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A suborbital trajectory is an ellipse that intersects the ground, and it will do so twice within less than half the world's circumference. If you can make it ha

by DavidSJ 12y ago

jessaustin 12y ago
A suborbital trajectory is an ellipse that intersects the ground, and it will do so twice within less than half the world's circumference. If you can make it halfway around the world, you're orbital. My experiments with Flappy Space Program contradict this. b^) It is perfectly possible to miss orbit even after a complete circumnavigation. Trajectories are shaped like parabolas, not ellipses. New York to Tokyo is nearly half that circumference, so the energy required is nearly that of orbit. Well it's more like a quarter, but even if it were half it would take significantly less energy than orbit.
- DavidSJ 12y ago
  > It is perfectly possible to miss orbit even after a complete circumnavigation. Yes, if you have a source of lift, and you're within the atmosphere, then you can circumnavigate the globe without reaching orbital velocities. A ballistic rocket generally has no significant source of lift and spends nearly all of its time in space. > Trajectories are shaped like parabolas, not ellipses. All orbits are conic sections: either an ellipse, hyperbola, or a parabola (the limiting case between the two). But a parabolic or hyperbolic trajectory has escape velocity, whereas only an elliptic trajectory is planet-bound. The apogee of the ellipse is locally approximated well by a parabola, which is why for non-orbital mechanics ballistic trajectories are often modeled by a parabola, but all suborbital trajectories are actually ellipses, not parabolas. If the Earth were flat and the gravity vector were constant, then they would be actual parabolas. Orbital mechanics is very counterintuitive. I recommend Fundamentals of Astrodynamics if you'd like to learn more, or play KSP rather than FSP. > Well it's more like a quarter On this you are correct, the map I looked at deceived me. :)
  - jessaustin 12y ago
    OK, thanks for the knowledge. Given all that, and the fact that there are several ICBMs with ranges longer than Tokyo-NYC, I still suspect that the speed-energy-distance combination will eventually work out for some segment of the travelling public.
    - DavidSJ 12y ago
      Yes, but even one quarter the way around the world turns out to be very close to orbital energy, because your delta-distance per delta-v increases rapidly as you increase energy. Nearly all ICBMs are multi-stage rockets for this reason. Vehicles designed for suborbital tourism like Spaceship Two, Lynx, and New Shepard aren't traveling more than a couple hundred km without a second stage. Math: Reaching the edge of space requires 100 km altitude, or 1,000,000 m^2/s^2 of specific energy, which is 1,414 m/s velocity. Redirect that to a 45° angle and you have 1,000 m/s in both the vertical and horizontal direction, which comes close to maximizing your distance. That gives you 200 seconds of flight, which puts you 200 km downrange.
deleted 12y ago
[deleted]
- DavidSJ 12y ago
  The shape of the curve isn't different just because the ground's in its way. This post has an illustration that makes the concept clear: http://forum.kerbalspaceprogram.com/threads/108970-Help-with-orbital-mechanics-for-a-school-project?p=1710399&viewfull=1#post1710399 http://forum.kerbalspaceprogram.com/threads/108970-Help-with... (Note: I'm approximating by assuming no forces other than gravity, which is an extremely good approximation for a ballistic rocket. In perpetually powered flight the trajectory can of course take other shapes.)

by DavidSJ 12y ago

jessaustin 12y ago

A suborbital trajectory is an ellipse that intersects the ground, and it will do so twice within less than half the world's circumference. If you can make it halfway around the world, you're orbital. My experiments with Flappy Space Program contradict this. b^) It is perfectly possible to miss orbit even after a complete circumnavigation. Trajectories are shaped like parabolas, not ellipses. New York to Tokyo is nearly half that circumference, so the energy required is nearly that of orbit. Well it's more like a quarter, but even if it were half it would take significantly less energy than orbit.

DavidSJ 12y ago
> It is perfectly possible to miss orbit even after a complete circumnavigation. Yes, if you have a source of lift, and you're within the atmosphere, then you can circumnavigate the globe without reaching orbital velocities. A ballistic rocket generally has no significant source of lift and spends nearly all of its time in space. > Trajectories are shaped like parabolas, not ellipses. All orbits are conic sections: either an ellipse, hyperbola, or a parabola (the limiting case between the two). But a parabolic or hyperbolic trajectory has escape velocity, whereas only an elliptic trajectory is planet-bound. The apogee of the ellipse is locally approximated well by a parabola, which is why for non-orbital mechanics ballistic trajectories are often modeled by a parabola, but all suborbital trajectories are actually ellipses, not parabolas. If the Earth were flat and the gravity vector were constant, then they would be actual parabolas. Orbital mechanics is very counterintuitive. I recommend Fundamentals of Astrodynamics if you'd like to learn more, or play KSP rather than FSP. > Well it's more like a quarter On this you are correct, the map I looked at deceived me. :)
- jessaustin 12y ago
  OK, thanks for the knowledge. Given all that, and the fact that there are several ICBMs with ranges longer than Tokyo-NYC, I still suspect that the speed-energy-distance combination will eventually work out for some segment of the travelling public.
  - DavidSJ 12y ago
    Yes, but even one quarter the way around the world turns out to be very close to orbital energy, because your delta-distance per delta-v increases rapidly as you increase energy. Nearly all ICBMs are multi-stage rockets for this reason. Vehicles designed for suborbital tourism like Spaceship Two, Lynx, and New Shepard aren't traveling more than a couple hundred km without a second stage. Math: Reaching the edge of space requires 100 km altitude, or 1,000,000 m^2/s^2 of specific energy, which is 1,414 m/s velocity. Redirect that to a 45° angle and you have 1,000 m/s in both the vertical and horizontal direction, which comes close to maximizing your distance. That gives you 200 seconds of flight, which puts you 200 km downrange.

deleted 12y ago

[deleted]

DavidSJ 12y ago
The shape of the curve isn't different just because the ground's in its way. This post has an illustration that makes the concept clear: http://forum.kerbalspaceprogram.com/threads/108970-Help-with-orbital-mechanics-for-a-school-project?p=1710399&viewfull=1#post1710399 http://forum.kerbalspaceprogram.com/threads/108970-Help-with... (Note: I'm approximating by assuming no forces other than gravity, which is an extremely good approximation for a ballistic rocket. In perpetually powered flight the trajectory can of course take other shapes.)