On Wed, Aug 16, 2017 at 01:35:20PM -0700, C. Berry wrote:
>    There's zero energy cost for hovering. Otherwise, by your analysis, I
>    would be expending a gigantic energy cost for hovering 400,000km over
>    the surface of Luna. :) An object motionless in a g field has constant
>    potential energy, hence no energy input is required to keep it there.
>

I'm not 100% certain that this is the case. In your example g is very
small being a function of a large r^(-2). But in fact an energy
transfer is happening between objects on Terra (the oceans) and
Luna. The current balance of that transfer is giving energy to Luna
such that it's orbital semi-major access is slowly getting larger
while Terra's day is slowly getting longer. In this example the energy
cost/transfer becomes measurable because the mass of the Terra's
oceans is much much larger than the mass of a single human.

Here's a relevant thought experiment. Can you hold a 20kg mass, 1m off
of the sea level surface of Terra without other support forever? For a
day? For an hour?  Or do you get tired from paying the ~ 200J energy
cost and have to put it down at some point in time.

Another relevant question: If you want to hold a 20kg mass exactly 1m
off of the ground on Terra by putting it on a real, rather than
theoretical, table or support, how "tall" is the support
when it isn't holding the mass?

The point here is that there is an energy cost being paid to keep the
mass off of the surface of Terra. If you put a 20kg mass onto an
exactly 1m tall table made of real materials, but capable of
supporting the mass without yielding, the mass will be closer than 1m
to the surface of Terra. In the real world the table is better
represented by a spring that compresses under the load rather, than an
infinitely rigid body that doesn't.

I don't know the names for these two balanced forms of potential
energy. Someone else would have to tell me whether or not ~ 720kW are
spent keeping the mass off of the ground for an hour. But I'm fairly
certain that there is an energy cost involved.

--
Chris

     __o          "All I was trying to do was get home from work."
   _`\<,_           -Rosa Parks
___(*)/_(*)_____________________________________________________________
Christopher Sean Hilton                    [chris/at/vindaloo/dot/com]