Do changes in speed always affect orbit size, and vice versa?

[syfry]

TL;DR Summary

Trying to get the hang of how speed and orbits affect each other.

For example, does even a tiny boost to an orbiting object widen its orbit a tiny amount?

Let's use a hypothetical teleporting asteroid in orbit around the sun. If we teleport the asteroid a millimeter outward, then a kilometer inward, then an AU outward, does its orbit slow a tiny amount, then speed up a bit more, then slow a lot more?

I'm thinking that'd be the case from conservation of angular momentum.

But if the asteroid slows and quickens by teleporting outward and inward (in that order), does the teleporting additionally slow and quicken the time it takes the asteroid to complete an orbit, because the distance is longer and shorter? (in that order again)

In other words, are there two separate reasons why teleporting to a wider orbit would result in a longer year: the slower speed + the longer path, and the two reasons combine into a total longer duration of year? (similarly for the faster year when teleporting inward)

Also, does a 1 mm per day change to the asteroid's speed of faster or slower result in a slightly wider or slightly shorter orbit?

If anyone plays any space games that let you play around with such things to see what happens, please let me know what the game is.

 

[DaveC426913]

If we teleport the asteroid a millimeter outward, then a kilometer inward, then an AU outward, does its orbit slow a tiny amount, then speed up a bit more, then slow a lot more?

For example, does even a tiny boost to an orbiting object widen its orbit a tiny amount?

Yes. Technically.

Let's use a hypothetical teleporting asteroid in orbit around the sun. If we teleport the asteroid a millimeter outward, then a kilometer inward, then an AU outward, does its orbit slow a tiny amount, then speed up a bit more, then slow a lot more?

A: Initial condition. We assume the asteroid has orbital velocity to be in a circular orbit.
B: One millimetre farther out.
C: One kilometre sunward.
D: One AU outward.

The asteroid at position C finds itself one kilometer closer to the sun than when it was a position A (Or, technically, 1,000,0001mm closer than position B). But it only has the orbital velocity that it had at position A. That is not enough to maintain a circular orbit this close the sun. The sun's (classical Newtonian) gravity begins to accelerate it sunward. That is what causes it to pick up speed.Can you extrapolate from there?I'd suggest you stick with just one change in orbit. The rest of your post is complicating matters by first getting closer then farther. The extra step(s) serve no explanatory function.

In other words, are there two separate reasons why teleporting to a wider orbit would result in a longer year: the slower speed + the longer path, and the two reasons combine into a total longer duration of year? (similarly for the faster year when teleporting inward)

No. It's two ways of looking at the same cause. If you were to do the math, it would apparent that they're the same thing.

A given velocity at a given distance (from a given mass) will result in a definite orbital period (and path length). Change any one parameter, you get different results.

 

[berkeman]

Let's use a hypothetical teleporting asteroid in orbit around the sun.

Why introduce some non-physical mechanism to explore your question? Just use a rocket engine to make changes to the asteroid's orbit, and frame your questions in a more realistic way.

 

[Drakkith]

If anyone plays any space games that let you play around with such things to see what happens, please let me know what the game is.

If you're interested, try Universe Sandbox. You can play around with all of the physical and orbital details of an object to see what happens.

 

[FactChecker]

Any new force (rocket engine, impacts with other objects, escaping gasses, etc.) that changes the velocity vector will change the orbit. You should realize that practically no orbit is circular. Orbits obey Kepler's laws and the gravitational forces, velocities, and relative distances are constantly changing accordingly.

 

[snorkack]

TL;DR Summary: Trying to get the hang of how speed and orbits affect each other.

For example, does even a tiny boost to an orbiting object widen its orbit a tiny amount?

Let's use a hypothetical teleporting asteroid in orbit around the sun. If we teleport the asteroid a millimeter outward, then a kilometer inward, then an AU outward, does its orbit slow a tiny amount, then speed up a bit more, then slow a lot more?

I'm thinking that'd be the case from conservation of angular momentum.

Teleporting does not conserve angular momentum.
Impacts also do not conserve angular momentum of target though they conserve it globally, and are more physical than teleportation.
Vis viva equation says that all orbits that have the same speed at the same radius have the same semimajor axis. Does not mean they have the same size or length... they don´t, because the other axis differs.

 

[syfry]

Any new force (rocket engine, impacts with other objects, escaping gasses, etc.) that changes the velocity vector will change the orbit. You should realize that practically no orbit is circular. Orbits obey Kepler's laws and the gravitational forces, velocities, and relative distances are constantly changing accordingly.

That's why I chose teleporting.

Wasn't sure if simply moving faster or slower would change the orbit, so wanted to be sure that the only things able to affect the speeds and the orbits were the change in speed or the orbital position.

Thanks everyone for your answers. And Drakkith for suggesting Universe Sandbox!

Any idea if Kerbal space program is good for this too?

 

[DaveC426913]

That's why I chose teleporting.

I don't have a problem with the OP's use of this thought experimental stratagem.

But OK, never mind the teleporting. Here's a more palatable demo:

We set up a controlled, repeatable experimental demonstration, designed so that any given test does not pollute the subsequent tests with residual properties. After each observation, our lab stopwatch is stopped, initial conditions (in particular the orbital velocity) are re-established, then one - and only one - parameter (orbital radius) is changed. As soon as the new radius and velocity are re-established we reset and restart our lab stopwatch for experiment 2. That's a perfectly valid reconstruction of the OP's teleport stratagem.

This allows the OP to observe the effect of changing one - and only one - variable (namely orbital distance) at a time, and observe its effect.

On the other hand, employing rockets between scenarios to change orbits and velocity, etc. would mess up the pristineness of the scenarios, obfuscating the variable(s) that the OP wishes to isolate.

We good?

 

[Tom.G]

An easy way to remember the interactions is Kepler's Second Law:

"Kepler's Second Law: the imaginary line joining a planet and the Sun sweeps equal areas of space during equal time intervals as the planet orbits."

from:
https://solarsystem.nasa.gov/resources/310/orbits-and-keplers-laws/

Cheers,
Tom

 

[Drakkith]

Any idea if Kerbal space program is good for this too?

Short of actually having a job calculating orbital properties and trajectories, you will never understand orbital mechanics better than by playing KSP. It will give you an intuitive grasp on how orbits change as you apply a force (at least it did for me).

 

[snorkack]

An easy way to remember the interactions is Kepler's Second Law:

"Kepler's Second Law: the imaginary line joining a planet and the Sun sweeps equal areas of space during equal time intervals as the planet orbits."

from:
https://solarsystem.nasa.gov/resources/310/orbits-and-keplers-laws/

Cheers,
Tom

This is conservation of angular momentum. Applies while you are not interfering to change it (by propulsion or teleportation).
Vis viva equation is one important thing to notice. Kepler´s third law says that all orbits of different eccentricity which have same semimajor axis have same period. Vis viva equation, which is not Kepler´s law, says that they have equal speed at any given radius from the center.

 

[FactChecker]

Suppose that you have an object in a perfectly circular orbit of radius $r$ and velocity $v_o$. Suppose it has a negligible mass, $m_o$, compared to the mass, $M$, of the central object. Then $v_o = \sqrt {GM/r}$. (see this)

Now consider another object with the identical mass, $m_o$, and velocity vector but at a greater distance, $r' \gt r$, from the center of the first object's orbit. Then its velocity will be too great for a perfectly circular orbital at the greater radius since $v_o = \sqrt {GM/r} \gt \sqrt {GM/r'}$. Since the velocity is too great, it will start to be thrown farther from the center. It will eventually reach its correct circular orbit distance but will keep going and overshoot it while slowing down. Later, its orbit will fall back nearer to the center. In other words, its orbit will have some eccentricity.

A similar analysis indicates that if the object is closer to the center, its velocity will be too slow for a circular orbit. It will fall toward the center, gaining speed, overshoot the radius for a circular orbit, and then begin to go farther from the center. It would also have an orbit with eccentricity.

 

[PeroK]

Teleporting is just starting again with new initial conditions.

 

[jbriggs444]

I don't have a problem with the OP's use of this thought experimental stratagem.

But OK, never mind the teleporting. Here's a more palatable demo:

We set up a controlled, repeatable experimental demonstration, designed so that any given test does not pollute the subsequent tests with residual properties. After each observation, our lab stopwatch is stopped, initial conditions (in particular the orbital velocity) are re-established, then one - and only one - parameter (orbital radius) is changed. As soon as the new radius and velocity are re-established we reset and restart our lab stopwatch for experiment 2. That's a perfectly valid reconstruction of the OP's teleport stratagem.

What, exactly, are we holding constant while we mess with starting position?

Are we holding angular momentum constant? Then we cannot hold velocity constant.
Are we holding velocity constant? Then we cannot hold angular momentum constant.
Are we holding energy constant? Then we likely cannot hold either velocity or angular momentum constant.
Are we holding the obital shape constant? Then we likely cannot hold any of the other stuff constant.

In other words, "how does teleporting work"?

 

[syfry]

What, exactly, are we holding constant while we mess with starting position?

Are we holding angular momentum constant? Then we cannot hold velocity constant.
Are we holding velocity constant? Then we cannot hold angular momentum constant.
Are we holding energy constant? Then we likely cannot hold either velocity or angular momentum constant.
Are we holding the obital shape constant? Then we likely cannot hold any of the other stuff constant.

In other words, "how does teleporting work"?

Originally was thinking that all the values would readjust accordingly to a constant angular momentum since it's a conserved quantity. But now, I don't know what would happen to any energy lost. (nor where any gain of energy would come from)

 

[jbriggs444]

Originally was thinking that all the values would readjust accordingly to a constant angular momentum since it's a conserved quantity. But now, I don't know what would happen to any energy lost. (nor where any gain of energy would come from)

Angular momentum is a conserved quantity for a system evolving according to the laws of Newtonian physics. Angular momentum is not a conserved quantity for a system evolving in ways that do not respect those laws.

To take a simple example, consider a 1 kg ball moving at 1 m/s rightward. You reach into the simulation and arbitrarily change the ball's velocity to 1 m/s leftward. That manipulation is forbidden by the laws of Newtonian mechanics. It does not conserve momentum. [In particular, there is a third law violation. There is a change in momentum (a force) without an equal and opposite reaction force].

You can make the manipulation. It is your simulation. You can do as you please. But you cannot expect conservation laws to apply across your manipulations.

 

[syfry]

Angular momentum is a conserved quantity for a system evolving according to the laws of Newtonian physics. Angular momentum is not a conserved quantity for a system evolving in ways that do not respect those laws.

To take a simple example, consider a 1 kg ball moving at 1 m/s rightward. You reach into the simulation and arbitrarily change the ball's velocity to 1 m/s leftward. That manipulation is forbidden by the laws of Newtonian mechanics. It does not conserve momentum. [In particular, there is a third law violation. There is a change in momentum (a force) without an equal and opposite reaction force].

You can make the manipulation. It is your simulation. You can do as you please. But you cannot expect conservation laws to apply across your manipulations.

Fair point. I was thinking more like Noether’s symmetries where the physics continue to work in the usual ways regardless of where or when you place the scenario into.

So only the varying values would readjust, while the conserved value wouldn't.

 

[Vanadium 50]

This thread got off to a very bad start.

(1) Once teleportation enters into it, the question becomes not "How do orbits work" but "How do orbits work in Portal."

(2) Some mechanics texts devote an entire chapter to the central force problem. "You guys explain it to me" is a big ask. Especially before reading it yourself. @jbriggs444 recent message asking what is and is not held constant shows the range of possibilities to cover is enormous.

I suggest starting over is the fastest way to make progress,

 

[syfry]

Some mechanics texts devote an entire chapter to the central force problem. "You guys explain it to me" is a big ask. Especially before reading it yourself.

I'll check out the games since they automate the 'what ifs' (now that I realize it's a big question). Hadn't even known about the central force problem, or that a seemingly simple change could complicate the mechanics so much.

Thanks!

 

[syfry]

The video below talks about two people who did 2,000 simulations of the solar system's orbiting bodies, and in each one they nudged Mercury less than a millimeter, which resulted in chaos or destabilized orbits for the solar system in 1% of the simulations!



Had no idea the sensitivity of orbits to tiny changes in motion.

 

[Vanadium 50]

Well, that's 5 minutes of my life that I won't get back.

 

[hmmm27]

If the +/- thrust is tangential, then the orbital radius will +/- as well, symmetrically.

If it's radial... umm, I think it returns to the original orbit a bit ahead or behind of where it would've been if you didn't poke it.

 

[snorkack]

To take a simple example, consider a 1 kg ball moving at 1 m/s rightward. You reach into the simulation and arbitrarily change the ball's velocity to 1 m/s leftward. That manipulation is forbidden by the laws of Newtonian mechanics. It does not conserve momentum. [In particular, there is a third law violation. There is a change in momentum (a force) without an equal and opposite reaction force].

You can make the manipulation. It is your simulation. You can do as you please. But you cannot expect conservation laws to apply across your manipulations.

Indeed. On the other hand, you can just kick the ball. The combined momentum of ball and your foot is conserved, but the momentum of the ball alone is not. Note that the location of the ball is the same before and after the kick - only its speed has changed.

If the +/- thrust is tangential, then the orbital radius will +/- as well, symmetrically.

If it's radial... umm, I think it returns to the original orbit a bit ahead or behind of where it would've been if you didn't poke it.

If the orbit initially has a radius (i. e. zero eccentricity), then after a tangential thrust it will no longer have it (because it acquires nonzero eccentricity).
Since location is conserved on poking, a body that is poked will always return to the location it was poked if the orbit after poking is a bound one.

 

[jbriggs444]

If the +/- thrust is tangential, then the orbital radius will +/- as well, symmetrically.

If it's radial... umm, I think it returns to the original orbit a bit ahead or behind of where it would've been if you didn't poke it.

For an instantaneous thrust and assuming that both the new and old orbits are closed, the two orbital paths will intersect exactly at the point of the thrust. The orbitting object will return to this point over and over forever.

For a tangential impulse on a circular orbit, this will mean a new elliptical orbit that is tangent to the old circular orbit.

For a radial impulse on a circular orbit, this will mean a new elliptical orbit that crosses the old circular orbit twice.

If one was expecting a new circular orbit... then one needs to switch expectations.

 

[hmmm27]

Well, one was sortof expecting that...

So, long story short, an object in any orbit can be kicked into any intersecting orbit, which makes sense. Orbits which don't intersect (like circular to circular) require two impulses.

 

[jbriggs444]

Well, one was sortof expecting that...

So, long story short, an object in any orbit can be kicked into any other orbit that intersects (which, specifically circular to circular does not do), which makes sense. Orbits which don't intersect require two impulses.

Which may be a good point to Google for "Hohmann Transfer Orbit"

 

[PeroK]

Well, that's 5 minutes of my life that I won't get back.

You never get any time back.

 

[snorkack]

So, long story short, an object in any orbit can be kicked into any intersecting orbit, which makes sense. Orbits which don't intersect (like circular to circular)

If the kick is tangential or radial. You can also kick an object from a circular orbit to another circular orbit with exactly same radius but in a different plane/inclination.

 

[syfry]

For an instantaneous thrust and assuming that both the new and old orbits are closed, the two orbital paths will intersect exactly at the point of the thrust. The orbitting object will return to this point over and over forever.

That's really interesting about its returning to the same spot in its new orbit where it had gotten a speed boost in its old orbit!

For a tangential impulse on a circular orbit, this will mean a new elliptical orbit that is tangent to the old circular orbit.

For a radial impulse on a circular orbit, this will mean a new elliptical orbit that crosses the old circular orbit twice.

Looked up tangential and radial but had difficulty interpreting the definitions.

Does tangent mean the new orbit would (barely) touch the old orbit's boundary?

And does radial mean in direction that's perpendicular to a curve? (like spokes on a wheel)

Also from the discussion here, wondering if any eccentricity in an orbit would eventually become a perfectly circular orbit over time.

 

[jbriggs444]

Also from the discussion here, wondering if any eccentricity in an orbit would eventually become a perfectly circular orbit over time.

A closed orbit under an inverse square central force is stable. It will follow the same elliptical path forever. That path will not precess. Nor will its eccentricity change over time.

Complications due to general relativity or additional bodies may change things.

 

[snorkack]

Looked up tangential and radial but had difficulty interpreting the definitions.

Does tangent mean the new orbit would (barely) touch the old orbit's boundary?

Yes.

And does radial mean in direction that's perpendicular to a curve? (like spokes on a wheel)

Yes.
The third direction is axial.
Note that any finite kick at right angle to the speed increases the speed, as per Pythagoras´ theorem. Leaving the speed unchanged requires a kick at obtuse angle.