I was wondering how much more energy, from the Sun, that Venus receives as compared to the Earth. Of course Venus is closer but it is also smaller so more of the Suns energy that is available will “fly” right by Venus. I decided to think about it as a percentage of the total surface area of a hypothetical sphere around the Sun at the point of the planet in question compared to the “profile area” (the diameter of the planet squared times pi). Heres my calculation (all values are in km).
The area of the sphere around the Sun at Venus is
108,208,930^2 * 4 * PI = 1.47141802 * 10^17 sq km
Venus “profile area” is
6,051.8^2 * PI = 115,058,579 sq km
So Venus share of all the energy available at its distance is
I did the same thing for Earth and got 4.5342152 * 10^(-10)
Divide them by each other and it seems to me that Venus gets 1.7246 more energy from the Sun than the Earth. Am I right? Even if I am not it was fun doing the math
I get 1.727 instead, but that’s probably just Google Calculator uses slightly different numbers of the radius of the earth and/or the orbits than you used. In any event, yes, this is the technique you would use.
That 7.8 x 10[sup]-10[/sup] fraction that you obtained, by the way, is the fraction of the sun’s luminosity that Venus would receive. So if you want to convert that into an absolute number, multiply it by 3.84 x 10[sup]26[/sup] watts.
I think diameter squared times pi is too big. If you want the surface area of the disk which a planet presents to its star, you need the expression for the area of a circle. Which is *radius *squared times pi.
Since diameter squared = 4 x radius squared, your calculation gives numbers 4x too big. But … the relationship between your Earth & Venus values is unaffected by this mistake, so your 1.72 final result remains good.
Luminosity goes as the square of distance. Venus’s mean orbital radius is .72 Au, so a square meter on venus gets 1/(.72)^2=1.9 as much solar energy as the Earth. Area goes as the square of the radius,Venus is .95 Earth’s radius, so its size is .95^2=.9 times the area of the Earth.
.9*1.9=1.71
Just as a general rule, its usually easier to do these types of problems by just taking the ratios of the variables that actually change and ignoring the “scaling constants” and factors of pi, since they divide out anyways. So you don’t have to know the actual areas and distances involved, just their relative sizes)
(even easier in this case, since wikipedia gives orbital radii as fractions of Earths (1 AU) and planetary radii by fractions of Earth’s radius).
Note that the total energy a planet receives from the Sun usually isn’t actually all that relevant: A larger planet will gain more energy, but it’s also spread out over more area, and there’s also more area to radiate away energy. For something like the temperature, all you really need is the energy the planet receives per area, which for Venus is 1.9 times that for the Earth.
