Solar-powered space flight
7d. Achieving the desired level of
optical precision: Why it is harder to achieve these characteristics in low-g
conditions
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7.6 It is more
difficult to achieve the desired position accuracy in a very low or zero g
environment because 
is then several
orders of magnitude smaller than the circa 8 – 14 ms-2 applicable in the above
proposed pre-orbital trajectory. We can still ensure that 
predominates in the
calculation of 
by making 
large
enough. But in the calculation of 
we find that 
generally has the
‘wrong’ sign and hence (for small ) is in the positive
rather than negative x direction.
Overcoming this
undesirable feature when is small is likely
to require an impractically large 
or some sort of boom
that allows us to apply a force to the mirror in the positive x
direction. Such a boom adds mass. Alternatively, we would need to use an
inflatable concentrator (the pressure within the inflated part then providing
the necessary force in the positive rather than the negative x direction).
We might seek to dispense
with most of the stanchions and instead include concentric wires within the
mirror surface that mitigate tension differentials that would otherwise arise
across the mirror surface. 
would then be
non-zero in each region within consecutive concentric wires, and at each edge
of each such region we would, in effect, be able to reset 
and 
to be closer to what
we would like by choosing a suitable tension for the wires themselves. However,
it would then be difficult to avoid having some stanchions scattered across the
mirror as if they were all attached to the outer rim of the mirror then they would
in aggregate provide too much centripetal acceleration, causing the rim to bend
back in on itself.
7.7 The above
comments apply, in broad terms, to any optical concentrator. Suppose that we
have a concentrator with focal length 
. To first order, near
its optical axis, 
and 
, so to first order
we have:
So if we want 
whenever 
(which would be
desirable in any region where there wasn’t a stanchion or if we wish to avoid a
boom or inflated structure) we ideally want 
. Practical
concentrators are likely to have dimensions not hugely different to their focal
length, so we conclude that ideally their sizes should also be of the order of
at least 
.
Ideally, we would also
want 
and whenever 
in any region where
there wasn’t a stanchion or a tension wire, i.e. for 
to be small in
relation to 
. But if is too small then we
would have negative at the
mirror rim, since needs to be negative
there for a practical stanchion configuration, see earlier.
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