If half the Earth dissappeared what would our orbit be like?

Shouldn't make any difference since the mass of the earth drops out of the equations. There is no actual "outward repulsion," just inertia doing its job.

Which is totally correct thinking, yet your end result is wrong...

Go deeper

The earth-sun barycenter would move toward the center of the sun which would increase the effective radius of the earth's orbit by a couple hundred km, which would reduce the sun's wobble. The earth would be going a little too fast for its new orbital radius, but the net effect would depend on where the moon was at the time, since the earth-moon barycenter would also change. The moon's inertia would not change and the half-mass earth could not hold it in its current orbit. The moon's pull on earth would diminish as it got further away, and the net effect on earth would depend on whether its orbital velocity relative to the moon was currently in the same direction as its orbital velocity relative to the sun.

A hint, for your base thinking is right. The motion of the two bodies themselves aren't changed, Kepler or Newton will show you that.

Yet when you suddenly "lose" mass and energy - in a way that doesn't conserve matter and energy - are you governed soley by the laws of Newton and Kepler?

There is a 3rd variable you aren't considering, in fact you are treating it as a constant when in this case it certainly isn't (and no it's not the moon!).

Re: If half the Earth dissappeared what would our orbit be l


I would guess that the remaining half of the Earth would immediately break orbit and begin to move away from the Sun.

[Because] It no longer has sufficient mass to remain in a stable orbit at its currentl velocity and distance from the Sun.

No, if every second atom in the Earth just dissappeared, its velocity wouldn't be affected and the forces of attraction and explusions which are both a factor of mass would cancel themselves out. Yes there would be an orbital shift due to a change in barycentre of the Sun/Earth pair, but an even more exotic thing would happen that is not due to Newtonian science (hint, hint - gravity is not a force, said Einstein, its the curvature of spacetime...).

The curvature of spacetime due to the sun's mass shouldn't change, so any remaining mass in orbit around the sun should not be affected. If half of the earth's mass disappeared without taking its spacetime deformation energy with it, there would suddenly be a whole lot of stressed spacetime without the mass to maintain it. The deformation is probably asymmetrical due to the earth's orbital velocity, and when the excess spacetime deformation energy is shed as gravitational waves it might accelerate the earth slightly more in that direction.

Are you suspending conservation of energy? If half of the Earth's mass disappeared, there'd suddenly be a very bright, very brief star where it used to be....

Slow down a minute. Half the Earth's mass disappears and the moon stays put? I'm thinking with suddenly half of the Earth's gravitational pull you can wave bye bye to the moon, no?

Terry - essentially correct.

Its not the objects that undergo a sudden change, but the spacetime they move through alters when they suddenly change in mass. Mass (or energy) curves spacetime, change a large mass as proposed (yes not conserving energy or momentum or matter - as Heinsenberg or quantum mechanics appears to allows us to do, on at least a very small and localised scale) and you change the spacetime and hence the paths through it.

So you would see a compounded shift in orbit, from both a new barycentre added to spacetime itself curving less once the mass dissappears.

So had the thought experiment been every second atom in both the Sun and Earth just dissappear into the quantum foam, leaving no change in barycentre, you'd have a slightly harder problem - still solved the same way under relativity.

Neat huh?

PS

Moon not need in this experiment, maybe it would be better to say if Mecury...

PPS

No bright star, just a loss of rest mass that would keep theoretical physicists scratching their heads for years

All I said was that there would be a change in orbit, and that the earth would move away from the sun.

You agreed below.



So my answer was correct, the earth (the half remaining) would move away from the sun. No?

(For purposes of this thought experiment, I'm thinking of a simple sun/earth system in which each thing is represented purely by a gravitational well, nothing more.

If a little gravitational well is in orbit around a big gravitational well, and you suddenly redefine the smaller well as half its original size (AND you don't allow it to decrease it's velocity to conserve energy), without changing velocity, then the two wells will move away from each other.)

Am I getting this right, or am I picturing something wrong?

You may not have intended to include the effects of the moon, but they can hardly be ignored since the eventual loss of the moon would affect the tides as well as the earth's velocity.


The physicists have lost half of their atoms as well, which makes brain function questionable. Imagine a cubic chessboard, 8x8x8 or 512 cubes. Now take out all 256 black cubes. Either you have holes or you squeeze the remaining cubes together - and they do not fit neatly anymore (try it with a smaller size if you cannot visualize this). Your brain would be a sponge, as in mad cow disease. Not to mention what happens when you take an oxygen atom out of carbon dioxide or start taking random atoms out of other molecules.

Then we have massive earthquakes as the earth settles into its smaller diameter and angular momentum tries to rip it apart, shallower oceans and atmosphere as half as much total material (assuming that you spirit away molecules instead of atoms) is spread out over .63 of the previous surface area (a lot of surface water would also disappear into cracks and voids), buildings collapsing, chaotic weather patterns as air was sucked to a lower level without losing its angular momentum …

Yes, maybe you'd better say Mercury.

Ah but Terry in the begining I defined this as a thought experiment around the Earth and the Sun, the moon was superfluous. Maybe we could choose a time in the past before the Moon was captured by the Earth or a time in the far future when the Moon has escaped, I never said the experiment had to be done today!

But seriously the Moon makes it a three body system which is too hard for folk to analyse in a forum such as this, and hence detracts from what I'd hope they would learn.

The shift in Barycentre is a goodpick-up that I hadn't originally intended them to consider - my bad!

The loss of mass in a closed system leading to no change in a Newtonian / Kepler framework, but a significant change to a relativistic framework is where I wanted folk to head. Throughtout school and most of our life we see space as a fixed entity that only Captain Kirk (or Piccard) moves through easily, as if he was going down to the corner store, or driving across country.

But space isn't always like that. If on a cosmic scale matter can be created and destoyed without apparently conserving energy or momentum, in finite spots for a finite time, then there is a different framework for studying cosmic expansion other than dark energy or dark matter (or perhaps offering a candidate for them).

Hawking has showed its possible for matter or energy to jump from the cosmic foam (alah the world of the really tiny quantum mechanics that our universe appears to float in) and not necessarily spell doom and gloom. Hawkings initial postulate was a pair of virtual particles (pro and anti to conserve mass and energy) tunnel into our reality then immediately zap each other and annihilate... except if they appear near the event horizon of a black hole, so one escapes and one is sucked in. In this situation you've just added mass and energy to the Universe.

My thought experiment was a simple two body test of what are the effects of a sudden large extract of mass from the universe - answer spacetime uncurves and we can detect this change in an an otherwise unexplained shift in the orbit of planets. The sun is losing mass every day as its converted into energy and it radiates past us. So spacetime around our solar system is uncurving (very, very, very slowly) every second of our lives.

But what if around galactic centres matter is coming into existence? Physicists studying MOND have shown you only need a very small adjustment to explain why galaxies don't fly apart. Calculated as if this force was attributed to mass gain you need about 1 hydrogen atom per cubic metre of space per year. Theoretical physics has shown that empty space should contain about 10 ^ 120 Joules of energy per cubic metre, the greatest whoopsie in the framework of our thinking - or is it? What if that energy is there - but it manifests very, very slowly over all time - not just all at once? If there is that much potential energy, but in only leaks in in the form of 1 Hydrogen atom per year, maybe all parties could reconcile some pretty wierd theories.

But all that at the moment is just pure theoretical spectulation with no solid grounding - yet. But as said the thought experiement was to get folk thinking and have them realise space, the final frontier, is not a constant, but a variable dependent on localised mass and energy.

This is simply an ill-posed problem... and you are both right (depending on what your assumption is).

The question is when the mass changes...

1) Does the velocity stay the same (meaning the kinetic energy changes)?

or,

2) Does the kinetic energy stay the same (meaning the velocity changes)?

In case 1, the orbit stays the same. In case 2, the orbit changes.

You can easily devise (as has been shown here) a proper solution for either case.

The only problem is that the question is ill-posed.

I'm with you ebrown. If the mass is suddenly reduced by 50% that initial kinetic energy is going to have an orbit increasing effect. If the velocity doubles as the mass is halved then no change in orbit.

F=MA

ebrown

Actually in both cases velocity is not directly affected in the way you're thinking. It's not the body's velocity that changes (at least not its magnitude) its direction appears to change because the fabric of spacetime itself has changed, so relative to its own perspective it has changed direction.

So direction changes (think shifting a compasses bearings).

Even in case 1 as you put it orbit changes - becuase geometry changes...

Chumly

No and no. Imagine if a rifle bullet hits a Katana blade and is split in two. The two pieces follow roughly the same trajectory and land close to each other. Velocity can't just double because mass halves - that's kinda so wierd its colourful, and doubling velocity would hugely alter orbit, so somehow your thinking has got all messed around.

I did not suggest / infer / claim that velocity simply doubles because mass halves, you have missed the point. The fact of the matter is that you said 50% of the matter poofed itself out of existence in some fashion, that is an entirely different thing than splitting a single mass into two equal but smaller masses at some given (non-relativistic) velocity. Thus the question of the body's (after 50% mass loss) kinetic energy remains ambiguous.

Also in your post the phrase "outwards replusion" is a misnomer as the two masses are not repelling each other. It would be more correct to use the phrase "centrifugal force" in the Newtonian sense and warped space in the Einsteinian sense.

It's all well and good that Newton's theory of gravitation says the earth moves around the sun because of gravitational force, and Einstein's general theory of relativity says the earth chooses its shortest path around the sun in space-time because the sun's mass has warped space, but in either case however, kinetic energy is not precluded.

Here is a real nifty site called Ask A Scientist

Chumly - note that kinetic energy is connected to mass, so if the mass goes poof so to must the K.E.

There is even a much better site called Advanced Physics Forum, were real research grade PhD's and other informed folk hang, I encourage you to peruse it at your liesure http://www.advancedphysics.org/forum/
you'll often find me in the Astronomy and Astrophysics sections.