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- n_2/3 ) + A₃ n₃  + A₄(n₁ + n_1/4 )

 

 

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

           regions.

-         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

practicality,

 

-        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,

I