration can be constant and very high speed can be achieved

It's quite a promising technology. Even with our current level of understanding we are already planning to do some very impressive stuff with it, like sending tiny probes to other star systems in just the span of decades.
https://en.m.wikipedia.org/wiki/Breakthrough_Starshot
https://en.m.wikipedia.org/wiki/DEEP-IN

Current technology would allow us to use lasers propell the more massive Orion spacecraft to Mars in one month. If a second laser array were present there we could also decelerate the ship and make a delivery. It's not much of a handwave to say that this technology could be used for intrasystem hauling in your future setting.

The ships crew is only needed for mainenance of the sails. All repairs on the lasers and generators are conducted by the settlements.

A laser sail such as this is being considered for the mission to send a probe to the newly discovered Oumuamua interstellar asteroid. Project LYRA: https://arxiv.org/pdf/1711.03155.pdf

Answer 4

Well, the problem will be that most contemporary propulsion systems (or near future ones) will have quite low thrust. And you need the heavy radiators to dissipate waste heat from your antimatter reactors.

Therefore, let's build mass accelerators. There will be at least a few in orbit at your origin and destination points. You would pay a fee, then the thing would orient according to the velocity vector you need, and shoot you into space.

The mass accelerator is stationary, thus it can have huge solar panels and plenty of energy. In this case, all the propulsion you need is to correct course and ensure you arrive at the destination decelerator with proper alignment (this is going to be tricky...) so it can decelerate your ship. Alternately you can decelerate with a slingshot maneuver and/or atmospheric braking at the destination planet, which is a lot harder to miss...

EDIT

Here is an example of how a mass accelerator would work.

In 'The Moon is a Harsh Mistress', Heinlein proposed that rail guns would be installed on the moon. These would be very long, high-powered electromagnetic guns. Since the target (the earth) was always stationary to the moon, they could be permanently built into the moon foundation, and could be miles long. The moon's low gravity and lack of atmosphere made then feasible. The moon miners would load huge payloads of minerals onto the gun sleds, launch them at the earth, re-load, and launch again. The packages would effectively be nothing but large rocks. I think he had the rocks enter low earth orbit, where space tugs would collect the material.

However, When they arrived at earth, and entered low earth orbit, they would be moving at a low enough velocity that they would simply be like deorbiting space junk. The atmosphere would slow the packages down, some outer fringes would burn off, but the basic payload would splash down in some desert, basically at terminal velocity. A large thud, but not widespread damage. In this regard, Heinlein was probably incorrect about using the rocks as weapons against the earth. They wouldn't gain enough velocity.

Answer 5

Hohmann Orbits are the minimum delta-V it takes to get from one planetary orbit to another. These are computed in the Chemical Rubber Handbook. https://en.wikipedia.org/wiki/Hohmann_transfer_orbit These take a long time -- something between the orbital period of the two planets. (I think using the geometric mean will get you in the right ballpark)

Article here: https://en.wikipedia.org/wiki/Hohmann_transfer_orbit Tutorial on how to calculate one here: http://openmdao.readthedocs.io/en/1.7.3/usr-guide/tutorials/hohmann-transfer-tutorial.html

Light sails: Light exerts pressure. Not a huge amount. Sunlight on an acre could lift a cigarette paper. But .0001 g's will add up. And the price is right. Maneuvers get interesting. https://en.wikipedia.org/wiki/Solar_sail

Ion systems. These all depend on using an easy to ionize metal, then accelerating it to high velocity. https://en.wikipedia.org/wiki/Ion_thruster Ion thrust gets you about 7-12 times as much delta-V per kg of mass.

Torch ship. See Heinlein's "Double Star" and a bunch of his juveniles. This was a hydrogen fusion reactor, where all the energy (besides parasitic energy to run the reactor) accelerated the helium. This makes it reasonable to run a 1 G all the way. Earth to Pluto in 17 days.

Periodically there is a storm of fuss and feathers about someone who discovered a 'reactionless' drive. Don't buy stock in any of these just yet.

https://en.wikipedia.org/wiki/RF_resonant_cavity_thruster

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Consideration: You have a huge pile of money invested in a ship. You need to explain why they will use a slow way if another way allows them to run more cargos. This is a balance between operating costs and lost opportunity costs.

E.g. A perfect Hohmann transfer orbit is half an ellipse that is tangent to the starting planet's orbit on one side of the star and tangent to the final planet's orbit on the other side. But with a little more fuel, you can get there sooner. Historical parallel: The Clipper ships were designed to sail FAST because the first cargo of tea from China/India got a huge premium in London. The starting date was dictated by weather and the harvest. Coming in a week earlier could make your fortune.

E.g. Big ocean freighters move at around 10 knots. Moving at 20 knots would cut the time in half -- but would take something like 8 times the amount of fuel. Further, you would haul less because you need 8 times larger engines and 8 times larger fuel tanks.

Bear in mind that different propulsion systems take a different amount of effort and training to run. E.g. Hohmann orbits are pretty much do nothing. Take a nap. Solar sailing or something like a torch ship will require someone standing watches. I wouldn't want everyone asleep with riding a continuous hydrogen bomb in a bottle.

Compare the transition between sailing ships and coal powered ships. Sail -- generally slower (but see clippers...) but free fuel. Coal -- faster, but you had to go where you could get more coal. You might have fun with the economy in transition between modes. The last such ship was the Pamir. https://en.wikipedia.org/wiki/Pamir_(ship) which sank in 1957

Answer 6

I am not a physicist or aerospace engineer so I will provide figures that have already been pre-calculated by others with greater mathematical prowess.

The idea that I found a while ago while browsing the web is a concept known as a Nuclear Salt Water rocket, it was theorized by Dr. Robert Zubrin and is one of the few designs that we know can deliver torchsip levels of performance, and is ideally suited for constant acceleration space travel.

How it works is it consists of a fuel tank composed of small cylindrical containers holding the nuclear fuel solution wrapped in a boron carbide neutron moderator that prevents it from reaching critical mass while in storage. The to ignite the engine the nuclear fuel solution is sprayed in small amounts at a time into a plenum without the neutron moderator where it reaches critical mass and creates a continuously detonating nuclear explosion that propels the craft forward.

Now the fuel solution consists of a mixture of 2% Uranium tetrabromate mixed with 98% water, which means the propellant can be stored without need for cooling and the steam created by the nuclear explosion creates lots of extra thrust.

It uses open-cycle cooling so it is not power limited like other nuclear power concepts and can produce jet power ratings in the thousands of megawatts range.

General theorized specifications:

Total engine mass: 33,000kg (excluding fuel mass)

T/W: 40

fuel: fission Uranium Tetrabromate

reactor: gas-core open-cycle

reaction mass: water

reaction mass acceleration: thermal acceleration from reaction heat

thrust director: nozzle

specific power: 0.8kg/MW

The estimated performance for a craft using 20% enriched fuel is as follows:

Exhaust velocity: 66,000 m/s

Specific impulse: 6,728 s

Thrust: 12.9 million N

Thrust power: 425.7 GW

nozzle efficiency: 0.8

mass flow: 195 kg/s

The estimated performance for a craft using 90% enriched weapons grade fuel:

Exhaust velocity: 4.7 million m/s

Specific impulse: 479,103 s

Thrust: 13 million N

Thrust power: 30.6 terawatts

nozzle efficiency: 0.9

mass flow: 3kg/s

So in conclusion, you get the efficiency of an ion engine with the thrust power of an Orion project spacecraft without much more mechanical complexity than your average chemical rocket.

Now of course there are some obvious issues with this device, as it is a contiuously burning nuclear flame with the intensity of an atomic bomb. The materials required in the engine would have to be extremely strong and at the cutting edge limits of our current metallurgy unless you want to replace the engine after every trip , however they wouldn't have to be insanely strong to the point of impossible , because while the initial reaction would take place within the reaction chamber the expanding steam would force the rest of the fuel outwards having the rocket ride on the aftershock of the main detonation occuring outside. This means that the reaction chamber doesn't have to contain the nuclear detonation.

Now while this rocket is so powerful it would barely notice the cost of takeoff, it would leave a burning nuclear crater, so other solutions would be needed like maybe having the craft dock at an orbital spaceport, and the pilot get to the surface by other means.

If you are worried about the exhaust contaminating space, don't because as long as it doesn't directly intersect with any planet's surface it's velocity is so high it would exceed the planets escape velocity and leave the atmosphere as quickly as it entered. And over time it would diffuse so that the contaminants would spread over a huge distance eventually entering concentrations where they are no longer harmful.

Happy trails!!!

sources:

http://www.projectrho.com/public_html/rocket/enginelist2.php#nswr

https://en.wikipedia.org/wiki/Nuclear_salt-water_rocket

https://www.npl.washington.edu/av/altvw56.html

Answer 7

So, travel time in space isn't typically a big function of your engines. In the game of cosmic billiards, you're stuck with launch windows and their set travel times. You can deviate from these travel times by a bit (10-20%) but beyond this can become very very expensive from a fuel consumption perspective. Hard science-wise, I can derive the interplanetary motion of space ships in terms of their velocity, but it's a 3-4 page affair. Not very useful here, I think, but please let me know if you'd like me to post it.

What would be useful is the Cosmic Train Schedule!! It basically does exactly what you want, showing the travel times and launch windows for Mercury through Jupiter for the next 50 years or so. It even shows the fuel requirements (deltaV).

Also useful would be a quick glance at the Hohmann transfer, which space ships use to travel from planet to planet. The time to do the trip one way is the "transfer time". The amount of fuel required is measured by the "DeltaV" of the transfer. Your fuel efficiency is measured by "Isp". Relating these concepts, is: $$fuel burned = weightBefore - weightAfter $$ and $$weightAfter = weightBefore * exp(-deltaV/(Isp*g0))$$

where g0 is 9.81 m/s^2 (pronounced 'gee not'), and on a nice near future (next year) 'methalox' engine suited for interplanetary travel, you might get 375s Isp. Make sure deltaV is in m/s, not km/s!

Finally, it takes a lot of fuel to land places. Check the Low-orbit to landed deltaVs on this deltaV map posted in redit for reasonable estimates.

Good luck with your world building!