Vertical Travelling taking Advantage of Earth's Rotation

[ahmadca]

As per our current scientific knowledge the earth rotates on its axis and it rotates at a speed of 1670 kilometers/hour. This decreases by the cosine of your latitude so that at a latitude of 45 degrees, cos(45) = .707 and the speed is .707 x 1670 = 1180 kilometers/hr

 

Earth atmosphere has 5 distinct layers :

1. First there is the troposphere, which contains more than half of the overall atmosphere. Near the poles, it starts at the Earth’s surface and stretches more than 30,000 ft (9 km), and about 56,000 ft (17 km) at the Equator

2. The Second layer is the stratosphere ,it begins where the troposphere ends, extending above 31 miles (50 km) above that. This is where many airplanes fly, due to the stability of this layer.

3. Going onward up, there is the mesosphere — the area in which meteors generally burn up

4. Just above the mesosphere is the thermosphere

5. Exosphere is the area where earth atmosphere ultimately merges with space. Space starts at 188 KM above the earth surface.

 

Keeping all the above in perspective, Let’s say that a space craft reaches an altitude of 800 KM above the earth surface and is well outside the earth’s atmosphere. Now since the earth below is rotating, would the space craft be able to land in different places by just hovering above and making a straight vertical descent. This would eliminate all horizontal travel distance as done by the airplanes when traveling from one point to another. Once we are at 800 km above the earth surface, all that is needed is to wait for the appropriate time when as a result of rotation of the earth, your destination point passes right under you and you descent your space craft to your destination. Do you think that this could revolutionize travelling? Less fuel and less time by just taking advantage of the rotation of the earth?

 

I am also attaching a diagram to clarify my question. The Diagram shows the various layers of earth’ atmosphere. The Orange tube just shows the vertical descent I am talking about from Point A in outer space (say at 800 km above the surface of earth). The Yellow line is the Imaginary karman line at distance of 110 km which serves the boundary between the earth’s atmosphere and the region where the space begings.

 

Please comment if the idea is feasible and the areas where you see flaws in this theory. One possible argument that people can give in the opposition of the idea is :

 

“Motion is relative and that the earth’s atmosphere rotates with the same velocity as the earth itself and therefore our spacecraft in question would also be in same motion as the atmosphere” - Relative Motion Concept

Please note that the relative motion concept would not apply in the case presented above because my assumption is that the space craft is no longer in earth’s atmosphere and is way beyond the karman line and cannot be considered as inside the earth’s atmosphere. The Space craft is 800 KM above the surface of the earth.

Do you think that this idea of vertical travelling taking advantage of earth’s rotation is possible? Please comment. Your feedback would be greatly appreciated.

 

 

[Janus]

The relative motion argument still holds. It doesn't matter whether you are above the atmosphere or not. That 1180 km/hr velocity you have on the ground stays with you as you climb. This would be true even if there were no atmosphere at all. Your hovering craft would still be traveling in a circle around the Earth, just a bigger one.

 

Here's a simple example: We'll start at the equator where you have an West to East motion of ~1670 km/hr. You fly up to your 800 km height. You will still be moving at 1670 km/hr from East to West. This is just due to your own momentum. Now you're traveling in a circle with a radius of 7178 km. It will take you 27 hrs to make one circuit. The ground beneath you takes 24 hrs to complete 1 circuit. So you will "drift" with respect to the ground, just not very fast, at ~186 km/sec.

 

Considering the amount of energy needed to get to an altitude of 800 km and safely lower yourself back down and the low "travel speed", this is just not practical as a mode of transportation.

[Enthalpy]

[...] That 1180 km/hr velocity you have on the ground stays with you as you climb. [...]

 

Complicated world... The horizontal speed is not conserved; it decreases at height. A way to understand it is that the "horizontal" direction changes over time, so the effect of Earth's gravity on the vertical component of speed becomes later an effect on the horizontal component.

 

The proper theory is an elliptic orbit that follows Kepler's laws. Fortunately we don't need all details. The notion we needfrom it is that the angular momentum is conserved, and this one tells that the product of the horizontal speed by the distance to Earth's centre of mass is constant.

 

So if vertical speed increases the distance to Earth's centre by n%, the angular velocity doesn't decrease by n% as would result from a constant horizontal speed; instead, the horizontal speed decreases by n% and the angular velocity decreases by 2n%.

[...] Considering the amount of energy needed to get to an altitude of 800 km and safely lower yourself back down and the low "travel speed", this is just not practical as a mode of transportation.

 

A factor of two won't change that. Agreed with the conclusion.

[Nicholas Kang]

You may want to try Orbiter 2010 for a simulation that really makes sense and free but it is something like 2GB.

You might like Basics of Space Flight by JPL NASA for a quite complelling explanation and fact-filled. Last but not least, you get a certificate for your tutorial

http://www2.jpl.nasa.gov/basics/index.php

http://orbit.medphys.ucl.ac.uk/

In my opinion, the spacecraft retains its momentum and velocity in outer space. Since there is no air drag/resistance, to slow down the spacecraft in space would require retro thrust. Or simply rotate your spacecraft and engage thrust. You didn`t mention slowing down of spacecraft in the OP. So, I think here is the point. To stay together with earth above it isn`t possible but not effective, usually, we fly spacecraft at the same speed as earth rotation, this is applied in GTO and GEO(geostationary/geosynchorous orbit/transfer orbit) In this way, the spacecraft/satellite would travel at the same speed and remains the same position above the sky. You can always find it and it is above your head.

 

All in all, geosynchrous/geostationary orbit would be more efficient and it does not require much fuel. Satellites launched backed in 1960s still orbit Earth today without fuel but they keep moving. Of course, to change direction or raise apoapsis/periapsis would require minor burn of fuel.

[Enthalpy]

In my opinion, the spacecraft retains its momentum and velocity in outer space. Since there is no air drag/resistance, to slow down the spacecraft in space would require retro thrust.

 

That's your present opinion, but not the one from Newton and Kepler, unfortunately.

 

As a craft on its orbit goes farther from Earth, its azimutal speed (in m/s, not just angular) slows down. That's the conservation of angular momentum. It's one of Kepler's laws.

 

What's not completely intuitive here is that Earth's attraction slows the craft down. It seems that the vertical force shouldn't act on the horizontal speed, but in fact it does, because the "vertical" and "horizontal" rotate along the trajectory.