From: Tucker Hiatt (hiattu00@usfca.edu)
Date: Fri Aug 09 2002 - 09:29:50 PDT
Message-Id: <a0510031eb9799e6f47d4@[12.236.121.220]> Date: Fri, 9 Aug 2002 09:29:50 -0700 From: Tucker Hiatt <hiattu00@usfca.edu> Subject: Re: Acceleration to (near) the speed of light
I don't know the sustained acceleration limits of an average human
body. That info may be unnecessary, however, since a steady
acceleration of 1g (roughly 10 m/s/s) will get you near the speed of
light in less than a year. (Such an acceleration would also feel
perfectly comfortable: The starship's floor would push on the crew
just as the Earth pushes on us right now.) The non-relativistic
calculation is a straightforward application of the definition of
acceleration: a = v/t. Set a = 10 m/s/s and v = c and you find that
t = 30 million seconds = 350 days!
This is the time that a 1-g starship needs to reach near light-speed
as measured by the "stay-at-homes" on Earth. The starship crew will
see it somewhat differently, however. A relativistic calculation
based on info from "The General Limits of Space Travel" by Sebastian
Von Hoerner (reading #37 in The Quest for Extraterrestrial Life,
Goldsmith, 1980, p.197), yields t = 81 million seconds = 940 days
ship time (called "proper time") to reach 0.99c. This solution is
confirmed in Spacetime Physics by Taylor & Wheeler, 1963, p.142.
The point is that a sustained 1-g acceleration will get you near
light speed in a reasonable amount of time: about 1 year from the
Earth's frame of reference; about 3 years from the starship's frame.
However, time is not the space cadets only concern; energy is, too.
It turns out that an enormous amount of energy is necessary to
sustain a 1-g acceleration for a starship of even modest mass.
Non-relativistically, the figure is more than 10^21 joules for a 100
ton craft (and relativistically it's even worse). That's more than
the total energy used by all of humanity in an entire year.
On the bright side (?), 10^21 joules is "only" about one hour's worth
of solar energy that falls on Earth's surface.
- Tucker
-- *********************************** Tucker Hiatt Physics Instructor & Wonderfest Director The Branson School P.O. Box 887 (39 Fernhill Avenue) Ross, CA 94957 Tucker_Hiatt@branson.org 415-577-1126 (voice) 415-454-2535 (fax) http://www.wonderfest.orgTruth is a great flirt. - Franz Liszt ***********************************
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