Solar sail breaking

[Nick Tosh <101765.2200@compuserve.com>]

Hello everybody.

You may not remember me - I haven't contributed anything for nearly a year
now. I had computer problems that kept me off the net for over six months,
and for various reasons I've been very busy since. Anyway, I'd like to
'rejoin' LIT. I'm a student in England, and I'll be going to study physics
at university next year. You already have me on your mailing list, so I'm
pretty much up to date.

>From what I've gathered from reading past mailings, stopping a starship
powered by a Sol based particle/EM rad beam is a major problem. The (fairly
obvious) idea that occurred to me was that a solar sail would be much more
attractive as a braking device when approaching a target star at high
relativistic speed than as an accelerating device for leaving Sol. The
doppler shifts that are such a pain in the latter case, or for the Sol
based microwave beam, become a significant help if the sail is moving
towards the energy source (i.e. Tau Ceti, or even better, the multi-star
-triple?- Centauri system). If the starship is moving towards the target
system at velocity v, expressed as a fraction of c, then the the impulse
imparted per reflected incident photon of frequency Fo measured in the
star's frame is:
                  _____
2(h Fo)    /  1 + v
----------   /  -------- (by the way, do any of you use Mathcad? I hate
typing out maths like this and would much rather e-mail Mathcad files).
    c        \/    1 - v

(The photons is reflected, so its change in momentum is twice the magnitude
of its initial Doppler shifted momentum. I think that the reflected photon
is of the same -shifted- frequency of the incident photon, since otherwise
the solar sail would have to absorb more energy than it radiated, and this
surely cannot be a theoretical requirement; in any case, how would the sail
know what the 'proper' non-shifted frequency was meant to be?) The above
expression obviously shows that the impulse imparted to the ship by each
photon approaches infinity as the velocity of the ship approaches 1c.
Unfortunately, the mass of the ship also approaches infinity, so the
decellerating effect remains finite. However, the mass increase factor is 1
/ sqrt(1-v^2), while the impulse increase factor is sqrt[(1+v)/(1-v)]. If
we divide the impulse factor by the mass factor we get (1+v). So the
impulse per photon increases faster than the mass does - the decelleration
(in ship's frame) provided by the sail increases with speed. The limiting
case, v approaching 1, results in double the 'rest' decelleration. Since
for most other forms of propulsion relativistic effects make decelleration
more difficult at higher speeds, might not a sail be a useful additional
'brake' for the starship? (I wouldn't even suggest it as the only one). The
main disadvantage of this system would be that to reap the benefit of the
sails high velocity performance, the starship would have to still be moving
very fast while near enough to the target star to get a fairly intense
photon flux. Chances are it couldn't slow down in time. Some compromise
would be necessary. Could the ship purposely overshoot the star, so as to
get some big delta-V from the sail while VERY close to the star? As it
passed by, it could furl the sail to avoid getting accelerated away from
the star (I think I like that idea. Has it been considered before? Making
such a long journey even a little longer is an odd idea, but it could be
useful. I'll do some maths on it later).

I need some help on the following point. Does time dilation result in the
high velocity starship intercepting more photons per unit time than an
observer in orbit around the star sees the star emit in the ship's
direction? Does relativity really increase both the impulse gained from
each photon AND the photon flux (in the ship's frame)? I don't know enough
to answer this, and I'm too tired to think about it now. If the aswer to
this is yes, than I think some serious modelling of the sail brake should
be done immediately. Please could someone answer this for me as soon as
poss.

Could people tell me if this mail gets through? 

Nick