The Earth's temperature is given by a balance between solar heating and blackbody
I = Intensity of solar radiation
T = Earth temperature
dI 4 dT
I ~ T^4 --> ---- ~ ------
Changing the Earth's temperature by 1 Kelvin requires dI/I ~ .013,
corresponding to a sunscreen with area ~ .013 * 1.27e14 ~ 1.7e12 meters,
or (1300 km)^2.
The mass of an orbital sunscreen is
Surface area Thickness Density
Mass ~ 1.4*10^12 kg -------------- ----------- ---------
(1300 km^2) 10^4 m 8 g/cm^3
An orbital sunscreen can be built from a ~ 1 km metallic asteroid.
The energy required to retrieve this asteroid from the asteroid belt is
~ 10^18 Joules, easily achievable by a solar thermal rocket.
A above scaling is for a brute force sunscreen. With a gyroscope-equipped
fleet of orbital mirrors, finesse allows us to get by with a
smaller sunscreen. For example, sunlight that would have fallen on
equatorial mountains can be redirected to promote arctic agriculture, and
snow can be encouraged at the poles. It may even be possible to tame
hurricanes and turn them into tourist attractions. This presents an
opportunity for global cooperation.
Energy from space
An orbital mirror can power a steam engine and the power can be beamed with
microwaves to the Earth.
Power can be beamed from space to the Earth with 50% efficiency using microwaves.
The power used by civilization is ~ 2e13 Watts. A square mirror 100 km on a side
collects ~ 1.4e13 Watts of sunlight.
Raising the sea level
Earth surface area = 5.10e14 m^2
Earth land area = 1.49e14 m^2
Earth water area = 3.61e14 m^2
Vol = Volume of water in the top 10 cm of the ocean
= 3.61e13 m^3
E = Energy required to raise this volume of rock by 10 meters
= 3.61e13 m^3 * 2000 kg/m^3 * 10 m/s^2 * 10 meters
= 7.2e18 Joules
Ec = Energy produced by civilization in one year
= 6e20 Joules