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COOLING OR HEATING A PLANET BY USE OF RINGS J.H.L.Lawler Ó 1984 IJS Vol 4 page 33
It is possible either to cool or to heat a planet, or to redistribute the heat, cooling the equator while warming the poles, by use of rings of reflective material about the planet. For example if a planet were to be too hot at the equator, that could be climatically altered by placing a fairly low orbit ring to block and reflect part of the isolation that would have struck the equator, thus radiating it to space. and reducing the total heat input, In the reverse case a ring placed so that it does not obstruct incoming light, but so that it does reflect some light from the ring to the planet that would not have otherwise reached the planet can raise the temperature by rather large amounts, up to double the energy being easily obtained.
In the case of a low altitude ring the solid angle subtended by the planet and by the open space are approximately equal, and thus half the reflected light would reach the planet, and half would he reflected away into space. Thus the heat gathering ability is far less than the heat rejection ability which can approach 95% of the incoming light. The ring can be set to reject selectively into space- with virtually none of the reflected light striking the planet, The planet thus is cooled to the extent of the shadowing or the area of the planet times the percent loss from the presence of the ring.
In trying to re-distribute the energy, The problem becomes more complex. In the most general case there are four distinct areas to be entered into the computation.
A1 the area of the planet which is somewhat altered but receives light directly: A2 is the area of the rings which receives light and reflects it to the planet, which would not have directly received light without the rings: A3 is the area which receives light onto the rings which would have normally fallen onto the planet (the shadowed area) and A4 is polar area which is NOT shadowed in part like A1 and is not altered at all except by the added light from A2 and A3
The total area of the planet is A1+ A3 +A4 as seen from the primary (Sol).
The light before the alteration would be LIGHT IN = (A1+ A3 +A4) n1
The energy afterward would be:
LIGHT IN = A1n1 +A2 n2 + A3(1- n2/3 ) + A3 n3 + A4(n1 + n1/4 )
where the n’s are a combination of the reflectivity and geometry (i.e. the fraction of the planetary surface that receives light from that area)- with the third term having been simplified by assumption that the reflected light half strikes the planet and half is rejected to space- which is not always true...i.e. that light which passes thru strikes the planet anyhow--and of that which Is reflected still some strikes the planet.
Because of the energy rejection that area Shadowed (A1) is cooled to the extent of the loss by the shadowing area A3, and heated by the added light received from A2-note that the cooling is strongest at the equator which receives virtually no A2 light, and tapers to A4 which receives maximal benefit with no cooling and much A2 enhancement.
International Journal of Science VOL 4 P 33
Let us examine a point on the equator. It looses light by the ratio of A3R/2 to A1 since
the ring A 3 reflects, with R, light, but in a low orbit roughly half the light reflected
strikes the planet in any case. The light not reflected passes on into the planet thru
the ring and is adsorbed to the normal extent of the albedo as if the ring were not there
____ Only the reflected light is lost & Only half of that. However, the energy is increased to
the extent of the light reflected from A4 (both parts). Thus depending on the ratio of
A3 to A2 the net gain could be positive energy or a net loss resulting in negative
energy balance. If the ring crosses at 30º North and 30° South latitude
(note sine 30° = 0.5)
then the net energy balance at the equator is zero change. At higher angles the net
effect will be cooling, and at lower the net effect will be heating of the equatorial
- The polar areas (A) have no shadowing at all, and receive 's more light by the ratio of
A2 /4 to A4/2 plus A3 R/4 +to A4/2 (the pole itself sees only half of A2 and half the light
- from A3 which is reflected (R) strikes the planet if the ring is at low altitude with
half the light escaping. At higher altitude a correction for the geometry must also be
applied, further reducing the capture from both A2 and A3. The portion of A3 away from
the poles is fairly compensated by added A2 area added or lost so the net is about
uniform at the whole polar area A4
The fractional gain or fractional loss in A1 depends en latitude, but the effect at
any latitude will be proportional to the equatorial effect. The fractional effect then
varies in the transitional zone from the equatorial effect to the polar effect-linearly Across the
transitional zone. Thus the energy input at any part of the planet, or the net resultant can
be computed by simply adding the three zones ( A1 A4 and A5). Together. If
one wanted to cool the equatorial regions say 1% energy loss and add 2% to the poles
then a Specific ring system is designated. It is not possible to quite get uniform global
temperature in any real case. A small planet with a huge ring would approach this;
however, the ring effect is such that it is possible to moderate any planet~ to raise or
lower the mean temperature up to equivalent of about 50% energy either direction, and
to shift about half the mean temperature extremes between poles and equator out of the
system with a realistic ring system. Any shift past about the point where the ring equals
the diameter of the planet in cross measurement would seem to be pushing the limits of
- That however allows areas of 4 times the collection in the ring or double the energy to
the planet, so that more than doubles the "habitable zone in planetary systems frump that
which would be natural. This then allows terra-forming planets that require twice the
energy -or half the energy (the square root of 2 in distance) of the optimal distance,
and with some allowance for not using all of the planet as. tee hat or too cold, would
allow a zone of about Venus to Mars roughly for acclimatizing planets. Venus is on the
marginally close end while Mars is well within the allowable range Mars will be easier,
but I have little doubt that Venus may well be terra-formed to provide mere living room in
the near solar System (lebensraum). These are well within the projected technology of
the 21st century and not in the far distant realm of speculation,
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