Oberth Maneuvers Using Sun, Jupiter & Saturn: Formulations & Assumptions

[James Essig]

I am going to run the computations for the use of Jupiter and Saturn along with the Sun for Oberth Maneuvers. The escape velocities of these two gas giant planets is very close to that from the Sun at the Earth and Venus radial coordinates.

I was wondering if anyone could provide the formulations for compound Oberth Maneuvers where the Sun, then Jupiter then Saturn would be utilized. I assume closest approaches to the Sun equal to that of Earth, Venus, and Mercury orbits.

I am assuming that accelerations as high as 2 to 4 Earth g's can be tolerated such as required for Oberth Maneuvers using Jupiter and Saturn.

Note that I am working on very large mass ratio chemical rocket assumptions and high impulse nuclear thermal rockets.

I assume that Delta v for each of the above three bodies can be as high as 250 km/second or higher. For chemical rockets, I assume extreme specific impulses such as those perhaps obtained by theoretical chemical reactants.

Note that I had no problem running the numbers maneuvers using the Sun for sun centered radial coordinates for closest approaches equal to that of Earth, Venus, and Mercury orbits.

 

[mfb]

What do you mean with "formulations for compound Oberth Maneuvers"?
If you want to fly past several objects, you first need a trajectory that actually reaches those objects. That will limit the way you can use the Oberth effect.
You also get some effects of gravitational assists, those depend on the direction of flight.

I assume that Delta v for each of the above three bodies can be as high as 250 km/second or higher.

Then Saturn and even Jupiter won't help you much. Trying to get all the speed within such a short time just leads to other problems (you need much more power for a short time, the spacecraft has to be stiffer, you are severely limited in the available target directions, ...).

For chemical rockets, I assume extreme specific impulses such as those perhaps obtained by theoretical chemical reactants.

Let's be optimistic and assume you get a factor of 2 more energy per mass. That increases the exhaust velocity from ~4km/s to ~6km/s. Still impossible to get 250km/s with that.

 

[James Essig]

There are theoretical chemical fuels that may obtain a specific impulse in the 3,000 sec range or higher. So far, they have proved unstable but perhaps nanotech fabrication and confinement mechanisms might work to enable safe storage or large quantities. Also, with plausible materials of construction such as carbon nanotubes and graphene, tensile strengths of up to 10,000,000 Newtons per square centimeter are possible. New materials and approaches to nuclear thermal rockets can likely significantly increase the specific impulse over that developed by the NERVA engine. Also, drop away stages are possible to reduce inert mass. I would not rule out 250 km/sec. Crew members may be provided improved g-suites or remain immersed in hydrostatically sealed vessels during acceleration with perhaps breathable oxygenated liquids. Such liquids are currently research items. Divers can experience on the order of 100 PSI while scuba-diving which translates into hundreds of time their weight on land in terms of water pressure. A hydrostatically sealed tank could easily enable 100's of g's.

We already have manned spacecraft technologies which can handle several g's and then so carrying several hundred metric tons of propellant per fuel tank.

For compound Oberth Maneuvers, I mean flying toward the Sun on a pre-planned optimal trajectory which would cause the spacecraft to approximate an Oberth Maneuver using Jupiter followed by Saturn, perhaps followed again by Uranus and/or Neptune. Optimal planetery alignment would be required, however, there is no reason why the spacecraft could not be positioned before hand so that all of this can work.

Target destinations I am considering are for long flight duration space arks and generation ships to local stars perhaps aided by cryogenic preservation and/or hibernation states optionally perhaps controlled with nanotechnology based precision.

 

[mfb]

3000s? Where? That would be more than an order of magnitude above all typical reactions. Please give a source for that.
I don't doubt that nuclear propulsion can get way higher I_sp. But that is not a chemical rocket.

tensile strengths of up to 10,000,000 Newtons per square centimeter are possible.

Rockets usually have their exhaust at the "back" (in acceleration direction), so they work with compression.

Divers can experience on the order of 100 PSI while scuba-diving which translates into hundreds of time their weight on land in terms of water pressure.

There is a difference between pressure and pressure difference.

A hydrostatically sealed tank could easily enable 100's of g's.

Please provide a source for that claim.

For compound Oberth Maneuvers, I mean flying toward the Sun on a pre-planned optimal trajectory which would cause the spacecraft to approximate an Oberth Maneuver using Jupiter followed by Saturn, perhaps followed again by Uranus and/or Neptune. Optimal planetery alignment would be required, however, there is no reason why the spacecraft could not be positioned before hand so that all of this can work.

You can position the spacecraft , but not the planets. If you approach Jupiter with 100km/s, you get a maximal course change of 18° (less if you keep accelerating or do not fly the closest possible path). If you come from the inner solar system, Saturn has to be at one of two specific places for the optimal effect. The change of direction there is even smaller (<7° at 100km/s, ~3° at 150km/s), and having Neptune and/or Uranus at the right place at the same time is really rare. If you have some specific target direction, you can easily wait hundreds or thousands of years. It is possible, but you do not gain so much from it:

Approaching Jupiter with 100km/s and accelerating by 50m/s^2 over 1000s gives you a final velocity of 155.5 km/s while without Jupiter you would get 150000m/s. 10% more, that is very interesting.
Now go to Saturn and try the same trick: Approaching Saturn with 150km/s and accelerating by 50m/s^2 over 1000s gives you a final velocity of 201.0 km/s while without Saturn you would get 200 000m/s. 2% more. Uranus would just give an advantage of 0.5%, similar for Neptune.

We already have manned spacecraft technologies which can handle several g's and then so carrying several hundred metric tons of propellant per fuel tank.

Yes, and they have a lot of structural mass.

 

[James Essig]

Regarding compression, the same or similar magnitudes for compression strengths are available from carbonaceous super-materials as tensile strength. Diamond can handle in excess of 10 mega-Newtons per square centimeter. These supermaterials could be ideal for confining bulk quantities of fuel in one or more large tanks making such g handling ability all the more easy

Mice have withstood over 3,800 Gs in water immersion tests with lungs filled with fluid for 15 minutes. Humans may withstand in theory, not 100 Gs but 100s of Gs using the same techniques. Read all about this interesting research in a paper published at

http://www.esa.int/gsp/ACT/doc/MAD/pub/ACT-RPR-MAD-2007-SuperAstronaut.pdfOrion's arm has a good review of chemical rockets with chemical fuels with Isp of 2,000 to 3,000 seconds and above.

See:

http://www.orionsarm.com/eg-article/493687ff373fd

Note the following:

Free H radicals based chemical rocket fuels have a maximum theoretical specific impulse of Isp = 2,130 seconds.

Consider a free H-radicals fueled rocket having a mass ratio of 1,000 such as might be accomplished using a large tank where the tank mass to fuel mass ratio is 0.0005, and where the remainder of the vehicle is crew quarters, radiation shielding, rocket engines, and life support systems.

The above spacecraft would obtain a terminal velocity of 144.34 km/s. The transit time of the spacecraft to Pluto would be about 33.9 million seconds or roughly 1.095 years or about 13 months provided the spacecraft could accelerate to this velocity in under a few days.

Such a large craft might use magnetic sail based breaking to slow to plutonian orbital velocity.

Now suppose we wanted to utilize reverse rocket thrust to slow a craft down to reach Mars. We will once again assume a mass ratio of 1,000 for the craft at the very beginning of its journey. However, for the acceleration phase of the trip, we will assume that the effective mass ratio of the craft is 10 3/2.

Consequently, the terminal velocity of the craft will be 72.17 km/s. As a result, the craft will arrive at Mars in about 9.56 days or about 1 ½ weeks. The left over fuel could be used to slow the craft down thus eliminating the need for aero-breaking.

Hydrogen is a natural element choice for fabricating chemical fuels because it is ubiquitous throughout our solar system. What can be synthesized on Earth can be synthesized elsewhere.

We will assume a fully fueled initial mass ratio of 1,000 and a tank mass to fuel mass ratio of 0.0005 for the rest the the examples given in this chapter.

Metastable helium chemical rocket fuels have a maximum theoretical specific impulse of Isp = 3,150 seconds.

The respective spacecraft would obtain a terminal velocity of 213.46 km/s. The transit time of the spacecraft to Pluto would be about 22.9 million seconds or about 0.74 years or about 8.9 months provided the spacecraft could accelerate to this velocity in under a few days.

Such a large craft might use magnetic sail based breaking to slow to plutonian orbital velocity.

G-forces as high as 65 where practiced by human volunteers without differential tissue density induced ruptures.

A hydrostatically sealed chamber would result in uniform pressure over an entire person's body for persons sub-merged in a liquid for which no air is available for additional compression. Yes, there would be differential tissue pressures based on tissue density variations but this should not matter at all. The density variations in human organic tissues such as the brain are very small and of low distance scale patterns thus making the differential forces even smaller.

There are plenty of opportunities to travel around the solar system to so position a craft to enable Oberth Maneuvers using the Sun, then Jupiter, the Saturn. Even the orbital period of Saturn is less than 30 years. Certainly, a planned system of the desired series of Oberth Maneuvers could be well planned in advanced.

Why accelerate near Jupiter and Saturn with an acceleration of only 50 meters per second squared when we can theoretically do so with an acceleration of 1,000 to 3,000 meters per second squared? Carbonaceous super-materials such as graphene are as much as 200 times the strength of steel yet having a density roughly equal to that of water.

 

[mfb]

Regarding compression, the same or similar magnitudes for compression strengths are available from carbonaceous super-materials as tensile strength.

That is the value where they completely break down, it is not the value where they remain in a beam-like shape to support a rocket. We can build cables of 100km length that would support themself hanging at 1g, but we cannot build skyscrapers of that height. Anyway, not an important point here.

Mice have withstood over 3,800 Gs in water immersion tests with lungs filled with fluid for 15 minutes. Humans may withstand in theory, not 100 Gs but 100s of Gs using the same techniques. Read all about this interesting research in a paper published at

http://www.esa.int/gsp/ACT/doc/MAD/pub/ACT-RPR-MAD-2007-SuperAstronaut.pdf

Interesting paper, thanks.
I don't get the same conclusion ("To improve acceleration tolerance, it seems too risky, diffcult and complex as procedure to be practically implemented for space applications" and just up to 24g quotes for humans), but there is no point in more than 24g anyway I think.

http://www.orionsarm.com/eg-article/493687ff373fd

Science fiction pages are not sources for actual science.

If you have such a powerful spacecraft and want to go to Pluto, where is the point in waiting for Jupiter that is just there for ~1 year every ~12 years?

Why accelerate near Jupiter and Saturn with an acceleration of only 50 meters per second squared when we can theoretically do so with an acceleration of 1,000 to 3,000 meters per second squared?

It does not make a difference. Only the total velocity change and where you get it (i. e. as close to the planet as possible) matters.
And it does matter if you need 1 unit of whatever material you use or 20-60 units. It also matters because your engine needs to be significantly larger to deliver 20-60 times the acceleration.

 

[James Essig]

Orion's Arm does consider some serious science. Simply do a google search on metastable helium chemical rocket fuels and other similar fuels and you will generally see the same results for Isp. I'll do the search if you want.

Yes, diamond breaks down at is maximum compression resistance, but not with half of the load of its compression strength. Regarding buildings, they are made of structural steel and concrete, and then so, of ordinary mild steel in general. Areospace grade steels are five or more times stronger than construction steel. If carbonaceous super-materials are ever mass produced, then buildings as high as 20 kilometer or higher should be possible. Certainly, space elevators will then be producible.

Construction steel generally come close to failure at 50,000 PSI stress, but at 25,000 PSI, it is completely safe, So why should not the same hold true for many carbonaceous supermaterials. Supermaterials may support a cable hanging from itself that is not 100 km long under 1 G, but 10,000 km long under 1 G.

Regarding the risk of hydrostatic pressure vessels, I simply do not agree. Since no physical or engineering laws prevent such 300 g crew suites, I see no reason by they cannot be developed. Remember that engineering ability and materials have made radical improvements over the past several decades and there is no reason to assume that this will not be the case for hydrostatic systems such as those which can support live human persons in 300 G's.

I am not talking only about Plutonian missions here, but mostly about interstellar possibilities.

Regarding engines, why not simply use entire plates or planar arrays of drop away engines that are 90 to 95 percent rocket fuel. That way, the specific impulse is reduced by only about 5 to 10 percent over the case where the engine itself and otherwise inert mass would be used for fuel. You do not necessarily need a large engine, hundreds or even thousands of smaller drop away engines would work in theory.

SpaceX is going forward with the Falcon-9 Heavy which will use three cores of 9 engines each so the idea of using many smaller engines is not without precedent.

 

[James Essig]

The metastable Helium fuel with Isp > 3,000 seconds comes right from the JPL organization. See reference in a peer reviewed paper at http://trs-new.jpl.nasa.gov/dspace/bitstream/2014/7684/1/03-1848.pdf

 

[mfb]

Orion's Arm does consider some serious science.

Having some scientific elements does not make the whole site scientific.

The metastable Helium fuel with Isp > 3,000 seconds comes right from the JPL organization. See reference in a peer reviewed paper at http://trs-new.jpl.nasa.gov/dspace/bitstream/2014/7684/1/03-1848.pdf

A purely theoretical value. And that value does not even consider the mass of the matrix where those atoms are supposed to get stored.

Regarding the risk of hydrostatic pressure vessels, I simply do not agree. Since no physical or engineering laws prevent such 300 g crew suites, I see no reason by they cannot be developed.

I don't say they cannot be built, I say it is pointless. Like designing the tires of a typical car for mach 2. You can probably do that, but where is the point?

Since no physical or engineering laws prevent such 300 g crew suites

Apart from the issues with liquid breathing mentioned earlier.

I am not talking only about Plutonian missions here, but mostly about interstellar possibilities.

Even there, leaving with 250km/s is faster than waiting hundreds of years to go <1% faster (unless the wait calculation is still relevant, but that nothing to do with fly-bys.).

Regarding engines, why not simply use entire plates or planar arrays of drop away engines that are 90 to 95 percent rocket fuel.

The rocket engine needs some mass that is not fuel, there is no way around that. You are suggesting to increase it by a factor of 20 to 60 for no reason. Many small engines are not lighter, in general they tend to be heavier than a single more powerful one. They can have other advantages, but simply replacing 10 powerful engines by hundreds of smaller ones does not magically reduce their mass.

 

[James Essig]

I'd read the paper on metastable helium which is peer reviewed and also do a comprehensive search on metastable helium fuel. I am sure the JPL folks are considering inert mass with the fuel portion which in reality can simply be a membranous or other porous structure. I stand by Orion's arm as having serious and visionary prose.

Chemical rocket propulsion to the stars may have some merit especially where long but no too long of transit time is considered. As I mentioned earlier, space arks carrying cryogenically preserved or hibernating humans with chemical controls in my opinion will be possible in the not to distant future. I have a sibling that has just used in-vitro fertilization to reproduce an embryo frozen cryogenically for several months. The result, a perfectly happy and super-intelligent 6 month old infant. Large space arks can support breeding while in route. Only a very small percentage of cells rupture in cryogenically preserved animals. A form of invertebrate the size of a tadpole winters over completely frozen below ground and thaws to come back to life the next season.

Sure it has to do with fly-by's. Simply wait until the gas giant planets are aligned so that the proper angle of attach can be used for all of them. We also can adjust spacecraft position before the Oberth maneuvers are done. It not just a matter of waiting for proper planetary alignment, we have the spacecraft positioning option as well.

Well, perhaps many smaller engines can replace more powerful ones while enabling reduced mass. I do not see how this proposal is a problem. SpaceX is already up to 27 engines per vehicle in their research. Simply besting this by an order of magnitude should be possible.

Actually, the rocket engines used in common liquid fuel rockets are one to two orders of magnitude lower in mass than the fuel. Rocket engines are really an insignificant part of the mass of the vehicles considered. Even the fuel tanks are much lighter than the rocket fuel. Meanwhile, NASA has figured out how to make the tank mass to fuel mass ratio a factor of 3 to 5 lower than it currently is as commonly practiced by the most advanced rockets. They even figured this out with carbon composite material tanks so no one can say that it cannot be done because carbon graphite composites are too brittle at cryogenic temperatures. I'll bet that the ratio can be reduced by another factor of between 10 and 50 if pure carbonaceous supermaterials are used.

Regardless, I stand by my opinion that Orion's Arm is a serious and visionary website.

 

[mfb]

Sure it has to do with fly-by's. Simply wait until the gas giant planets are aligned so that the proper angle of attach can be used for all of them. We also can adjust spacecraft position before the Oberth maneuvers are done. It not just a matter of waiting for proper planetary alignment, we have the spacecraft positioning option as well.

This is not a choice - if you want to use more than one planet and have some specific target in mind, you have to do both. And again, where is the point? You do not gain anything from it. Doing the whole acceleration close to Jupiter is much more effective.

I do not see how this proposal is a problem.

Reducing mass relative to some baseline is always a problem, otherwise the easy solution would be the baseline.

Simply besting this by an order of magnitude should be possible.

You can use ten thousand engines, but there is no reason to assume they are better in any way. Without an actual design, there is no way to tell.

Rocket engines are really an insignificant part of the mass of the vehicles considered.

They are a relevant part once most of the fuel got used. Lighter tanks make that even more important.

Regardless, I stand by my opinion that Orion's Arm is a serious and visionary website.

The forum rules exclude it as a source.

 

[James Essig]

Well, you can use the Sun, and the gas giant planets as I mentioned before. You always have the angle of attack from the Sun to work with to approach the planets.Whether its 30 years or 300 years, meaningful chemical rocket propulsion to the stars is a valid concept using the Oberth maneuvers as I mentioned above. I stand by this assertion. As I mentioned before, the time for alignment is more like 10 to 30 years or less and not hundreds.

Reducing the mass of computer chips was never a problem as well as increasing chip complexity. I see no reason why the same cannot be applied to mini-rocket engines. Just because it has not been done before does not mean that it cannot occur. SpaceX has had no problem with using 29 engines in its design which is on the order of one magnitude greater in number than typically used.

Just because no one has miniaturized rocket engines does not mean it cannot be done. They use mini rocket engines all the time to propel munitions in warfare, and achieve up to 100 Gs or more doing so. With R & D, I think we could crank out the engines for rockets in a very affordable and effective manner. The Stinger Surface To Air missile is a great example.

We so not have planar arrays of hundreds and even thousands of engines because they simply have not been developed yet. There is no reason to suggest that they cannot. Saying something is impossible or improbable because it has not happened yet does not make sense in a world of exponentiation technology growth and industrial might.

Lighter thanks make the engine mass less important. Remember that it is the tank mass plus the engine mass that is significant. Reducing the tank mass per mass of fuel contained even it the engines' mass stays the same is actually better.

Too bad Orion's Arm is against the rules, Orion's Arm is a visionary and noble website and has lots of factual information.

Using Saturn for an Oberth Maneuver is a great idea after the Sun followed by Jupiter is thus used. I bet that another 40 to 100 km of second perhaps much more additional velocity could be obtained using Jupiter after the previous maneuvers were done.

 

[mfb]

Well, you can use the Sun

I always took that as starting point. Which means you approach Jupiter from a direction that is very close to the sun (or vice versa). If you want maximal final velocity, then your deflection angle at Jupiter is fixed, which gives you four launch windows every 12 years - no problem for interstellar travel. If you also want to use Saturn, it has to be within the narrow Saturn deflection angle relative to your target - that gives you (optimistic) one launch window every three Saturn orbits, roughly one per 100 years. The 84-year-orbit of Uranus and its low escape velocity makes everything worse (the hundreds of years mentioned before, but I did not study the orbital relations in detail), it has to be in a really narrow window to be useful (remember: you come directly from the position of a planet or the sun, no way to change that).
And so far, I did not see an argument to use them at all. Doing the full acceleration close to Sun and Jupiter will give a higher final velocity.

I stand by this assertion.

Science is not a question of opinions.

Reducing the mass of computer chips was never a problem as well as increasing chip complexity. I see no reason why the same cannot be applied to mini-rocket engines.

Rocket engines are not semiconductors. If you make them smaller, they get less powerful (per engine) simply because they have less volume to burn things and area to get fuel in and exhaust out. You miss the point: I do not question their possibility, I question their benefit (and I do not see any argument for them so far).

Lighter thanks make the engine mass less important. Remember that it is the tank mass plus the engine mass that is significant. Reducing the tank mass per mass of fuel contained even it the engines' mass stays the same is actually better.

With arbitrary numbers: If your tank has a mass of 100 tons, then it does not matter much whether the engine has a mass of 1 or 2 tons (1% effect on the final mass and therefore on the mass ratio). If your tank mass goes down to 10 tons, suddenly the difference is 10% and the difference will have a large influence on the mass ratio this stage can reach.

Using Saturn for an Oberth Maneuver is a great idea after the Sun followed by Jupiter is thus used. I bet that another 40 to 100 km of second perhaps much more additional velocity could be obtained using Jupiter after the previous maneuvers were done.

Check the numbers, I calculated that above. The faster you are, the smaller the effect becomes. 40km/s is unrealistic, unless you want to go extremely close to the Sun (possible, but with its own issues).

 

[James Essig]

I cry uncle on this one Staff Mentor. I was more or less playing Devil's advocate to see if I could learn anything from your responses. Sounds like unless one wants to tolerate extreme g's, the Oberth Maneuvers using Saturn do not make sense unless one wants to squeeze every once of velocity out the method as they can.

Going forward, I was curious as to what the maximum velocity gain would accrue using said Jovian and Saturnian Oberth Maneuvers assuming an initial in bound velocity of 100 km/sec, 200 km/second and 300 km/sec that is assuming some way attaining such velocities is possible with the aid of a purely solar Oberth Maneuver for which the planetary maneuvers would follow. If the result is too trivial, that is fine. If I can get even say 20 to 40 km/sec or perhaps a little more velocity gain, that would be helpful for me to know.

I apologize if I seemed to stubborn with this concept. I was a little wedded to the concepts of my inquiry so now I am convinced that your velocity results are good.

Anyhow, I'd like to wish you and yours happy holidays.

Best Regards;

Jim

 

[willem2]

Going forward, I was curious as to what the maximum velocity gain would accrue using said Jovian and Saturnian Oberth Maneuvers assuming an initial in bound velocity of 100 km/sec, 200 km/second and 300 km/sec that is assuming some way attaining such velocities is possible with the aid of a purely solar Oberth Maneuver for which the planetary maneuvers would follow. If the result is too trivial, that is fine. If I can get even say 20 to 40 km/sec or perhaps a little more velocity gain, that would be helpful for me to know.

I think the best you can do would be going to Jupiter first where you use a gravitational slingshot to get to the sun, and after that to burn all your fuel as close to the sun as possible. The reason for this, is that the potential energy when you are closer to the sun than about 50 million km is lower than on the surface of jupiter, so you will be going faster there. This is nicely illustrated here http://xkcd.com/681_large/
We already sent probes to mercury, so this is possible. Moreover you can be this close to the sun for days, so you can burn all your fuel there without needing a large engine.

 

[James Essig]

Sound good. Thanks for the info.

 

[mfb]

You can calculate it yourself: If the point of closest approach has an escape velocity of v_esc (this can be the actual escape velocity from the surface of planets, for the sun you probably want some minimal distance) and you approach the object with velocity v_i, then the spacecraft will accelerate up to $\sqrt{v_i^2 + v_{esc}^2}$. Then you add v_thrust and afterwards you have to leave the gravitational well again, for a final velocity of $$v_f = \sqrt{\left(\sqrt{v_i^2 + v_{esc}^2}+v_{thrust}\right)^2-v_{esc}^2}$$

At the speeds you consider, the gravitational well of sun is negligible at the distance of the outer planets, so you can consider all fly-bys as completely independent events.

 

[James Essig]

Thanks awesomely much, Staff Mentor. I'll run the numbers just so I can see for myself if the method of propulsion makes any sense or not. Again, thanks for the firm critique of my comments.

 

[James Essig]

Thanks for correcting me, Staff Mentor. I got the same numbers you have. Definitely, the notion of using Jupiter does not make much sense in consideration of the 10 percent velocity gain. 5 km/s second extra velocity is not worth the effort. The 2 percent gain using Saturn is even more impractical. As you mentioned, the best bet is to simply dive closer to the Sun and not use the planets.

 

[James Essig]

Hey Staff Mentors;

Just thought to mention that I am co-authoring a popularizing book on interstellar travel possibilities. I cannot not thank you folks enough for correcting my assumptions and providing guidance. I was not too familiar with the Oberth Maneuver but I am pleased to mention that I've learned some cool stuff from you folks about the maneuver and its practical limits.