Gravity in the outer solar system

[Yora]

I was idly thinking about how I would do science fiction if I would do science fiction, and one of my thoughts was that I would want to stick as close to established physics and economic practicability as possible and only use technobabble magic when there isn't any way to do something realistically. The main thing would be hyperspace travel, which I still would like to make as impractical as it can get before it comes pointless. To this end my idea was to have hyperspace relays that send ships trough higher dimensions to get to other stars. And I like the idea that these relays have to be constructed far away from gravitational sources to make them more energy efficient. The Sun-Neptune Lagrange points sound like a fun option.

But this had me wondering. How strong is the gravity of the sun at 30 AU? How much weaker is it compared to the gravity at 1 AU?

I found various numbers and calculators online that talk about the gravitational effect of the sun, but all the numbers I get are vastly contradicting.

Edit:
Keeps searching for online tools.
Uses one that requires solar mass in kg and distances in m.
Makes a table to write down the gravitational effect at the orbital radius of the planets.
Calculates the ratios between the various planets and Earth.
Neptune has a solar gravity effect of 0.11% compared to Earth.
Thinks: "That's a bit less than 1/1000th."
Looks at orbital distance of Neptune: "30 AU"

...wait a minute!

Quick check: 30² = 900
Quick check: 1/900th = 0.11%

So gravity drops off quadratically over distance.
I knew that!

General question still stands: Did I get it right this time?

[factotum]

Yeah, it's just the inverse square law in action, as you've figured out. A body 30x as far from the Sun as Earth will have 1/900th of the solar gravity effect.

Incidentally, the idea of hyperspace travel only being possible at long distances from stars isn't new--Larry Niven's Known Space books all use that principle. The idea is that hyperdrive was discovered by the Outsiders, creatures that live in the void between stars, because they're the only ones who naturally experimented along those lines while far enough from a stellar gravity well for the experiments to actually work, and they then sold the tech to the more planet-bound races of the galaxy. Piloting a ship in hyperspace basically involves watching a "mass sensor" and dropping out of hyperspace when it shows you're getting too close to a gravity well...it's unclear what happens if you go too far in, because any ship that's done so has vanished without trace. (It's kind of cute that Niven never realised that "switch off the engine when the mass sensor gets above a certain level" is something that would be easily done with discrete electronics, never mind computers!).

[Yora]

I calculated that with 1g acceleration and deceleration, you'd get to the orbit of Neptune in 22 days. Then you use the only hyperspace relay in the solar system to make a jump that takes about 1 day per lightyear between the start and end point. For breaking you just get close to a star. (For the return trip you use a hyperspace relay that was send in pieces and assembled by automated construction ships. When the ships come back, you know the relay is ready for service.)
One interesting side effect of not being able to use such a form of travel in significant gravitational fields is that even when you move to the outer solar system first, the star would block a great fraction of the possible straight line trajectories to other stars. You'd have a spherical bubble of impassable space surrounding the star. When you're right at the edge of a sphere tens of AU in radius, the curvature of the sphere would be almost flat on space ship scale, so it would block half of all possible trajectories. So it makes sense to move the hyperspace relay considerably farther out to reduce the blind spot. If the minimum distance from the sun were at 20 AU, then going at 30 AU reduces the blind spot from 180° to under 90° in 2D space. (Yay, graph paper scribble.) And if I am doing the translation into 3D correct, this reduces the number of blocked trajectories from 1/2 to under 1/8.

I think I really have to do something with this. This is fun.

[Radar]

I think I really have to do something with this. This is fun.

Go for it. :) The key thing is, what kind of story do you want to tell in your setting? This will help you focus you worldbuilding toward things you need from which some other interesting details will emerge.

At one point just for the kicks I started looking into how Earth-like planet would look like, if it was a moon of a gas giant (still in the habitable zone of the star). It evolved into a fantasy setting that never went anywhere, since I had no particular goal in mind. I got the general stuff down in reasonable depth, but could not get down to any significant details because of lack of focus.

On a somewhat unrelated note, this idea of hyperspace relays got me thinking of Cowboy Bebop. If for some reason you have not watched the series yet, I really, really, really recommend it. It is a masterpiece.

[danzibr]

One cool thing about Cowboy Bebop is it all takes place in Sol. Lots of exotic things, but all near home.

[Seppl]

I calculated that with 1g acceleration and deceleration, you'd get to the orbit of Neptune in 22 days.

Holding a constant 1g for 22 days may sound harmless but is actually quite the feat. You should rethink if you want this in your setting if you want it to be on the hard-ish side of science fiction. This level of performance is practically impossible with chemical thrusters. You would need something like a nuclear pulse drive or (a bit more on the speculative fiction side) a Bussard ramjet. Both of which would put interstellar distances into the feasible range of such a spacecraft, which would put the need for hyperspace into question.

Or if you have a magic drive that can hold 1g indefinitely and are not afraid of relativity: This would make even intergalactic distances possible to cross in just years of onboard time (including acceleration and deceleration) due to time dilation.

[Yora]

I once did the calculation, and at infinite 1g acceleration, every journey to any place in the universe would take 10 years. Even on the 4 lightyears to Alpha Centauri you would get so close enough to the speed of light for time to basically freeze for the middle stretch of the journey.

But three weeks of 1g seems much less far fetched and in complete violation of all physics than 10 years.

My cheap excuse would be: Fusion Power.

Because fusion power solves all energy problems.

[factotum]

I once did the calculation, and at infinite 1g acceleration, every journey to any place in the universe would take 10 years.

Are you sure about that? The Wikipedia article on constant acceleration in space (yes, there is such a thing: https://en.wikipedia.org/wiki/Space_...t_acceleration) says that crossing our galaxy at 1g constant acceleration would take 12 years "ship time", and the universe as a whole is obviously much larger than just our galaxy.

[shawnhcorey]

My cheap excuse would be: Fusion Power.

Because fusion power solves all energy problems.

Yes but you'll need a propellant. Or invent a reactionless drive.

[Seppl]

Yes but you'll need a propellant. Or invent a reactionless drive.

The Bussard ramjet that I mentioned above addresses the problem of propellant. And does not really work, unfortunately. But at least it does not require breaking the fundamental laws of physics

Maybe some similar idea could be made to work.

Larry Niven even has a short story where two spaceships using such drives go out of control and do exactly what the past few posts suggest: Accelerate indefinitely and leaving known space far, far behind. Or at least close to indefinitely; at some point they would be limited by the maximum exhaust speed of a fusion drive.

[Chronos]

The maximum speed of a ramscoop is 12% of c, because that's the point at which drag from collecting your propellant matches the thrust from fusing it.

And Niven did consider the possibility of automating the mass sensor, but because he wanted to make the pilot still necessary, he said that his hyperspatial mass sensors were partly psionic in their mode of operation, and so required a living, awake pilot.

Back to the OP, the question "how strong is gravity?" depends on what you mean by the strength of gravity. It could depend on the gravitational field, in which case the answer is as you calculated. It could also mean the strength of the gravitational potential, which scales as 1/r instead of 1/r^2. Or it could mean the strength of tidal forces, which scale as 1/r^3. Any of those three could plausibly be the limiting factor on your jump-tech. No matter which one you choose, you can arbitrarily set the numbers so it comes out to "around the distance to Neptune", if that's what you want for your story, but it'll make a difference when you're jumping to stars with different masses. That is, if you're going to a star with half the Sun's mass, the potential will be the same as it is at Neptune at half Neptune's distance, the field will be the same as at Neptune at 71% of Neptune's distance (1/sqrt(2)), and the tidal effects will be the same as at Neptune at 79% of Neptune's distance (1/cube root of 2).

[Seppl]

Back to the OP, the question "how strong is gravity?" depends on what you mean by the strength of gravity. It could depend on the gravitational field, in which case the answer is as you calculated. It could also mean the strength of the gravitational potential, which scales as 1/r instead of 1/r^2. Or it could mean the strength of tidal forces, which scale as 1/r^3. Any of those three could plausibly be the limiting factor on your jump-tech. No matter which one you choose, you can arbitrarily set the numbers so it comes out to "around the distance to Neptune", if that's what you want for your story, but it'll make a difference when you're jumping to stars with different masses. That is, if you're going to a star with half the Sun's mass, the potential will be the same as it is at Neptune at half Neptune's distance, the field will be the same as at Neptune at 71% of Neptune's distance (1/sqrt(2)), and the tidal effects will be the same as at Neptune at 79% of Neptune's distance (1/cube root of 2).

If you want to be realistic regarding relativity then the only real choice is tidal forces. Which could nicely be explained as the hyperdrive requiring reasonably "flat" spacetime.

The other choice would imply the existence of some universal frame of reference. Come to think of that, a hyperdrive already kind of implies such a universal frame, making relativity obsolete in the setting.

[Yora]

Though it's always nice when the technobabble actually makes sense.

I like the idea of a requirement for pretty flat spacetime. It would mean that there would be a hard limit for the size of ships or jumpgates, since their own mass would be warping spacetime. Not sure if that would actually matter, though. Even at 30 AU from the sun, it probably would take a really big mass to surpass its gravitational effect.

[Seppl]

It could also mean, that ships with bigger hyperdrives have to get out further before they work. Because a drive with a larger spatial extend would 'see' more of the curvature (Just like Earth looks pretty flat for normal humans but it would not if you were the size of a mountain). That is some nice way to have justified advantages and disadvantages for different ship sizes.

Self-gravity, huh? Yes, that is a good point. The math on that one would probably not be trivial if you want to account for that. But you could just handwave it by saying that the hyperdrive has to be positioned in or close to the gravitational center of the ship, where those forces cancel each other.

[shawnhcorey]

Self-gravity, huh? Yes, that is a good point. The math on that one would probably not be trivial if you want to account for that. But you could just handwave it by saying that the hyperdrive has to be positioned in or close to the gravitational center of the ship, where those forces cancel each other.

The forces balance themselves out but General Relativity does not. GR is caused by the additive effects of mass. The denser the mass, the greater the effects of GR.

[Seppl]

The forces balance themselves out but General Relativity does not. GR is caused by the additive effects of mass. The denser the mass, the greater the effects of GR.

Not what was meant and not how GR works. The spacetime is still flat when forces cancel each other, and there is no universal reference which to compare the local potential to. Meaning that the local shape of spacetime is all that counts, tidal forces are the only "real" gravitational forces in GR.

[shawnhcorey]

Not what was meant and not how GR works. The spacetime is still flat when forces cancel each other, and there is no universal reference which to compare the local potential to. Meaning that the local shape of spacetime is all that counts, tidal forces are the only "real" gravitational forces in GR.

Nope. If you are between the Earth and Moon exactly at the point were their gravities cancel each other, you would still experience the effects of GR from both. GR changes time and time is a scalar. That's why GR effects add, not cancel each other.

[Seppl]

Nope. If you are between the Earth and Moon exactly at the point were their gravities cancel each other, you would still experience the effects of GR from both. GR changes time and time is a scalar. That's why GR effects add, not cancel each other.

No. Just no. You have a totally meaningless absolute potential. You have the same in every classic field theory. The absolute value of the potential does not mean anything, only the local rate of change. There is no universal time that you could compare your local clock rate to. You could just say that someone with a different potential than yours has a clock that runs faster or slower.

[shawnhcorey]

No. Just no. You have a totally meaningless absolute potential. You have the same in every classic field theory. The absolute value of the potential does not mean anything, only the local rate of change.

Nope. The effects of GR are definitely additive.

[Seppl]

Nope. The effects of GR are definitely additive.

Yes, of course it adds up. Just as in every field theory. It just does not mean anything. There is no experiment that can tell you, what your local value is, only if it is more or less than elsewhere, and how fast and in what ways it changes.

[shawnhcorey]

Yes, of course it adds up. Just as in every field theory. It just does not mean anything.

No. The time dilation of the Earth and the Moon add up. The time dilation if you are at the balance point between the Earth and the Moon is the sum of the time dilation of the Earth (at that distance from it) and the time dilation of the Moon (at that distance from it). It is not, as you say, one.

[Seppl]

No. The time dilation of the Earth and the Moon add up. The time dilation if you are at the balance point between the Earth and the Moon is the sum of the time dilation of the Earth (at that distance from it) and the time dilation of the Moon (at that distance from it). It is not, as you say, one.

So? I do not think you understood what I was saying. Again: There is no universal clock to compare yours to. All you can say is that elsewhere, with a different energy density, clocks will run at a different speed and by how much.

[shawnhcorey]

So? I do not think you understood what I was saying. Again: There is no universal clock to compare yours to. All you can say is that elsewhere, with a different energy density, clocks will run at a different speed and by how much.

I understand what you saying. You're refusing to understand what I'm saying.

It is the depth of the gravitation field that causes time dilation. That makes time dilation additive.

[Seppl]

It is the depth of the gravitation field that causes time dilation. That makes time dilation additive.

Again: So what? So you experience a different time dilation at the (gravitational) half-way point between Earth and Moon than at the half-way point between the Milky Way and Andromeda. That does not change the curvature of spacetime, which is what determines the forces felt by an object at those places. It just tells you something about the relative energy density when comparing those two points. The curvature does not care the slightest about the absolute energy-density, it is determined solely by the distribution of energy/mass here and elsewhere. And you can totally arrange things so that the curvature becomes (almost) flat. And a good strategy to achieve that, is to be a) far away from any other masses, and b) distribute you local mass symmetrically around the point where you want the forces to cancel out. Which was the question OP asked.

[shawnhcorey]

That does not change the curvature of spacetime, which is what determines the forces felt by an object at those places.

You have it backward. It is the time dilation that causes the difference in measurement of distance. Also, saying space is curved is an oversimplification. The difference in measurements is more than a simple curve.

And so what? I thought we were talking about possible effects than may be used to deny why hyperspace cannot be used deep in a gravitational well. What you are saying is fly to the point between the Sun and Jupiter where the forces are equal and opposite and you can hyperjump because the effects of the Sun' gravity has been neutralized.

[Seppl]

And so what? I thought we were talking about possible effects than may be used to deny why hyperspace cannot be used deep in a gravitational well. What you are saying is fly to the point between the Sun and Jupiter where the forces are equal and opposite and you can hyperjump because the effects of the Sun' gravity has been neutralized.

No? Such a point would be among the worst possible locations if we propose that the hyperdrive requires "flatness", i.e. close to zero higher derivatives.

[Yora]

Under my idea, you could enter hyperspace at that point, but you couldn't go anywhere. As soon as you move, you get the significant gravitational effect of Jupiter pulling you out again.