# How would a spaceship not affected by gravity navigate between planets?

Presume there exists a metal called X-matter that has all the properties of steel, except it is repulsed by normal-matter instead of attracted. (For instance, a block of it would accelerate 9.81 m/s/s away from the surface of the Earth. It experiences gravity in the same magnitude, but opposite direction.) By combining or layering X-matter and normal-matter, you can create a structure with net-zero gravitational acceleration. (Or any acceleration between 9.81 m/s/s and -9.81 m/s/s). Let's refer to this combination with net-zero attraction as null-matter.

(Housekeeping notes: X-matter has positive "inertial mass". That is to say it responds to all other forces, such as a hand pushing on it, as normal matter would. Normal-matter is repulsed by X-matter, to avoid runaway motion. You can also presume X-matter to have properties of a different metal like aluminum, if it is more suitable to your solutions.)

Consider a spacecraft made from one or multiple of these materials.

1. How can X-matter be exploited to make space travel easier? Would you use it to accelerate off the surface of the Earth, then "drop ballast", and establish a traditional orbit? Or would you ignore orbits all together, and head straight for the moon, using the "negative mass" to both accelerate off the surface and to slow down towards the moon. What is most efficient?

2. How would a null-matter craft not affected by gravity navigate between, say, the Earth and moon? Would it travel in a straight line? Would this be more energy efficient than a traditional translunar injection?

3. Since null-matter isn't affected by gravity, it would no longer be "trailing" the Earth or Sun through interstellar space, correct? Meaning, from our rotating reference frame, would it appear to arch out and away from the Earth and Sun, despite no forces acting on it?

4. Would X-matter or null-matter be attracted to LaGrange points, or some analog of LaGrange points? My understanding is they would not, from the lack of a centrifugal force alone. X-matter essentially wants to be as far away from mass as possible, preferably in intergalactic space. The only "stable" "orbits" involve being trapped within rings of mass, whose forces cancel out. (Regardless assume we have unlimited quantities of the stuff locked down on Earth for use).

How would you exploit these materials for cheap and easy space exploration! Have I missed anything? Thanks for the help.

• That's why I specified to assume we have unlimited quantities. The means in which its acquired is specific to my world. The short of it is that it was embedded within geological formations on the Earth's crust long after the planet formed. So you just mine it out. Just don't drop it! It would fly into space. I'm sure you can imagine that while transporting it would take some thought, is entirely feasible. Jun 20 at 3:17
• It is "repulsed" in equal and opposite magnitude to normal gravity. So it is repulsed from the earth at 9.81 m/s/s. You don't need to worry about it being repulsed away from your hand, since such a force is as tiny as the force pulling a steel ball into your hand, which is to say, negligible. Jun 20 at 3:19
• Like I said, it didn't form with it, it was embedded later, magically as you say. And just because its fantasy doesn't mean you can handwave any problem you have, that's not really how stories work. The Hobbits didn't just teleport to mount doom because "they had magic anyways". I don't believe you're engaging with the actual prompt and questions (I'm not asking how planets form or how someone would gather this material), but thank you for your input. Jun 20 at 3:42
• One thing that you could do with X-matter would be to build a perpetual motion machine and create energy for free. Just use the X-matter to cart a mass to the top of a tower where it can be lowered via a cable running around a wheel attached to a generator, then use the layering technique to return the X-matter to the ground. rinse and repeat (and many other ways are possible). Jun 20 at 11:23
• Well that's not a perpetual motion machine ... thats a machine turning the gravitational potential of X-matter into another form of energy. Remember X-matter operates exactly like a very strong lifting gas. You don't think a helium balloon generates infinite energy, right? It produces upwards lift, exactly like an X-matter balloon does. Yes X-matter can lift stuff into the air, but then you have to pull the X-matter back down, using just as much energy. Jun 20 at 14:55

Hmm... Interesting.

You could use X-matter's antigravity to get out of the Earth's atmosphere, I suppose, but I don't think there'd be much point. X-matter is probably expensive, so you wouldn't want to jettison it if you didn't have to. And there are plenty of other, inexpensive and well-developed ways to get through the atmosphere. Like propellers.

Also, if your ship has exactly enough X-matter to perfectly cancel the gravitational mass of itself and its passengers and cargo, it would float into the air all on its own, just like a balloon. Balloons float because they weigh less than the air they displace. A well-calibrated X-matter ship would weigh nothing at all.

As far as interplanetary travel goes, I see two possible approaches.

The simpler, by far, is to make sure that the gravitational mass of the regular matter of your ship is exactly canceled out by the antigravity of the X-matter on board at all times. This lets you ignore gravitational fields entirely. Simply point your ship at where your destination (whether that be the Moon, or Mars, or whatever else) is going to be at some time in the future, then burn your engines to make sure you get there at the same time. You'll need to match speeds with your destination planet (or moon) once you get there, but that's the only real delta-V expenditure necessary.

As an example, let's take the Moon.

We start by floating out of the atmosphere, and then performing a burn that'll get us to the Moon's orbit in a reasonable amount of time. We can choose this entirely arbitrarily, and can make it as low as we like if we don't mind the trip taking a long time. But for the sake of example, a 2 km/s burn will get us there in 2 days and 5 hours, which seems reasonable enough to me.

Once we get to the moon, we'll need to cancel out that 2km/s with another burn, and also burn to match our speed with the Moon's orbital velocity, which is almost exactly 1 km/s. We can combine these into a single maneuver, by burning diagonally for about 2.2 km/s.

When we want to return home, we'll need to repeat the 2.2 km/s diagonal burn to put us back on a collision course with Earth, but we do not need to use propellent to slow ourselves down from 2 km/s. We can use a heatshield for that.

So that's to the Moon and back in four and a half days, with a total delta-V of about 6.4 km/s.

For comparison, the orbital speed in Low Earth Orbit (for spacecraft made of ordinary matter) is about 7.8 km/s. Putting a satellite into LEO requires more delta-V than that, to push through the atmosphere and get it up to altitude. And if you want to get from LEO to the moon, you'll need another 6 km/s. And yet another 6 km/s on top of that to get back to Earth.

In short: Using X-matter to cancel your gravitational mass (and carefully jettisoning it as you burn your engines, to keep your ship's total gravitational mass exactly zero) can cut the delta-V needed to get to the Moon and back by at least a factor of three. That sounds like a good deal, although it does still require jettisoning a lot of X-matter. The more efficient your engines are, the less X-matter you'll need to jettison.

Aside: Is X-matter chemically reactive at all? I know some solid rocket fuels use aluminium as an ingredient. If the X-matter that you're jettisoning while you're burning your engines can contribute to the thrust you're producing, that'd be much more efficient than just dumping it overboard.

As an alternative to keeping your ship's gravitational mass constantly neutral and relying on conventional rocket engines for delta-V, you could instead produce delta-V (as suggested in the OP) by using X-matter's antigravity properties.

A trip to the Moon by this method might look something like this:

You start by hauling your ship to a very precise location on Earth's surface, somewhere near the equator. Your ship, at this point, has considerably more X-matter than normal matter. At just the right time, you cut the tether and shoot into the sky.

Once you get close enough to the Moon that its gravity starts to become stronger than Earth's, you jettison some normal matter, making your ship's gravitational mass even more negative. This is necessary because Earth's gravitational well is much deeper than the Moon's. If you didn't do this, you'd crash right into the Moon.

At this point, you're somewhere between Earth and the Moon, but also a little bit ahead of the Moon in its orbit. The Moon's antigravity on your X-matter both slows you down and pushes you forward, helping to match your speed with its orbital speed.

The Moon continues in its orbit and passes by you just before you fully match speeds. You jettison some X-matter, bring your gravitational mass back into the positive, and use rockets to set yourself down in a very precise location on the Moon's surface.

When it's time to leave, you jettison some normal matter to take off. Because of where you landed, this counters the Moon's orbital velocity and puts you on a direct collision course with Earth. When you leave the Moon's sphere of influence, you jettison more X-matter to make sure the Earth doesn't push you away.

Once you reach the Earth, you can brake and land using heatshields and parachutes.

The exact amount of X-matter you'd need to jettison will depend on a number of factors, including the mass of your ship and how long you want the trip to take.

I've no idea which of these approaches would end up wasting more X-matter. But the second approach requires far less rocket fuel, so based on that alone, it'll probably be the preferred approach. That is, unless X-matter is so incredibly expensive that it's not worthwhile to use any of it at all.

A gravitationally-neutral object will be affected by centrifugal and Coriolis forces in exactly the same way as normal matter. If you launch it off Earth, it'll follow a straight-line path through the solar system, as seen from an observer in a non-rotating, non-accelerating reference frame. In any rotating reference frame, it will appear to take a curved path. Just like how a ball thrown on a spinning platform appears to curve to the side.

That is to say, the mass term in the centrifugal and Coriolis force equations is inertial mass, not gravitational mass.

You're right that a gravitationally-neutral object would not be affected by Langrange points. Lagrange points are places where gravity and the centrifugal force cancel out. Without gravity, they don't exist.

However, a chunk of X-matter with negative gravitational mass will have its own version of the L1 Lagrange point.

L1 is a point between (let's say) the Earth and the Moon where the Earth's gravity, the Moon's gravity, and the centrifugal force all balance out.

For ordinary matter, the Moon's gravity pulls away from Earth, in the same direction as the centrifugal force; while Earth's gravity must counter them both.

For X-matter, it's Earth's antigravity that pushes in the same direction as the centrifugal force, and both of those forces must be countered by the Moon's antigravity. So for X-matter, the L1 equivalent is closer to the Moon than normal-matter-L1 is. It still won't be a stable place to park a spacecraft, though. Any perturbation out of the plane of the orbit (or probably forward or backward, though I'm not certain of that), will send the X-matter flying off into interstellar space. And for X-matter, the other Lagrange points (L2-L5) simply don't exist at all.

• Thank you for such an excellent response! You cleared up multiple confusions I had. I would like to bounce one idea of you. The idea is that X-matter is used like a gravitational battery to power "free" space travel, where X-matter ships "fall" for free to a L-point (L1 maybe), and then you switch onto a normal-matter ship, which falls for free towards Earth/Moon. The main issues I see with this are 1. you have to make ships at LaGrange point, 2. you still have to slow the ship down despite free speed-up, and 3. instability of L1. Jun 20 at 5:20
• Using X-matter to "fall for free" from the surface of a planet will only let you accelerate directly away from the planet. L1 moves in a circle around the Earth, at nearly the Moon's orbital velocity. Even with careful usage and jettisoning of X-matter, you'd still need to burn about 1 km/s of propellant in order to rendezvous at L1. And if you want to park at normal-matter-L1, you can't have any X-matter on board whatsoever. Jun 20 at 5:35
• Just to clarify .... Lets call L1 L1(+1) and the X-matter L1 equivalent L1(-1). Can a normal-matter ship not park with X-matter onboard because all that X-matter wants to get to L1(-1), and would destabilize it? Would there not be an equilibrium point midway, L1(.5)/L1(0)/L1(-.5), that would become the L1 point for a ship with a mixture of normal and X-matter? Jun 20 at 5:55
• @SeanHarris Consider a ship an entirely-normal-matter ship at L1(+1), that exchanges some of its cargo (say, 1/3 of its mass) for an equivalent mass of X-matter. The gravitational forces from Earth and the Moon get cut in half, but centrifugal force stays the same, so it'll start drifting away from Earth and towards the Moon. To reach an equilibrium point (i.e. L1(+0.5)) it'll need to increase the gravitational pull from Earth and decrease the centrifugal force, by moving closer to Earth. Jun 20 at 18:24
• More generally, as the gravitational-to-inertial mass ratio λ goes from +1 to 0, L1(λ) moves from L1(+1) to the center of the Earth. And as λ goes from -1 to 0, L1(λ) moves from L1(-1) (which is already somewhere between L1(+1) and the Moon) toward the center of the Moon. The only way to get an L1-equivalent between L1(+1) and L1(-1) would be to have more gravitational mass than inertial mass, i.e. λ > 1 or λ < -1. Jun 20 at 18:37
1. It would be utilizing Null matter to reduce fuel required on take off and/or reduce the hassles from landing process since less acceleration needed = less fuel required to do so(ie orbiting/creating drag force to slow down). [X-matter still have inertial mass, it's repulsing nature help cancel out gravitation pull from planet]

since normal matter would required

• [fuel to win earth's gravitational pull] + [extra fuel for acceleration to reach escape velocity]

while x/null matter

• [fuel to win earth's gravitational pull] + [extra help from X/Null-matter repulsing to earth' gravitational pull] + [extra fuel for acceleration to reach escape velocity]
1. X/Null-matter will exert an acceleration to counter both of them, and stay in Neutral Buoyancy state (mostly: incase of Null Matter),(similar to Buoyancy but in 3D).

2. Yes, from 2nd point, it would appear as floating substance that would stay in place (in larger scale observation plain) but as observator on earth it would seem like it moving away it opposite direction of earth's rotation, earth orbiting sun, solar system orbiting galaxy and so on, unless there is other force apply to it such as wind/ magnetic(if said null matter is contained metal) etc

3. Null-matter will, even if there are objects at L-points already, since larger celestial body's gravitational force is much greater, lesser mass at L-points wouldn't be affecting much, so it would still be within the same approximate area. while pure X-matter won't since it's repulsing acceleration cancel out gravitation force at any point which = 0 centrifugal = stay still

Further more than this is building a structure out of X-matter (let say it 70-90% of total materials) as a node staying at L1 (or either of others L-points due it's nature) between planets as terminal or depot station. [not going full on max 100% b/c you will probably utilized Null matter from 1st points. if it 100%, it gonna required quite more energy for Null-matter spacecraft to enter said X-matter Station].

So all in all, imo these X-Matter/Null-Matter will improved STL travel significantly, especially within star system. but if it between system or FTL, not so much

more thing to noted, so X-matter won't get pulled by blackhole too (or getting pulled less for Null-matter by exerting same/almost same amount of acceleration oppose to blackhole gravitational force)

• Thank you! By what reason do you say X-matter would be attracted to L-points? At an L-point, the centrifugal force perfectly balances both gravitational forces. However for X-matter, those gravitational forces are reversed, and I believe there is no centrifugal force at all, since there is no orbit. Jun 20 at 4:33
• OP clearly stated that the inertial mass is still positive. So point 1 in your answer is wrong.
– L.Dutch
Jun 20 at 4:49
• There is no "escape velocity" if the ship is not attracted by Earth. It can move in whatever direction it wants as slow as it wants. Jun 20 at 6:41
• fixed, sorry for misinterpret -1st point: not less mass, mass still the same, escape velocity still the same, X/Null matter's repulsing force is just an extra discount to force required to achieved escape velocity -and 4th points, Null-matter still go toward L-points like normal object do (just slower) while X-matter won't be affected by gravitational since it cancel out Jun 20 at 6:41

## Fuel consumption will make your math more complicated... but the technology is still worth exploiting

If you have a rocket ship in a perfect state of null gravity, and try to launch it, it will consume fuel meaning that it will slowly become more and more Negative Gravity biased. In fact, I'd suggest you make the whole ship out of X-matter so that you can offset that weight with normal matter fuel and cargo. So, a rocket ship will never actually be at null gravity for long, rather some offset of null gravity based on how much fuel it has used up and its current cargo load.

For this I would recommend starting your journey at Null or Positive Gravity using space elevators. A space elevator would be MUCH easier to construct once you can offset it's gravitational stress with X matter. It could simply be a normal steel and x-matter cable with enough X matter at the tip to hold it up. By using an elevator to get to space, you don't need any reaction mass to bypass the atmosphere; so, by the time you get there, you are still close to Null Gravity. Once in space, you just need to hang onto the ship until the Earth is lined up in the right direction and let go. The rotation of the Earth means you are imparting angular momentum on the ship allowing you to fling it about 460mps in a more or less straight line out into space.

While this is a good start, it's still not very fast as far as space travel is concerned; so, you will want to keep pushing it along. This is where you want to switch to rocket powered flight. While your initial path might include a slight fall, if you start at a positive weight, your course will arc you away from astral bodies as you consume fuel, but not as quickly as normal matter falls into it since you will still have a certain ratio of normal matter to work with.

As you approach your destination planet, this is where your exact fuel consumption becomes super important to plan in advance because the planet will repel you as you get closer helping to slow your approach and match speeds with the target world. If you plan it out just right you will slow to a zero net speed right as you come in line with a space elevator on the other world that will need to hook onto you to keep you from falling back out into space. The elevator will then reel you down to the planet surface to delivery your cargo and refuel for your next trip.

• This was my first thought. X-matter would make space elevators considerably easier. Spaceships would stay in space and be more or less conventional, and people/material moved to and from orbit via an X-matter elevator (far more efficient than rockets).
– bta
Jun 20 at 20:06

LaGrange points aren't just a gravitational phenomena. They're based on both gravity and momentum.

L1 would still exist as a quasi-stable null gravitational node, but for all of the rest, momentum and gravity cancel each other out, but if gravity were reversed, they would be additive. Anything there would just fly off.

It wouldn't be the same L1, though. It would be closer to the orbiting body. The orbital momentum would need to be cancelled by a greater push from the orbiting object.

How would it effect space flight? That depends on how prevalent it is. Basically, take the total mass of the stuff, and that's a mass that you can get into orbit easily. You wouldn't need to put things in orbit, they'd just hang there. It would be like starting with an unlimited supply of space elevators.

Remember, though, that you're only talking gravity, not momentum. The biggest obstacle to us visiting other planets is the long travel times. You'd get a boost from being pushed away from Earth, but you'd still wind up with long travel times.

You'd also still need rockets to equalize momentum. It would be cool if you could switch the material's polarity by, for instance, oxidizing and reducing it.

Edit: When I said "floating in place", I wasn't taking into account the negative force of the Sun, or the rest of the galaxy for that matter. I looked these up, and I'm going to stick with my original answer.

The gravitational force of the Sun at Earth's orbit is 0.0006 the strength of Earth's gravity on the surface. That would require station keeping engines, but I think that would be manageable. The gravitational force of the galaxy at that point is 1% of the Sun's influence.

This would put an upper end on how long a satellite could hang above the planet before it was pushed out of the solar system by centrifugal force. There would still be a pseudo-L1.

• Thing is I don't think null-matter would just hang above the planet motionless because its not following the Earth as it rotates or arcs around the sun. Within the atmosphere its different, because the air is like a current in a river dragging the craft along with it, but outside of the atmosphere, a null-matter craft basically "doesn't know" its next to a planet. It will just continue with whatever velocity it had, as the planet arcs away, rotating towards the sun and around it's own axis. And an "on-off" switch to the polarity gives you perpetual energy IMO. Basically free grav potential. Jun 20 at 8:19
• The "hanging motionless" thing just depends on your timescale. A null-matter ship initially at rest relative to Earth's surface would hang there without moving noticeably for minutes, but would start to drift away (due to its linear velocity and Earth's rotation) over a few hours. If it was directly over one of Earth's poles (or otherwise initially at rest relative to Earth's center of mass), it would stay near Earth for days, but over months it would drift away due to Earth's orbit curving away from it. Jun 20 at 18:47
• Actually, Sean is right. I hadn't considered the sun's gravity, or the gravity of the galaxy, or the gravity of the Great Attractor. I'm going to edit my response. Jun 21 at 4:32

Please do NOT do this. It's trivial to show that any kind of anti-gravity thingy is in fact a infinite energy source (i.e. even worse than a perpetual motion machine).

If you recall basic General Relativity, even photons and other massless particles experience attractive gravitational forces. The moment you introduce your magic anti-grav material you might as well call it a magic universe, not a Sci-Fi universe.

• Feel free to describe how the regime I described produces infinite energy. Jun 20 at 14:50
• @SeanHarris You can easily find the explanation at many physics "help" sites. Basically, you stick a block of mass into your antigrav magic material, float upwards, then drop the block of regular mass. Now you have free energy. Or, connect your X-material to a crankshaft like in a car engine, give it a push, and let it run forever. Jun 20 at 15:01
• @SeanHarris it's really worse than that - even if you somehow could create x-material, it will repulse in all directions and sooner or later be accelerated away from all mass, i.e. to the boundary of the univers Jun 20 at 15:03
• I think you should reread the original post. X-matter and a strong lifting gas operate in identical ways (that within a black box you could not tell them apart). X-matter has "anti" gravitational potential which can be converted into energy, but that's not free energy. No more than dropping an anvil from a blimp is "free energy". And I'm not interested in how X-material would behave from 13 billion years ago onwards, as I clarified it is embedded on a planet long after the planet forms. Jun 20 at 15:05
• @SeanHarris I did read it. You still can't create this stuff in the first place specifically because of its repulsive behavior. And if you did it would be much much simpler to use it as a perpetual motion machine to "charge up" any secondary rocket propulsion system in the first place. Jun 20 at 16:46