Space Forum / Shuttle / April 2007

I'd think that Mt Everest would be damned inconvenient for launches.  If you
wanted to work in that environment for any length of time, you'd need more
than supplemental oxygen, you'd need pressure suits and pressurized
buildings.

Jeff

Nit to pick.  You correctly point out that the distance you're
interested
in is r, or the distance from the earth's center.  But to maximize
that,
you wouldn't go to Everest, but instead to Chimborazo (or perhaps
Huascarán).  Remember that Earth is approximately an oblate
spheroid, and our reference for sea level is farther from the
center of the earth at the equator than at the poles.  Everest
is the highest above sea level, but Chimborazo is located
closer to the equator, so is farther from the earth's center than
Everest is.  Its equatorial location also has the added benefit
of giving you some velocity due to the Earth's rotation.

Agree with the major point, however.  Even the biggest
mountains aren't very high relative to the earth's radius.
And the logistical impracticalities of working at altitude
easily outweigh the slight energy advantage.

Reference on Chimborazo:
http://en.wikipedia.org/wiki/Chimborazo_(volcano)

In order to escape earth's gavity, you always have to be going at
least 11.2 km/s. Whet>

The escape velocity relative to any point A on the earth is always the
same regardless of the altitude of the point P from which you are
launching. The escape velocity relative to the point P from which you
are launching from varies with  point P's distance from the center of
the earth. When launching from a higher point, what you are actually
doing is borrowing some extra velocity from the increased rotational
speed of that point.

The tangential speed of any point P on a rotating object is

v=wr

where v is the tangential speed, w is the angular speed of the
rotating object, and r is the distance between the point P and the
center of rotation of the object. The further away from the center you
are, the faster your tangential velocity.

In order to escape earth's gravity, you always have to be going at
least 11.2 km/s relative to the center of the earth. If you launch
from a lower altitude, then you must design your craft to attain most
of that velocity on it's own. If you launch from a higher altitude,
your craft gets that extra speed boost and doesn't have to attain as
much of it on it's own.

If you are troubled with that explanation, consider this:

Imagine you have one of those cool Styrofoam airplanes. It is a calm
day- there is no wind at all. In order for your little plane to
generate enough lift to fly, it has to be going at least a certain
speed relative to the ground. Lets arbitrarily say that speed is 2 m/
s. You could get the plane to that speed by standing still and just
throwing it with your arm. Relative to you, to plane has a velocity of
2 m/s. Relative to the ground (the relative frame in which the air
exists), the plane is also going at 2m/s. Now imagine you throw the
plane a second time, but this time you give a little running start at
1 m/s. This time, since the plane still only has to be traveling at 2
m/s relative to the ground frame, you only need to throw the plane at
1 m/s relative to your now moving frame, but relative to the ground
frame, it is moving at 2m/s (your 1 m/s running speed plus the 1 m/s
throwing speed).

The plane still always needs to hit 2 m/s relative to the ground, but
depending on whether you are moving or not when you throw it, the
speed you need to throw it at may be lower than 2 m/s.

I hope that makes sense. It's all in the relativity. :-)

Another question:

If someone says that escape velocity is X, what does it actually mean ?

Is it really delta V value for a launch from the centre of the earth (no
earth rotation help) ?

Or is it a vertical speed you would need to launch at so that after all
the deceleration from the gravity, you would still have some velocity to
continue towards the rest of the universe ?

Also, if you go into low earth orbit, and gradually add delta V to
increase your altitude, your speed actually decreases, right ?

Is escape velocity defined as the orbital altitude where the speed
needed to remain in orbit is basically 0 ? (at which point any delta V
results in movement forwards and no ensuing deceleration ?)

Also, is there a difference in terms of total energy required to leave
the earth's gravity, between launching straight up towards the target,
versus going to low orbit and gradually increasing orbital altitude
until you've reached the ability to escape with just a tiny addition of
delta-V ?

(forgetting air drag for the sake of this question).