The dumb questions thread

[beero1000]

Imagine you have an object with mass you want to move over astronomical distances, and which you can not encase or otherwise directly push, and which is also electrically neutral so magnets won't help either. I can think of one and only one way to move such an object: have it orbit another body (say an asteroid) and push *that* body so it's pulled along by its gravity. Am I missing an obvious alternative?

What's the hypothetical maximal acceleration you can give the asteroid-target object system without losing the target? I know you can't go beyond the asteroid's gravitational acceleration at whatever altitude you have your target in orbit, but is there a precisely calculable even lower limit above which the orbit deteriorates into a highly eccentric one so you still lose your satellite at its periapsis? Or is *any* amount of continued acceleration eventually going to lead to this? (Preliminary calculations using the higher theoretical maximum suggest that it would take at least 3.5 years to accelerate Ceres to 0.1c without pushing hard enough for loose rocks on its surface to be left behind, more if you want to keep something in orbit.)

What would be the energy requirements for accelerating an asteroid (let's not be skimpy, take Ceres, anything smaller than that and we're probably too slow to be of much use) at such a rate?

If tried to do some of the calculations with Wolfram Alpha, but I seem to get the wrong kinds of units in the result: I was expecting watts and got newtons for Ceres gravity * Ceres mass.



I'm considering the logistics of moving a wormhole entrance to an interstellar destination. I'm assuming macroscopic wormholes can be created and stabilised for all practical purposes indefinitely, but in their creation the laws and speed limits of causality in 3d-space still have to be obeyed: Or in other words, the shortcut through a higher dimension the wormhole represents cannot be used for its own creation. I'm also assuming that it is, partly for this reason, impractical to create the entrances more than a few light-seconds, light-minutes at most, apart, and the only way to get a useful interstellar wormhole is to move it conventionally. And since the wormhole doesn't know the difference between a ship, a container hull, and a planet surface, and will transport them all across indiscriminately, the only safe place for it is in orbit and the only safe way to transport is is to pull it gravitationally.

I don't think that that idea would work, any constant amount of thrust would eventually unbind the orbit. You might be able to get it to work by timing thrust pulses to specific points on the orbit that are calculated to maintain the system (like pumping on a swing). An alternative would be to not try to maintain an orbit, but just shoot asteroids by the wormhole one after the other. Each one would add some energy as it goes by.

 

[beero1000]

(Suspects I'm being set up for a trap.)

It provides an evolutionary advantage. Changing seasons changes the background against which animals must hide. Animals that can blend in have a greater advantage in the game of hunter vs. prey. But a color that works well in a summer forest environment would stand out against a white wintry background.

No, not a trap or similar.

When I asked why, you just gave an answer of what a theory says about it.

However, the wolf have no idea that its skin changes, then, such is not camouflage because the animal has no control of it, same with other animals.

What that theory mentions is simply wrong.

It must be a real reason why some species have their skin color changes in Winter. Somebody knows it?

 

[Kharakov]

When a mathematician plays the πcard, your idea is worthy of being added to the circular filing cabinet! Good job!

 

[Jokodo]

On second thought, I'm unsure this would do the job: it's the wormhole as a whole that does something to the mass you shoot in, not just the far exit. So I guess this would shift both exits. So this might be useful for creating a shortcut from Sirius to Alpha Cen but less so for linking the Solar System to either.

Not so. If you had a water tank up nice and high, and used a hosepipe to siphon water from the tank down to the ground, the water coming out will push the hose outlet/nozzle backwards; But the water going in won't exert a significant force on the inlet end of the pipe.

I'm not sure that's true. I've seen improperly attached hoses fly off even though they were open at the other end.

If your reaction mass approaches the inlet from a wide range of directions, but all leaves the outlet moving in the same direction, the outlet will accelerate, but the inlet need not.

Why would it fly off all in the same direction though?

Of course, I don't know whether the wormhole has properties similar to a hosepipe. A rigid pipe would accelerate as a whole; but presumably there's nothing that fixes the distance between the two ends of your wormhole, and they are free to move independently - in which case the hosepipe might be a fair analog.

I hope there isn't anything to fix the distance, and I don't see why there would be - that's not the point though. The point is that a force that is applied to the wormhole as a whole should either move both ends (potentially in opposite directions in normal 3d space, but still both ends), or fail to move either.

I think a better analogy would be the classical folded paper 2d model of a wormhole. We're creating a shortcut between the two sheets close to the fold and shifting the location of the shortcut. Without moving the fold itself, doing so will move both entrances.

That model also predicts the wormhole to be a deterministic, information lossless system where every incoming angle corresponds to one and only one outgoing angle, and two objects entering at a given angle to each other will also leave at the same angle.

 

[Jokodo]

Imagine you have an object with mass you want to move over astronomical distances, and which you can not encase or otherwise directly push, and which is also electrically neutral so magnets won't help either. I can think of one and only one way to move such an object: have it orbit another body (say an asteroid) and push *that* body so it's pulled along by its gravity. Am I missing an obvious alternative?

What's the hypothetical maximal acceleration you can give the asteroid-target object system without losing the target? I know you can't go beyond the asteroid's gravitational acceleration at whatever altitude you have your target in orbit, but is there a precisely calculable even lower limit above which the orbit deteriorates into a highly eccentric one so you still lose your satellite at its periapsis? Or is *any* amount of continued acceleration eventually going to lead to this? (Preliminary calculations using the higher theoretical maximum suggest that it would take at least 3.5 years to accelerate Ceres to 0.1c without pushing hard enough for loose rocks on its surface to be left behind, more if you want to keep something in orbit.)

What would be the energy requirements for accelerating an asteroid (let's not be skimpy, take Ceres, anything smaller than that and we're probably too slow to be of much use) at such a rate?

If tried to do some of the calculations with Wolfram Alpha, but I seem to get the wrong kinds of units in the result: I was expecting watts and got newtons for Ceres gravity * Ceres mass.



I'm considering the logistics of moving a wormhole entrance to an interstellar destination. I'm assuming macroscopic wormholes can be created and stabilised for all practical purposes indefinitely, but in their creation the laws and speed limits of causality in 3d-space still have to be obeyed: Or in other words, the shortcut through a higher dimension the wormhole represents cannot be used for its own creation. I'm also assuming that it is, partly for this reason, impractical to create the entrances more than a few light-seconds, light-minutes at most, apart, and the only way to get a useful interstellar wormhole is to move it conventionally. And since the wormhole doesn't know the difference between a ship, a container hull, and a planet surface, and will transport them all across indiscriminately, the only safe place for it is in orbit and the only safe way to transport is is to pull it gravitationally.

I don't think that that idea would work, any constant amount of thrust would eventually unbind the orbit. You might be able to get it to work by timing thrust pulses to specific points on the orbit that are calculated to maintain the system (like pumping on a swing). An alternative would be to not try to maintain an orbit, but just shoot asteroids by the wormhole one after the other. Each one would add some energy as it goes by.

It would be pretty hard to use that technique to decelarate at the target with no infrastructure in place, though, wouldn't it?

Anyway we want to open trade with  Gliese_667_Cc through the wormhole before the end of the 24th century! We need a terminal velocity of no less than 0.1c, and an average acceleration to get us to that velocity in no more than 50 years!

My hidden agenda is actually to argue that even if stable macroscopic wormholes and their at-will creation are possible (which they probably aren't), the logistics of installing one under reasonable assumptions are so overwhelming that they aren't actually a solution to the vastness of space. Your contention that it's even harder than I may have thought seems to prove me right.

I'd still like to put some rough number on just how overwhelming, say as a multiple or fraction of global primary energy consumption during the acceleration phase assuming 100% efficiency with the cheapest method that gets us to a reasonable speed within mere decades.

 

[beero1000]

I don't think that that idea would work, any constant amount of thrust would eventually unbind the orbit. You might be able to get it to work by timing thrust pulses to specific points on the orbit that are calculated to maintain the system (like pumping on a swing). An alternative would be to not try to maintain an orbit, but just shoot asteroids by the wormhole one after the other. Each one would add some energy as it goes by.

It would be pretty hard to use that technique to decelarate at the target with no infrastructure in place, though, wouldn't it?

Anyway we want to open trade with  Gliese_667_Cc through the wormhole before the end of the 24th century! We need a terminal velocity of no less than 0.1c, and an average acceleration to get us to that velocity in no more than 50 years!

My hidden agenda is actually to argue that even if stable macroscopic wormholes and their at-will creation are possible (which they probably aren't), the logistics of installing one under reasonable assumptions are so overwhelming that they aren't actually a solution to the vastness of space. Your contention that it's even harder than I may have thought seems to prove me right.

I'd still like to put some rough number on just how overwhelming, say as a multiple or fraction of global primary energy consumption during the acceleration phase assuming 100% efficiency with the cheapest method that gets us to a reasonable speed within mere decades.

Not necessarily.

You could do it with a setup at the destination that can send the asteroids back at an appropriate course/speed. It wouldn't need anything to already exist at the destination, we could send the 'catcher' setup as the first object used to accelerate the wormhole. If your catcher is efficient at redirecting the incoming asteroids, then you might not lose much energy at all.

Depending on what the rules are for wormholes, you could have the catcher create a wormhole pair with adjacent endpoints, where the asteroids come in in one direction and then get spit out traveling in another direction. You could have just a few asteroids traveling in a loop to accelerate the wormhole, and then reverse the orientation of the loop to slow it down again.

I did a quick literature search and this paper (which proposes moving Earth's orbit to 1.5AU :O) says that gravity energy boosts by sending asteroids by the Earth can be up to 2.4 trillion ergs per gram of object mass, per pass. I didn't check the reference to see how that was calculated, but that might give you an idea of how much energy can be transferred by objects traveling by the wormhole and how much energy would be needed to get it where you want it to go.

 

[Jokodo]

I don't think that that idea would work, any constant amount of thrust would eventually unbind the orbit. You might be able to get it to work by timing thrust pulses to specific points on the orbit that are calculated to maintain the system (like pumping on a swing). An alternative would be to not try to maintain an orbit, but just shoot asteroids by the wormhole one after the other. Each one would add some energy as it goes by.

It would be pretty hard to use that technique to decelarate at the target with no infrastructure in place, though, wouldn't it?

Anyway we want to open trade with  Gliese_667_Cc through the wormhole before the end of the 24th century! We need a terminal velocity of no less than 0.1c, and an average acceleration to get us to that velocity in no more than 50 years!

My hidden agenda is actually to argue that even if stable macroscopic wormholes and their at-will creation are possible (which they probably aren't), the logistics of installing one under reasonable assumptions are so overwhelming that they aren't actually a solution to the vastness of space. Your contention that it's even harder than I may have thought seems to prove me right.

I'd still like to put some rough number on just how overwhelming, say as a multiple or fraction of global primary energy consumption during the acceleration phase assuming 100% efficiency with the cheapest method that gets us to a reasonable speed within mere decades.

Not necessarily.

You could do it with a setup at the destination that can send the asteroids back at an appropriate course/speed. It wouldn't need anything to already exist at the destination, we could send the 'catcher' setup as the first object used to accelerate the wormhole. If your catcher is efficient at redirecting the incoming asteroids, then you might not lose much energy at all.

Depending on what the rules are for wormholes, you could have the catcher create a wormhole pair with adjacent endpoints, where the asteroids come in in one direction and then get spit out traveling in another direction. You could have just a few asteroids traveling in a loop to accelerate the wormhole, and then reverse the orientation of the loop to slow it down again.

I did a quick literature search and this paper (which proposes moving Earth's orbit to 1.5AU :O) says that gravity energy boosts by sending asteroids by the Earth can be up to 2.4 trillion ergs per gram of object mass, per pass. I didn't check the reference to see how that was calculated, but that might give you an idea of how much energy can be transferred by objects traveling by the wormhole and how much energy would be needed to get it where you want it to go.

That seems like a rather different problem though. They're calculating with a Kuiper belt object on a highly eccentric orbit that sheds some of its kinetic energy to earth on its inward passage and gains some from jupiter on its outward leg -- and it doesn't even have to be every passage. With the timescales involved (they calculate that for an object with 1e22kg, one pair of encounters per 6000 years should be enough to maintain constant radiation flux at earth), this basically means you can let Kepler's laws do most of the work for you, with only minor corrections needed. (An obvious downside of that scheme is that, if and when the civilisation calculating and implementing the minor corrections collapses, you still have an earth crossing 1e22kg planetoid on an "optimal trajectory" where it'll "nearly graze the
Earth’s atmosphere" at least once every 6000 years. I wonder why that might be a bad idea...)

I grant you that the wormhole is likely going to be much lighter than earth, but if we're interested in getting it on an interstellar trajectory within mere decades or centuries, while we may be able to use lighter asteroids as our means of choice, we'll have to push them in the right place with brute thruster force instead of waiting till they're (almost) in their right place all by themselves, with only minor corrections needed.

 

[beero1000]

Not necessarily.

You could do it with a setup at the destination that can send the asteroids back at an appropriate course/speed. It wouldn't need anything to already exist at the destination, we could send the 'catcher' setup as the first object used to accelerate the wormhole. If your catcher is efficient at redirecting the incoming asteroids, then you might not lose much energy at all.

Depending on what the rules are for wormholes, you could have the catcher create a wormhole pair with adjacent endpoints, where the asteroids come in in one direction and then get spit out traveling in another direction. You could have just a few asteroids traveling in a loop to accelerate the wormhole, and then reverse the orientation of the loop to slow it down again.

I did a quick literature search and this paper (which proposes moving Earth's orbit to 1.5AU :O) says that gravity energy boosts by sending asteroids by the Earth can be up to 2.4 trillion ergs per gram of object mass, per pass. I didn't check the reference to see how that was calculated, but that might give you an idea of how much energy can be transferred by objects traveling by the wormhole and how much energy would be needed to get it where you want it to go.

That seems like a rather different problem though. They're calculating with a Kuiper belt object on a highly eccentric orbit that sheds some of its kinetic energy to earth on its inward passage and gains some from jupiter on its outward leg -- and it doesn't even have to be every passage. With the timescales involved (they calculate that for an object with 1e22kg, one pair of encounters per 6000 years should be enough to maintain constant radiation flux at earth), this basically means you can let Kepler's laws do most of the work for you, with only minor corrections needed.

I grant you that the wormhole is likely going to be much lighter than earth, but if we're interested in getting it on an interstellar trajectory within mere decades or centuries, while we may be able to use lighter asteroids as our means of choice, we'll have to push them in the right place with brute thruster force instead of waiting till they're (almost) in their right place all by themselves, with only minor corrections needed.

Not exactly the same, no, but definitely related. It's all about transforming gravitational energy to kinetic energy and vice versa. And you would be able to use gravitational slingshots and other tricks as well. Once you have wormholes, you could imagine doing clever things like repetitive slingshots between wormholes to build up crazy speeds, wormhole energy accumulators, etc...

But hey, it's your universe. Just make the wormholes really massive and energy expensive to create and you can severely limit what is possible with the energy available.

 

[Jokodo]

Not necessarily.

You could do it with a setup at the destination that can send the asteroids back at an appropriate course/speed. It wouldn't need anything to already exist at the destination, we could send the 'catcher' setup as the first object used to accelerate the wormhole. If your catcher is efficient at redirecting the incoming asteroids, then you might not lose much energy at all.

Depending on what the rules are for wormholes, you could have the catcher create a wormhole pair with adjacent endpoints, where the asteroids come in in one direction and then get spit out traveling in another direction. You could have just a few asteroids traveling in a loop to accelerate the wormhole, and then reverse the orientation of the loop to slow it down again.

I did a quick literature search and this paper (which proposes moving Earth's orbit to 1.5AU :O) says that gravity energy boosts by sending asteroids by the Earth can be up to 2.4 trillion ergs per gram of object mass, per pass. I didn't check the reference to see how that was calculated, but that might give you an idea of how much energy can be transferred by objects traveling by the wormhole and how much energy would be needed to get it where you want it to go.

That seems like a rather different problem though. They're calculating with a Kuiper belt object on a highly eccentric orbit that sheds some of its kinetic energy to earth on its inward passage and gains some from jupiter on its outward leg -- and it doesn't even have to be every passage. With the timescales involved (they calculate that for an object with 1e22kg, one pair of encounters per 6000 years should be enough to maintain constant radiation flux at earth), this basically means you can let Kepler's laws do most of the work for you, with only minor corrections needed.

I grant you that the wormhole is likely going to be much lighter than earth, but if we're interested in getting it on an interstellar trajectory within mere decades or centuries, while we may be able to use lighter asteroids as our means of choice, we'll have to push them in the right place with brute thruster force instead of waiting till they're (almost) in their right place all by themselves, with only minor corrections needed.

Not exactly the same, no, but definitely related. It's all about transforming gravitational energy to kinetic energy and vice versa. And you would be able to use gravitational slingshots and other tricks as well. Once you have wormholes, you could imagine doing clever things like repetitive slingshots between wormholes to build up crazy speeds, wormhole energy accumulators, etc...

But hey, it's your universe. Just make the wormholes really massive and energy expensive to create and you can severely limit what is possible with the energy available.

It's not my universe, it's meant to be our universe only with wormholes. I'm actually interested in how much if anything the creation of wormholes might buy us in this universe of ours otherwise as we know it for going interstellar, assuming known physics to hold wherever applicable (i.e. no FTL causality effects before the wormhole is in place - after that it is no longer FTL, just a shortcut in space; no intelligence on the side of the wormhole capable of distinguishing a ship that wants to go through from a ship that wants to push it, etc.).

My intuition is "not much" and my solution for the Fermi paradox thus remains "just not worth it once you run the numbers" with and without wormholes, but if you can prove me wrong, go ahead.

 

[Loren Pechtel]

Imagine you have an object with mass you want to move over astronomical distances, and which you can not encase or otherwise directly push, and which is also electrically neutral so magnets won't help either. I can think of one and only one way to move such an object: have it orbit another body (say an asteroid) and push *that* body so it's pulled along by its gravity. Am I missing an obvious alternative?

What's the hypothetical maximal acceleration you can give the asteroid-target object system without losing the target? I know you can't go beyond the asteroid's gravitational acceleration at whatever altitude you have your target in orbit, but is there a precisely calculable even lower limit above which the orbit deteriorates into a highly eccentric one so you still lose your satellite at its periapsis? Or is *any* amount of continued acceleration eventually going to lead to this? (Preliminary calculations using the higher theoretical maximum suggest that it would take at least 3.5 years to accelerate Ceres to 0.1c without pushing hard enough for loose rocks on its surface to be left behind, more if you want to keep something in orbit.)

You're describing a gravity tractor.

1) Your asteroid must be basically rigid, not merely gravitationally bound. I would expect failure if you tried to push Ceres.

2) You do not want it in orbit. Rather, you put your asteroid near the object and turn on your engines, maintaining an acceleration that is exactly the gravity at the altitude the object is above the asteroid. Your controls must be very good as this has a positive feedback loop--any errors are going to be magnified.

 

[Jokodo]

Imagine you have an object with mass you want to move over astronomical distances, and which you can not encase or otherwise directly push, and which is also electrically neutral so magnets won't help either. I can think of one and only one way to move such an object: have it orbit another body (say an asteroid) and push *that* body so it's pulled along by its gravity. Am I missing an obvious alternative?

What's the hypothetical maximal acceleration you can give the asteroid-target object system without losing the target? I know you can't go beyond the asteroid's gravitational acceleration at whatever altitude you have your target in orbit, but is there a precisely calculable even lower limit above which the orbit deteriorates into a highly eccentric one so you still lose your satellite at its periapsis? Or is *any* amount of continued acceleration eventually going to lead to this? (Preliminary calculations using the higher theoretical maximum suggest that it would take at least 3.5 years to accelerate Ceres to 0.1c without pushing hard enough for loose rocks on its surface to be left behind, more if you want to keep something in orbit.)

You're describing a gravity tractor.

1) Your asteroid must be basically rigid, not merely gravitationally bound. I would expect failure if you tried to push Ceres.

2) You do not want it in orbit. Rather, you put your asteroid near the object and turn on your engines, maintaining an acceleration that is exactly the gravity at the altitude the object is above the asteroid. Your controls must be very good as this has a positive feedback loop--any errors are going to be magnified.

#1 why? If your acceleration is low enough for gravity to overcome the inertia of an object above the surface, shouldn't it be implied that it's Löw enough to overcome the inertia of a rock loosely sitting on the surface?

#2 practically this means you can and indeed have to use and maintain the Maximum acceleration given by your tractors' gravity, right? It also means that you need to install capacities to decelerate if neccesary because maintaining exact target acceleration over decades isn't feasible, right?

And how does this scheme fare when it comes to decelerating at the target?

 

[bilby]

I'm not sure that's true. I've seen improperly attached hoses fly off even though they were open at the other end.

I am describing a siphon. There's nothing for it to 'fly off', the inlet end of the hose is just lose in the tank.

If your reaction mass approaches the inlet from a wide range of directions, but all leaves the outlet moving in the same direction, the outlet will accelerate, but the inlet need not.

Why would it fly off all in the same direction though?

Don't ask me; It's your story. I am assuming that it behaves like a hosepipe - the water all tends to come out traveling along the axis of the pipe. But for all I know, you are envisaging something where the direction of travel is conserved after transit, in which case, it's a whole different ball game.

Of course, I don't know whether the wormhole has properties similar to a hosepipe. A rigid pipe would accelerate as a whole; but presumably there's nothing that fixes the distance between the two ends of your wormhole, and they are free to move independently - in which case the hosepipe might be a fair analog.

I hope there isn't anything to fix the distance, and I don't see why there would be - that's not the point though. The point is that a force that is applied to the wormhole as a whole should either move both ends (potentially in opposite directions in normal 3d space, but still both ends), or fail to move either.

I think a better analogy would be the classical folded paper 2d model of a wormhole. We're creating a shortcut between the two sheets close to the fold and shifting the location of the shortcut. Without moving the fold itself, doing so will move both entrances.

That model also predicts the wormhole to be a deterministic, information lossless system where every incoming angle corresponds to one and only one outgoing angle, and two objects entering at a given angle to each other will also leave at the same angle.

So it's nothing like I was imagining. Fair enough - my idea can't work, given these criteria.

Still, if a folded paper is the analogy, why not build the wormhole at (or very close to) the crease, and make the crease (or midpoint of the fold) half way between your intended start and finish points. Movement away from the crease should appear to observers unaware of the fold in space to be movement of the two ends away from each other, and the relationship between the two ends and the middle should be constant - if the crease or fold is oriented orthogonal to the x direction, and you move one end a light year in the x direction, the other should move a light year in the minus x direction, so that the sum of the distances of the two ends from the crease is zero.

ETA of course that presents major challenges getting to the midpoint at sub-light speeds in order to start construction.

I also note from your other replies above that you are seeking to determine that (or whether) this approach to interstellar travel would be impractical. My feeling is that there are two important things you need to decide:

1) What is the mass of the wormhole or wormhole entrances - are they the mass of a proton, or of a sand grain, or of a planet, or of a super massive black hole? This makes a HUGE difference to the energy and effort needed to accelerate them.

2) When working in space, the fraction of Earth's energy output needed (as ye elude to above) is a poor indication of practicality. A more sensible threshold for impracticality would be the fraction of total solar output needed - solar power is much more abundant and much easier to obtain at a work-site in space than is energy generated on Earth.

It's the mass that's the big issue though. Unless you have at least a ballpark mass for the object to be accelerated, it's anybody's guess how easy the task might be. Accelerating a single proton mass (particularly if it carries a charge, and can be spun up in a particle accelerator) to a significant fraction of c is fairly easy. Doing the same with a mass in the order of kilograms or tonnes is much harder; And with planetary masses, it's a non-starter without some kind of vast energy source.

 

[Loren Pechtel]

#1 why? If your acceleration is low enough for gravity to overcome the inertia of an object above the surface, shouldn't it be implied that it's Löw enough to overcome the inertia of a rock loosely sitting on the surface?

Accelerate near the max where gravity can hold it together and if it's not a solid it's going to shift around. You won't have a round ball anymore.

#2 practically this means you can and indeed have to use and maintain the Maximum acceleration given by your tractors' gravity, right? It also means that you need to install capacities to decelerate if neccesary because maintaining exact target acceleration over decades isn't feasible, right?

Yes and no. Gravity tractors can only run at their maximum, but you can change the maximum--turn it up a little higher so you pull away from what you're towing--it's farther away, you can then lower your acceleration. Likewise, to turn it up you must first turn it down so the payload gets closer.

And how does this scheme fare when it comes to decelerating at the target?

Pull away a bit (see #2) and then maneuver so you're behind the payload.

 

[fast]

What information is needed to get to a particular point in or on a sphere?

 

[bilby]

What information is needed to get to a particular point in or on a sphere?

It's a three dimensional object, so as a minimum, you need three pieces of information. Typically geographers use great circles (circles whose centre coincides with the centre of the sphere) and measure angles on two orthogonal great circles (latitude, which is the angle above or below the equator; and longitude which is the angle along the equator from a selected datum), plus distance from the centre (usually expressed in terms of the distance from a datum approximating sea level, which in turn approximates the surface of the sphere). This is a specific case of a spherical coordinate system, and as the name implies, it is particularly well suited to defining positions within a sphere. In the general case of spherical coordinate systems, latitude is often called 'zenith angle' or 'inclination'; while longitude is often referred to as 'azimuth angle', or simply 'azimuth'.

Of course, there are an infinity of other options. You could take a Cartesian approach, and define three orthogonal lines, and measure distance from those to any point in three dimensional space, some of which will be in or on your sphere; Working out which points are outside the sphere is, in this case, more difficult than with the previously mentioned option, where you can simply define the sphere's surface in terms of its distance from the centre, and any distance less than that is inside the sphere, while any distance greater than that is not.

https://en.wikipedia.org/wiki/Three-dimensional_space#Coordinate_systems

 

[beero1000]

What information is needed to get to a particular point in or on a sphere?

What information is needed to get to a particular point in or on a sphere?

It's a three dimensional object, so as a minimum, you need three pieces of information. Typically geographers use great circles (circles whose centre coincides with the centre of the sphere) and measure angles on two orthogonal great circles (latitude, which is the angle above or below the equator; and longitude which is the angle along the equator from a selected datum), plus distance from the centre (usually expressed in terms of the distance from a datum approximating sea level, which in turn approximates the surface of the sphere). This is a specific case of a spherical coordinate system, and as the name implies, it is particularly well suited to defining positions within a sphere. In the general case of spherical coordinate systems, latitude is often called 'zenith angle' or 'inclination'; while longitude is often referred to as 'azimuth angle', or simply 'azimuth'.

Of course, there are an infinity of other options. You could take a Cartesian approach, and define three orthogonal lines, and measure distance from those to any point in three dimensional space, some of which will be in or on your sphere; Working out which points are outside the sphere is, in this case, more difficult than with the previously mentioned option, where you can simply define the sphere's surface in terms of its distance from the centre, and any distance less than that is inside the sphere, while any distance greater than that is not.

https://en.wikipedia.org/wiki/Three-dimensional_space#Coordinate_systems

A sphere is a two-dimensional object that is traditionally considered embedded in three-dimensional space. As such, two numbers are required to specify a point on a given sphere, with a third number only becoming necessary to describe other points in the enclosing 3D space. On Earth, those two numbers are generally chosen as latitude and longitude, with altitude being used only if we need to specify an elevation off the surface of the sphere.

 

[fast]

Okay, I'm guilty of asking the wrong question, although the answer lies close by those given.

We are traveling through space. Well, we're on a planet that's traveling through space, so I guess either way, we are at least in some sense traveling through space. Sometimes, we are going one direction and six months later, well, how do I say this, still going in the same overall direction but slower (and I guess, in a way, pointed in the opposite direction). But still, we are going in some overall direction. North? Nay. Some degree with an inclination?

I came up with the sphere question looking to add a third dimension to a compass heading. I figured some angle would be needed. We got to the moon, well, unless the moon got to us while we hauled ass away from it as it gained speed on us as we increased our thrust towards it slowing our run from it ... unless we weren't.

If I'm right and space is a medium that we pass through, then each point we pass is a point not moving. This lends us the opportunity to project a background 3-d checkerboard graph paper kind of perspective that enables us to find places of rest that neverless finds celestial objects passing furiously by. But, in what darn direction? I don't even know the words to use.

 

[Bomb#20]

Okay, I'm guilty of asking the wrong question, although the answer lies close by those given.

We are traveling through space. Well, we're on a planet that's traveling through space, so I guess either way, we are at least in some sense traveling through space. Sometimes, we are going one direction and six months later, well, how do I say this, still going in the same overall direction but slower (and I guess, in a way, pointed in the opposite direction). But still, we are going in some overall direction. North? Nay. Some degree with an inclination?

I came up with the sphere question looking to add a third dimension to a compass heading. I figured some angle would be needed. We got to the moon, well, unless the moon got to us while we hauled ass away from it as it gained speed on us as we increased our thrust towards it slowing our run from it ... unless we weren't.

If I'm right and space is a medium that we pass through, then each point we pass is a point not moving. This lends us the opportunity to project a background 3-d checkerboard graph paper kind of perspective that enables us to find places of rest that neverless finds celestial objects passing furiously by. But, in what darn direction? I don't even know the words to use.

627 km/s, in the direction: galactic longitude 276 degrees, galactic latitude 30 degrees. (Source) Okay, that's the motion of the Local Group. To get your motion you'll need to add in the motion of our galaxy within the Local Group, and the motion of the sun in our galaxy, and the motion of the earth in our solar system, and the rotation of the earth, but those are all a lot smaller. (This assumes the cosmic microwave background is stationary, for lack of anything bigger we can compare its motion to...)

Of course, mapping that to your compass heading will be tricky since the answer keeps changing as the earth spins around.

 

[bilby]

It's a three dimensional object, so as a minimum, you need three pieces of information. Typically geographers use great circles (circles whose centre coincides with the centre of the sphere) and measure angles on two orthogonal great circles (latitude, which is the angle above or below the equator; and longitude which is the angle along the equator from a selected datum), plus distance from the centre (usually expressed in terms of the distance from a datum approximating sea level, which in turn approximates the surface of the sphere). This is a specific case of a spherical coordinate system, and as the name implies, it is particularly well suited to defining positions within a sphere. In the general case of spherical coordinate systems, latitude is often called 'zenith angle' or 'inclination'; while longitude is often referred to as 'azimuth angle', or simply 'azimuth'.

Of course, there are an infinity of other options. You could take a Cartesian approach, and define three orthogonal lines, and measure distance from those to any point in three dimensional space, some of which will be in or on your sphere; Working out which points are outside the sphere is, in this case, more difficult than with the previously mentioned option, where you can simply define the sphere's surface in terms of its distance from the centre, and any distance less than that is inside the sphere, while any distance greater than that is not.

https://en.wikipedia.org/wiki/Three-dimensional_space#Coordinate_systems

A sphere is a two-dimensional object that is traditionally considered embedded in three-dimensional space. As such, two numbers are required to specify a point on a given sphere, with a third number only becoming necessary to describe other points in the enclosing 3D space. On Earth, those two numbers are generally chosen as latitude and longitude, with altitude being used only if we need to specify an elevation off the surface of the sphere.

The question specifies on or in. Hence my answer.

 

[James Brown]

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