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A friend and I were reading some of the more catastrophic predictions for climate change, and were wondering if it would be possible to recover from complete permanent loss of polar ice (which cools the planet by reflection).

One idea we kicked around was building a giant occulter in space. Technological considerations aside, how big a shadow could we cast?

I can't figure out how to handle the umbra and penumbra. If you have

  • Earth of radius $r_e$
  • orbiting the Sun of radius $r_s$
  • at a distance $d_{se}$
  • and an occulter of radius $r_o$ in between the two
  • at a distance $d_{so}=d_{se}-d_{oe}$

how much light would be blocked?

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  • $\begingroup$ Can you include a diagram of your system? That'll make it much easier for your audience to interpret what exactly you have in mind $\endgroup$
    – Semiclassical
    Jul 30, 2014 at 14:23
  • $\begingroup$ What an occult question. :-) $\endgroup$
    – Lucian
    Jul 30, 2014 at 14:58

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As long as the umbra and penumbra are fully falling on the Earth surface, the total deflected energy is simply the energy arriving at the shield, hence approximately 1.36 kW/m² (as long as the shield is not significantly closer to the Sun)

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  • $\begingroup$ The question asks about the shadow cast by the shadow, not the energy absorbed by the occulter. $\endgroup$
    – Semiclassical
    Jul 30, 2014 at 14:38
  • $\begingroup$ Hagen is right, overall the shadow is equal and opposite to the light hitting the shield. $\endgroup$
    – spraff
    Jul 30, 2014 at 22:57

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