Transfer orbits and high speeds

[Sigma_Orionis]

Hi all:

One question: looking through an old Quantum Mechanics book (Introduction to Atomic Physics by Enge Wehr and Richards), I was re-reading a section on Special Relativity and while checking on the Lorentz transformation for time and I was wondering:

Let's suppose we have the technology to accelerate in a very short timespan to .14c (which gives us a ץ of 1.01 so we could say time dilation would be bothersome but not all that much) Would we have to worry about things like transfer orbits if we had a spacecraft capable of developing such accelerations? I was wondering this because on all these sci-fi films/and movies the like, the only "orbits" we hear is when the characters have their craft orbiting a planet or so, but in the real world spacecraft HAVE to deal with things like that in order to be able to navigate through space.

[editted for spelling]

[Glom]

We usually deal with Keplerian orbits. If the velocities were sufficient to make relativity meaningful then we couldn't use good old Newtonian astrodynamics.

[Sigma_Orionis]

Ok. I get your point: Newtonian Orbital mechanics become meaningless if relativistic effects become non-negligible, do you have any idea if somebody took the time to sit down and describe Astrodynamics when relativistic effects become significant? my Calculus is way too rusty for anything of the sort

[Glom]

For the purposes of back of the envelope calculations we'd do on this board, that lorentz factor wouldn't have that much of an effect.

[Saluki]

Assuming your ship started from Earth orbit, then accelerated to a solar orbit roughly the same as the Earth's, and then rapidly accelerated to 0.14c, it would be placed on an escape trajectory from the Solar System as soon as the ship exceeded about 41 km/s. It would still technically be in the sun's orbit, but the orbit would have the shape of 1/2 of a hyperbola, extending out of the Solar System indefinitely. If you timed your burn correctly, you would end up on a trajectory toward another star. Once you reached the desired star, you would have to do another burn to slow your ship down to orbit that star. Then, going into orbit of a desired planet in the system would be a simple matter of calculating the proper transfer orbits, just like we do in our solar system.

[Sigma_Orionis]

Then even if we were capable of building a craft capable of achiving an acceleration high enough to reach .14c we would STILL have to worry about transfer orbits and the like, thanks a lot

[ngc3314]

Then even if we were capable of building a craft capable of achiving an acceleration high enough to reach .14c we would STILL have to worry about transfer orbits and the like, thanks a lot

Mind you, the hyperbolic trajectories you get in the Sun's gravity with such velocities are awfully close to straight lines. [Pedantic notes about what "straight" means in curved spacetime and when the Lorentz factor is noticeably different from one mercifully omitted.]

[Sigma_Orionis]

Then even if we were capable of building a craft capable of achiving an acceleration high enough to reach .14c we would STILL have to worry about transfer orbits and the like, thanks a lot

Mind you, the hyperbolic trajectories you get in the Sun's gravity with such velocities are awfully close to straight lines. [Pedantic notes about what "straight" means in curved spacetime and when the Lorentz factor is noticeably different from one mercifully omitted.]

Close enough for a Hard Sci-Fi novel though