Re: Minimum fuel launch termination point


<pstanley55@xxxxxxxxxxx> wrote in message
news:gja6b3luer26qrglsfrqvd4ppl2ak7jtub@xxxxxxxxxx
: http://www.braeunig.us/space/orbmech.htm
:
: This article on orbital mechanics seems excellent!!
: I had a question on one statement, whcih is just befoe the "Click here
: for example problem #3.8"
:
: It says, "Please note that in practice spacecraft launches are usually
: terminated at either perigee or apogee, i.e. =90. This condition
: results in the minimum use of fuel"



That's kinda funny, a self-fullfilling prophecy. If the burn
ends when you are not at 90 degrees to the Earth's surface
then you are not at perigee or apogee. If you thrust at apogee
or perigee then you'll have a new perigee or apogee.

: I'm thinking a spacecraft in orbit has the same energy (kinetic and
: potential total) at each point in the orbit.. And that there is only
: a set amount of energy available to provide to the spacecraft to put
: it at that orbit. Thus to achieve a designated orbit, the amount of
: fuel used would be the same regardless of where the thrust terminated.
: So why would it matter at what point in the orbit the launch is
: terminated? For simplicity, it appears the author is not considering
: air resistance on initial launch.
:
: Anyone with any thoughts? Stan

1) Energy is relative because E = 1/2mv^2 and v is relative.
For example a shuttle docking at a space station has a low
relative energy to the space station. Relative to the Earth it has
a high energy and will heat up on re-entering atmosphere, losing
its energy to radiation (heat). If it did not it would impact with
high energy.

2) Key to your question is the term "designated orbit".
You can shoot straight up vertically (minimum fuel) and then
fall straight back down, reaching zenith just as the space station
passes overhead, but the space station will be going too fast
horizontally to dock with it.
In other words you'll have high energy relative to the space station.
You need the same horizontal velocity as the space station
for the designated orbit. Remember that orbits are elliptical,
so even though you can go higher than the space station
and cross over to go to a lower perigee than the station has,
you have to match velocity as well. That burns more fuel
than needed.




.

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