# Super simple estimation of available solar energy

How much energy is actually renewable and humanity's cap in consumption

```
from sympy.physics.units import K, W, m, giga
sigma = 5.67 * 10**(-8) * W *m**(-2) * K**(-4)
T = 5778 * K
surface_energy = sigma * T**4
print(surface_energy)
```

```
from sympy import *
r_sun = 696_340 * 1000 *m
surface_of_sun = 4 * pi * r_sun ** 2
radiation = surface_of_sun * surface_energy
print(radiation)
```

```
R_earth = 6_371 * 1000 * m
D_earth_sun = 148.88 * 10**6 * 1000 * m
earth_perp_surface = pi * R_earth **2
sphere = 4 * pi * D_earth_sun **2
radiation_received = radiation / sphere
print(radiation_received)
```

```
power_received = radiation_received * pi * R_earth **2
surface_power_received = power_received / (4 * pi * R_earth **2)
print(surface_power_received)
print(power_received.n())
```

RADIATION RECEIVED BY SYSTEM EARTH = $345 W.m^{-2}$

MAXIMUM POWER WITH EARTH "DYSON SPHERE": $176 PW$

# Human consumption

13 511 MTep Source International Energy agency

```
from sympy.physics.units import J, s, W
from sympy.physics.units.util import convert_to
million = 10 **6
kilo = 10**3
giga = 10 ** 9
toe = 41.868 * giga * J
ktoe = kilo * toe
Mtoe = million * toe
hour = 60 * 60 * s
year = 24 * h * 365.25
base = sum([3852538,2949909,670298,335519,204190,1286064,4329220])
Humanity_total_annual_consumption = base * ktoe
humanity_power_consumption = Humanity_total_annual_consumption / year
print(convert_to(humanity_power_consumption.n(), [W]).n())
```

```
print(convert_to(humanity_power_consumption / power_received * 100, [J, s]).n())
```

We are currently consuming **0.01% of the maximum capacity of the earth covered by a Dyson sphere of solar panels**.

After the atmosphere only $168 W.m^{-2}$ hit the surface. It's quite complicated to infer it depends on the wavelength of the incoming light, clouds, composition of the atmosphere and so on, so we just take the value from here.

Then we only have 29% of the earth surface that is landmass (where we can reasonably put solar panels in large quantity)

Then solar panels are not 100% efficient. They are roughly only 20% efficient with current technology at a reasonable cost.

```
earth_power_received = 168 * W * m **(-2)
available_surface = 4 * pi * R_earth **2 * 0.29 * (1 -.31 - .384)
max_power = earth_power_received * available_surface * 0.2
print(max_power.n())
print(convert_to(humanity_power_consumption / max_power *100, [J, s]).n())
```

In the end we are currently consuming **1.2% of the realistic available solar power energy**. That's would require posing solar panels everywhere on the planet that is not a forest or agricultural land. And we don't account yet for Energy return on energy invested (EROEI) which is likely to increase that percentage.

NB: This is a very superficial attempt to evaluate these numbers, however the result should be correct within an order of magnitude.