Re: potential energy

"C. Roald" [email removed] writes:
>
> The physics convention is that potential energy is NEGATIVE, so that it
> increases (gets less negative) as you increase the separation. At
> infinite separation, the PE rises to zero. (A common definition is that
> PE represents how much energy has to be added to bring two objects to
> infinite separation.

Ah, this makes things a little easier.  In effect, if you are a long way
from something, your potential energy due to its gravity is approximately
zero; if you're sitting on top of it, your potential energy is large and
negative - you have to expend a lot of energy to get away.  If you're at
distance 0, you're in big trouble, but that's really only possible if the
something that you're trying to get away from has radius 0, i.e. it is
probably a black hole.

>				     On the other hand, if you were to
> jump from a distance r from Sol to a distance r from AC, then the net
> cost of the jump is
>
> 	G m M(AC)/r - G m M(Sol)/r = G m [M(AC)-M(Sol)]/r.
>
> A first approximation calls M(Sol) about the same as M(AC), so the net
> cost of the jump is ~= 0, plus the drive energy to make a jump of twice
> the distance.

Why twice the distance?  (I assume that in this sentence, "distance" means
"distance from Sol to Alpha Centauri".)  If the energy require to make a
jump of this distance is E, then you're saying you need to expend 2*E.

>		On the other hand, GmM/r is the escape energy of Sol,
> which is the kinetic energy required to produce a velocity of ~30 km/s.
> For a ship weighing say, 1 T, that's 4.5e11 J, or 450 000 MJ. Not to
> be sneezed at.

A ship accelerating at 1-G will achieve that velocity in less than an hour,
using just its manoeuvre drive.  (To get to 30000 m/s using an acceleration
of 9.8 m/s^2 will take 3061 seconds, i.e. 51 minutes.)  Maybe not to be
sneezed at, but that's the sort of figure that all spacecraft play with
routinely - that's why you don't want to collide with anything!

So the ship expends its 4.5e11 J, and get into jump space.  One week later,
it emerges from jump space near Alpha Centauri, and gets 4.5e11J back -
what happens to this energy?  Presumably it gains this energy as it emerges
from jump space, and the energy ends up back in the ship's jump capacitors.

- --
 "Keyboard?  How quaint!" - M. Scott

 Adrian Hurt			     |	JANET:  [email removed]
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