# How much additional light does Earth receive from the Sun due to Earth's gravitational field?

I was reading about how gravity affects light, and that got me wondering how much additional light is collected by the Sun due to the Earth's gravitational field.

Is it a significant amount of light (>1% of total light)? Is it significant enough to be considered when estimating the surface temperature of a planet?

The amount of deflection of light (the bending of the null geodesic) passing a star is a deflection angle of 4m/R where m is the mass of the star and R is the radius of the star. The mass of the sun is $2 \times 10^{30}\rm\,kg$, where as the mass of the Earth is $6 \times 10^{24}\rm\,kg$. The radius of the earth is $6 \times 10^6\rm\,m$, and the radius of the sun is $7 \times 10^8\rm\,m$. Very roughly, this seems to indicate that the extra sunlight attracted to the Earth is very much less than 10,000 times less than the effect of the sun itself, which is barely detectable.

• Inquiring (but lazy) minds want to know, is the extra power kilowatts or microwatts. – Keith McClary Feb 2 '16 at 20:54
• OK, I get deflection of 10mm x circumference of Earth = 0.4km$^2$ additional cross section. – Keith McClary Feb 4 '16 at 2:14

Earth's gravitational field causes Earth to retain a gaseous atmosphere, which both absorbs light itself and refracts light towards the surface. Estimating the altitude of the optically thick part of the atmosphere as somewhere between 6 km and 60 km, this atmosphere effectively increases the cross-sectional area of the Earth for interacting with sunlight by between 0.1% and 1%; the lower end is a better estimate. Not all of this atmospherically captured sunlight is absorbed by the Earth, but the same is true for directly incident light as well.

So, interaction with Earth's gravitationally-bound atmosphere increases insolation by something like 0.1%, subject to local, daily, and seasonal fluctuations due to things like clouds.

Atmospheric refraction of sunlight in the ideal case bends the light by about half a degree, or 1800 seconds of arc. In the same ideal configuration, the general-relativistic deflection of light by the sun is 1.75 seconds of arc. Scaling the GR deflection by $M/R$ for mass $M$ and radius $R$ to about 0.6 milliarcseconds, I get that the atmospheric refraction is about three million times larger than the general-relativistic refraction.

So general relativistic refraction of light is a parts-per-billion corrections to Earth's insolation. Not important.

Assuming you mean "collected by the Earth"... These effects are barely measureable when observing the Sun bending light towards itself. Earth bends light even less. The value will be much less than 1%. The light is red-shifted as it leaves the Sun (effectively becoming less energetic) It is blue-shifted to a lesser degree as it falls to Earth (becoming a little more energetic) Of much greater import for changing Earth's temperature are the following for solar radiation: The total energy emitted by the Sun varies Sunspots raise Earth's temperature, possibly via cosmic ray formation of high altitude clouds

• How do you describe it mathematically? – Scott Lawson Jan 13 '15 at 14:51