To Boldly Drive ...

[Southwind17]

So, I'm driving up the ramp at the multi-storey car park at work, and whilst it's pretty steep I realize that I can accelerate up it (somewhat surprising for a 1200cc car, but there you go!), and it starts me thinking about escape velocity. And it leaves me wondering: If the ramp were hypothetically long, what would prevent me, even without accelerating, simply driving steadily up it until my static kinetic energy exceeds the reducing gravitational potential energy and I boldly drive where no man has driven before (all other practicalities aside, such as surface friction, limited fuel, continuously reducing oxygen, etc. (oh ... and being late for work, of course, and probably getting fired!)).

 

[ImaginalDisc]

Technically, you are not static. You are in contact with a spinning planet and so you're already moving really fast along with everything else at Earth's surface at 7.29 × 10 raised to the negative fith radians per second, which is about 1040 miles per hour at the equator. Stay in contact with the surface but go higher and you would therefore be moving faster.

If the ramp was so long as to reach Clark orbit (or geosynchronous orbit, if you prefer) which is 22,000 miles above the sea level, then stepping or driving along a ramp that passed that orbit would cast you into space because your velocity would exceed escape velocity. If you fell off the ramp before that you would actually orbit the Earth but in a death spiral because you wouldn't have sufficent velocity for a stable orbit. If you were right at Clark orbit you would orbit with a period of 24 hours, so you would appear to hover over part of the planet. Go past that point along the ramp and jump off. Your velocity from Earth's rotiation would give an orbit that would make the Earth appear to rotate backwards under you and you'd move away from the Earth.

This is why a space elevator is a cool and useful idea. The trouble is mainly finding a material to make it.

 

[Mojo]

This is why a space elevator is a cool and useful idea. The trouble is mainly finding a material to make it.

And figuring out what music to play in it.

 

[shadron]

See Arthur C Clarke, The Fountains of Paradise^WPWP.

 

[Southwind17]

So one doesn't necessarily need to travel fast then to escape the Earth. What's 'escape velocity' all about then?!

From what I gather now, it's the initial velocity needed by an object at the Earth's surface to escape the Earth's gravitational force assuming no additional escape force is applied (and ignoring factors such as air resistance). So why do space rockets travel so fast when leaving Earth? Is it simply a product of putting a touch tape to 250 tonnes of unharnessed solid rocket fuel?!

 

[EHocking]

So one doesn't necessarily need to travel fast then to escape the Earth. What's 'escape velocity' all about then?!

From what I gather now, it's the initial velocity needed by an object at the Earth's surface to escape the Earth's gravitational force assuming no additional escape force is applied (and ignoring factors such as air resistance). So why do space rockets travel so fast when leaving Earth? Is it simply a product of putting a touch tape to 250 tonnes of unharnessed solid rocket fuel?!

The Wiki entry explains this quite simply (to my satisfaction, anyway),

http://en.wikipedia.org/wiki/Escape_velocity#Misconception

Misconception

Planetary or lunar escape velocity is sometimes misunderstood to be the speed a powered vehicle (such as a rocket) must reach to leave orbit; however, this is not the case, as the quoted number is typically the surface escape velocity, and vehicles need never achieve that speed. This surface escape velocity is the speed required for an object to leave the planet if the object is simply projected from the surface of the planet and then left without any more kinetic energy input: in practice the vehicle's propulsion system will continue to provide energy after it has left the surface.
In fact a vehicle can leave the Earth's gravity at any speed. At higher altitudes, the local escape velocity is lower. But at the instant the propulsion stops, the vehicle can only escape if its speed is greater than or equal to the local escape velocity at that position. At sufficiently high altitudes this speed can approach 0.

 

[seayakin]

Isn't this why some engineers have looked into a concept of a space plane that might achieve a near earth orbit to launch a vehicle past the Clark orbit? The plane is really at an extreme altitude and the launch vehicle would need less energy to achieve escape velocity.

 

[Myriad]

If the ramp was so long as to reach Clark orbit (or geosynchronous orbit, if you prefer) which is 22,000 miles above the sea level, then stepping or driving along a ramp that passed that orbit would cast you into space because your velocity would exceed escape velocity. If you fell off the ramp before that you would actually orbit the Earth but in a death spiral because you wouldn't have sufficent velocity for a stable orbit.

I don't think this can be correct. The geosynchronous orbit is only special because its period is the same as the rotational period of the earth. That doesn't imply that the orbital velocity of a geosynchronous orbit is right on the verge of escape velocity.

If you fell off the ramp too low, you could fall in a ballistic trajectory to the ground, but from higher up you'd go into an eccentric orbit. It would only be a "death spiral" if that orbit grazed the atmosphere.

To reach escape velocity you'd have to go considerably higher on the ramp. Since the space elevator must have its center of mass in geosynchronous orbit, it would most likely be constructed to extend well past that height, so that option should be possible. Note that past the geosynchronous height where you'd be weightless, you'd be "driving" on the underside of the ramp and you'd be coasting on tidal force; no engine power would be needed. But you'd need to maintain enough tire friction for the ramp to accelerate your car laterally to match its own velocity at each point.

Respectfully,
Myriad

 

[ImaginalDisc]

I don't think this can be correct. The geosynchronous orbit is only special because its period is the same as the rotational period of the earth. That doesn't imply that the orbital velocity of a geosynchronous orbit is right on the verge of escape velocity.

If you fell off the ramp too low, you could fall in a ballistic trajectory to the ground, but from higher up you'd go into an eccentric orbit. It would only be a "death spiral" if that orbit grazed the atmosphere.

To reach escape velocity you'd have to go considerably higher on the ramp. Since the space elevator must have its center of mass in geosynchronous orbit, it would most likely be constructed to extend well past that height, so that option should be possible. Note that past the geosynchronous height where you'd be weightless, you'd be "driving" on the underside of the ramp and you'd be coasting on tidal force; no engine power would be needed. But you'd need to maintain enough tire friction for the ramp to accelerate your car laterally to match its own velocity at each point.

Respectfully,
Myriad

I had thought that, but let me explain the logic and either I'll convince you or I'll reveal myself as a complete idiot.

The proposed ramp is affixed the the surface of the Earth. Ignore for a moment that it would need physically amazing properties. If the end of the ramp passes geosynchronous orbits, several things are all true.

Let's look at a Clark Orbit at 22,000 miles out. Something that far out is orbiting very slowly ( a 24 hour hour period rather than the 90 minute period of a daisy clipping low earth orbit) so you'd think that if something just fell off the ramp at 22,000 miles out it would fall to Earth. Any object on the ramp at 22,000 is already in geosynchronous orbit and doesn't have to do the work of getting there by accelerating in an orbit.

You're traversing 7.2921150 times ten to the negative fifth radians each second when you are rotating with the Earth. The farther you stand on the ramp into space, the longer a total distance that arc traverses, and thus, the higher your speed. Eventually you reach Clark orbit standing on the ramp and your speed is the same in radians of circle traversed, but the radius of that circle is now 22,000 miles. Ok, more like 26,000 since you're actually rotating the center of the Earth, not the surface.