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They dont lose energy unless they touch the top of the atmosphere.
No - because in this case the acceleration and force are perpendicular to the direction of movment of the satellite (assuming circular motion) so no work is done so the energy stays constant once the satellite is in a circular orbit.
Satellites do have to use fuel while in orbit. This is due to the corrections that they must make to hold a precise position. Geostationary satellites in particular are subject to gravitational pulls due to planets and solar wind. The amount a fuel available often determines the useful life of the satellte.
teachercol
No - because in this case the acceleration and force are perpendicular to the direction of movment of the satellite (assuming circular motion) so no work is done so the energy stays constant once the satellite is in a circular orbit.
Ok I sort of get it now. So how is this different with charges then? If an electron travels around the nucleus in a circle (which it doesn't), one argues that it loses energy because it is accelerating?
Well it doesnt lose energy in a stable orbital. (Quantum mechanics )
The difference is that charges radiate EM radiation generally when accelerated, masses dont - or at least negligible amounts of gravitational waves.
The difference is that charges radiate EM radiation generally when accelerated, masses dont - or at least negligible amounts of gravitational waves.
The satellite keeps changing direction. Change in direction implies change in velocity. Change in velocity is acceleration. When there is an acc. we need a force, according to Newtons second law.
The loss of energy is due to shift in potential; however, this concept need not be knows in detail. You just need to know centripetal force thing.
The loss of energy is due to shift in potential; however, this concept need not be knows in detail. You just need to know centripetal force thing.
Satellites in high-orbit do not "lose" energy. In order for there to be a change in energy of the satellite, there must be a force applied to it through some distance (Work done = Force x distance parallel to force). Since the gravitational force always acts perpendicular to the direction the satellite moves in, no work is done on the satellite, and hence its total energy remains the same. In a circular orbit, this means that the kinetic energy stays the same because the speed doesn't change, and the potential energy doesn't change because the distance from Earth remains the same.
Worzo
Satellites in high-orbit do not "lose" energy. In order for there to be a change in energy of the satellite, there must be a force applied to it through some distance (Work done = Force x distance parallel to force). Since the gravitational force always acts perpendicular to the direction the satellite moves in, no work is done on the satellite, and hence its total energy remains the same. In a circular orbit, this means that the kinetic energy stays the same because the speed doesn't change, and the potential energy doesn't change because the distance from Earth remains the same.
Okay, thanks for the confirmation. So why then do electrons spinning around the nucleus lose energy then? (Ok I don't need a lecture that this is not true/quantum mechanics - but this is just a model that is wrong. I need to prove that an electron does lose energy hence implausable as a model.)
Basically:
Why does a charge radiate EM radiation when it orbits another charge (perhaps opposite)?
well its not actually a particle as such - its more of a negatively charged wave probability calculation. remember that an orbit is defined as the space in with there is 90% probability the *cloud* of charge is to be found.
I would guess interactions between the Earths magnetic field and the electrical componants of the electron and the electric potential of the nucleus. The speed of the electron when treated as a particle can be derived from Gauss's Law.
This model is not quite as simple as Newtons Law of uiniversal Gravitation becaue -
- its not deterministic - its probability.
- the electric and magnetic componants interact as well.
Hence accurate predictions can only be made about the hydrogen nucleus - because the repulsion of other electrons cannot be accuratly quantised - its to do with maths not being able to deal with that many unknowns.
I would guess interactions between the Earths magnetic field and the electrical componants of the electron and the electric potential of the nucleus. The speed of the electron when treated as a particle can be derived from Gauss's Law.
This model is not quite as simple as Newtons Law of uiniversal Gravitation becaue -
- its not deterministic - its probability.
- the electric and magnetic componants interact as well.
Hence accurate predictions can only be made about the hydrogen nucleus - because the repulsion of other electrons cannot be accuratly quantised - its to do with maths not being able to deal with that many unknowns.
Classially it a property of charges that they radiate when accelerated. It comes out of Maxwell's equations. That's what limits the max energy of a synchrotron.
We need Quantum mechanics to explain why the electrons in an atom DONT lose energy.
We need Quantum mechanics to explain why the electrons in an atom DONT lose energy.
Wangers
Hence accurate predictions can only be made about the hydrogen nucleus - because the repulsion of other electrons cannot be accuratly quantised - its to do with maths not being able to deal with that many unknowns.
"Atom", if you're talking about electrons in atoms.
And what you say is not true. It's akin to saying that you can't accurately predict the motion of a simple pendulum because it's not analytic. (Which is, of course, predictable.)
Accurate predictions can be made about most atoms. The maths works perfectly well, and computers can calculate the solutions to the equations of these atomic systems to more than enough precision than we need for confirming experiments. It's just most QM systems cannot be solved analytically. This means you can't get a nice expression for them, not that they can't be "accurately quantised".
Worzo
Accurate predictions can be made about most atoms. The maths works perfectly well, and computers can calculate the solutions to the equations of these atomic systems to more than enough precision than we need for confirming experiments. It's just most QM systems cannot be solved analytically. This means you can't get a nice expression for them, not that they can't be "accurately quantised".
Its like pi. We know it exists. We know we cannot express it in numbers. However we know many different ways of getting a number as close to pi as we want. The only problem is that the more accurate we want pi (or the quantum levels) the longer and more computationally difficult it is. [try running a program called superpi, it can show how fast your comp and calc pi!]
However you are correct about the reason, being that there are too many unknowns.
The method we use currently is called pertubation theory. The idea is this. We have an unsolvable problem. So we look at a very similar problem which is solved. We then add in the removed terms. This gives us answer. But the answer changes some of the terms slightly, so we need to recalulate the answer. We repeat this until the answer is as close to the real answer we want.
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