When an object accelerates due to gravity, where does the additional energy come from?

Also, is there a limit to accelerating due to gravity? Could an object possibly reach the speed of light by using other massive objects as a gravitational ';sling';?When an object accelerates due to gravity, where does the additional energy come from?
Within simple Newtonian mechanics a mutual gravitational force of attraction by a massive body 'M' upon an object 'm', gives rise to a force of acceleration (from Newton's second law of motion F = ma or here F = mg): -





F = - GmM


........ ___


.......... r²





(The negative sign is a convention - meaning attraction towards a common centre)





This, force of gravitational attraction is that of a conservative central force whose potential V(r) is such that: -





F = -dV(r)


...... ____


....... dr








Thus, as an object and a large mass mutually accelerate towards each other, gravitational potential energy is converted into kinetic energy for both objects. However, a very large mass, such as a planet, has a substantial inertia or resistance to motion change (from Newton’s first law of motion) and therefore does not move as the object accelerates into it.





The gravitational potential energy for an object of mass ‘m’ and height ‘h’ above a massive body is: -





V(r) = mgh





This potential energy converts into kinetic energy, given by: -





E = ½mv²





This energy conversion may be expressed by a conservation of energy equation: -





½mv² = mgh








Thus, energy is conserved within a 'central conservative force field' and all of the potential gravitational energy is converted into kinetic energy as an object accelerates towards a massive object under mutual gravitational attraction. Hence, gravitational attraction does NOT ADD ANY EXTRA ENERGY!





NASA use gravitational 'sling shot' effects to boost the velocity of their inter-planetary probes by converting gravitational potential energy into kinetic energy.








Einstein's General Theory of Relativity (GRT) provides a Newtonian approximation to the gravitational potential energy so that: -





V(r) = - (K/c²).∫(ρ/r).dτ





The unit of time is 'τ' and Newton's constant G = K. Again, within Einstein's theory - potential energy is conserved and converted into kinetic energy under gravitational attraction. Einstein also placed a limit on the velocity that an object may attain under gravitational acceleration - too that of less than the speed of light in a vacuum.





A more detailed second order version of GRT allows the consideration of massive gravitating potential well such as black holes! If the intense gravity of a black hole object captures 'gas' it will accelerate the gas in a spiralling inward orbit until the ripped apart particles of the gas attain close to the speed of light velocities before crossing the event horizon.


However, this is just part of the picture where an intense gravitational field is concerned. An object or particle spiralling into a Black hole loses energy through gravitational radiation. As it reaches its last stable orbit, it falls rapidly into the Black hole and emits a last gasp burst of gravitational waves. The total energy radiated during the slow inward spiral is equal to the binding energy of the last stable orbit: -





E(radiated) = μ - E(last orbit)





Where 'μ' is the rest mass of the object or particle. It may be shown that for a Schwarzschild hole this has a value of 0.0573V and for a Kerr hole 0.4235μ. The total energy of the last gasp burst is about 0.01μ(μ/M) if μ%26lt;%26lt;M.





Certainly, a black hole could be used to create a very high velocity for a spacecraft using a ‘gravitational sling shot’ effect. However, the Special Theory of Relativity does not allow massive objects to attain the speed of light and, furthermore, such an attempt would be a ‘smidgen’ risky!!!!!!!!When an object accelerates due to gravity, where does the additional energy come from?
No additional energy,just a change from gravitational potential energy to kinetic energy.For a material body to reach the speed of light INFINITE energy would be needed and so it is therefor impossible.The centre of the earth is molten at more than 4000deg,K and most of this heat energy came from the fall of all the tiny and large meteorites falling from thousands even millions of miles out in cold space into the growing planet earth.When they hit earth the kinetic energy was transformed into heat energy: and is still there causing volcanoes and the drift of continents today.Shooting stars show that space dust is still falling into earth at many thousands of miles per hour,when they reach our atmosphere they are slowed down by rubbing against the air and change their kinetic energy into heat energy so that they shine like stars(shooting stars).Material falling throuh the earths air can only reach speeds of up to about 200 miles per hour ,human bodies no more thanabout 120 mph because of their need to push the air out of the way.
1) From gravitational potential energy--or to use a field point of view--from the gravitational field itself.


2) A limit to what? Speed?


3) Gravitational slings can certainly be helpful in accelerating interplanetary probes. I don't know about using one to achieve light speed--that would take infinite energy, and the fields apparently don't contain infinite energy.





High energy gravity problems are difficult to answer because all the working field theories have non-renormalizable infinities (which we don't observe). GR is the low energy limit of our effective field theories, but there's no reason to trust it at sufficiently high energies.
If you arrive from space the question is relevant. Then your body is given kinetic energy from the gravitational field. But as you hit the surface in your brutal way, you give the energy back.





But it ie more understandable for us living on this this loved erath.





We need to use enegy to get our elevators lifting us. But if we jump out of the window, we will have kinetic energy hitting the grond equal to that used in the elevator. I estimate no loss of energy in the elevator or to the air caused by by its resistance.
There is no additional energy ?





I think the ultimate speed something can reach using just gravity is 120mph in free fall though i might be wrong but i'm sure i read somewhere that is the max speed a falling person could reach regardless of from what height they fell ?
Gravity is energy too.But way is ellipse.So by gravity no but by chellinging gravity feild can reach star in 2 to 6 ch namly more directly way (no crooked).For gravity line is no line.
Gravitational potential energy. The gravity 10 N will force the object to accelerate, and if the mass is greater, it will pick up more drag faster.