power sat energy payback.

[hkhenson]

At 12:00 PM 5/15/2008, Alberto Monteiro wrote:

>Keith preached:
> >
> > There is plenty of energy around if we can figure out how to get
> > it.  For example, a solar power satellite repays the energy needed
> > to lift it to GEO in about a day (at 100% efficiency).  Five percent
> > efficient rockets would replay the lift energy in 3 weeks.
> >
>This is almost surely wrong. Did you do the math?

Yes.

Specific orbital energy is u/2r, (398,600/42,000)/2 or -4.75Mj/kg

Potential is -9.5Mk/kg and kinetic is 4.75Mj/kg

Potential at the earth's surface is -62.6 MJ/kg; the difference is 53.1Mj/kg.

Using a space elevator, the rotation of the earth provides the 
kinetic energy.  Since a joule is a watt-second; 53,100 
kW-s/kg/3600kW-s/kWh is 14.75 kWh/kg

A kW/kg power sat repays its lift energy 14 hour and 45 minutes after 
being turned on.  A 2kg/kW power sat would take 29.5 hours.

That is close enough to a day for back of the envelope 
calculations.  Five per cent efficient rockets would take 20 times 
this long to reach payback--but try to get them!

There is a heck of a lot of sunlight out there, and you don't need 
much structure to capture it in zero g.

Keith