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Jim pondered Eugene's free fall and wondered just how fast he would have gone if the planet didn't have an atmosphere. Jim pondered having a go himself and figured he needed two balloons and a big old tube (capable of holding a vacuum) between them.
Realising that the tube will curve around the planet
between the two balloons Jim reckoned on having a maglev sled to ride inside the tube. Note the sled is not powered it uses constant magnets and is just there to remove the Jim/tube contact friction.
...
Jim reckons that with a bit of jiggery pokery he could even get away with a pretty straight pretty rigid vacuum tube that floats independently in the atmosphere (and perhaps dips its middle in an ocean).
Escape Velocity?
http://en.wikipedia...iki/Escape_velocity
This fast maybe... [madness, Nov 11 2009, last modified Nov 13 2009]
Eugene Andreev
http://en.wikipedia.org/wiki/Free_fall
That crazy russian --- if only the planet didn't have an atmosphere... [madness, Nov 13 2009]
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Annotation:
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//Jim pondered Eugene's free fall and wondered just how fast he would have gone if the planet didn't have an atmosphere.// |
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Jim could just do maths, referring to the formula: |
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where m = Eugene's mass
and a = the acceleration exerted upon Eugene (and the Earth) due to Gravity |
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the acceleration due to gravity is governed by: |
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where G is the Gravitational constant 6.6742 × 10¯¹¹ N·m²/kg²
M is the (combined) Mass of the Earth (and Eugene)
R is the Radius of the Earth
and
H is the height of Eugene above the surface of the Earth. |
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You'd probably need to do some calculus as well in order to "sample" the various accelerations undergone by Eugine as he gets closer to the Earth, but doing calculus is still a lot easier than floating an intercontinental tube containing a vacuum up into the stratosphere using balloons. |
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True, I could sample but I would be better off integrating along a line coincident with the tube. |
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But the latter is more fun... especially if I don't need the balloons. The vacuum will bouy the construction all on its own. |
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//escape velocity - This fast maybe?// No. |
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Remove all friction, start Jim out from height h, slide^H^H^H^H^H hover him down the tube, and he'll get going fast enough to rise up to... h. |
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We could go into a discussion of why the "slingshot effect" doesn't apply when you're starting from a point at rest with respect to the gravity well, but I suspect it would be wasted breath. [marked-for-deletion] bad science. |
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Evelyn, a dog, having undergone
Further modification
Pondered the significance of short-person behavior
In pedal-depressed panchromatic resonance
And other highly ambient domains
"Arf", she said. |
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Short stories aside --- a suspect that the big old tube will spin (relative to the earth) as the earth spins. So [lurch] what is the effect on eugines velocity...? |
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Are things 'lighter' at the equator than the poles? The answer follows from the weightlessness of an orbiting mass (i.e. mass remains constant by weight is a result of balanced forces). |
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... and note [lurch especially] that no where in the main text is there a statement about achieving escape velocity ... |
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His initial height's much less than the diameter of the earth or geosynchronous orbit, so I'll ignore the earth's rotation and variation in gravitational pull |
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His energy would be roughly mass times 10m/s/s times 24500m and also equal to half mass times speed squared. |
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v*v/2 = 245 000 m m / s / s |
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v*v = 490 000 m m / s / s |
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Hmmm thing is that once eugene heads down this track his only escape will be to grab at the ends of the tube when he gets close (where his velocity will be zero). |
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Perhaps its best to have an eject button so eugene can take a flight at sea level doing mach2 (or a bit less higher up). And all after just walking up the side of the tube in the first place.... |
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Something more interesting is the ability to add to eugens momentum with a force less than one g. That is this particular tube arrangement allows one to accelerate eugene to lets say escape velocity with a force smaller than g. |
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This is as opposed to the conventional force that must be more than g to move eugene at all. |
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