Calculating solar irradiance at each planet?

In summary: Thank you for clarifying. In summary, the discrepancies in the calculated solar irradiance for the different planets can be explained by the fact that Wolfram-Alpha uses real-time values for distance from the Sun, while the calculations assume a circular orbit at the average distance. This results in significant differences for planets with highly elliptical orbits, such as Mercury and Mars, while the values for Venus and Neptune are closer to the calculated values.
  • #1
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So I'm getting somewhat weird numbers when trying to calculate the solar irradiance at each planet. Starting with a baseline of irradiance at Earth of 1376 W/m^2, I use the inverse square law against distance. I find the values for Mercury and Mars are really off, while Venus & Neptune are almost right on the money! What's wrong with my method?
  1. Planet: calculated value (W/m2), actual value (W/m2), percent diff
  2. Mercury: 9183, 6283, 46.15%
  3. Venus: 2630, 2600, 1.15%
  4. Mars: 592.7, 710.6, 19.89%
  5. Jupiter: 50.82, 47.42, 6.69%
  6. Saturn: 15.128245, 13.51, 10.70%
  7. Uranus: 3.736, 3.465, 7.25%
  8. Neptune: 1.522, 1.526, 0.27%
I'm taking the mean orbital radius and solar flux as stated in Wolfram Alpha, for example:
mars average orbital radius - Wolfram|Alpha
solar flux at uranus - Wolfram|Alpha
 
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  • #2
Possible problem for Mars, orbit is fairly elliptical, so average radius may not be accurate enough.
 
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  • #4
mathman said:
Possible problem for Mars, orbit is fairly elliptical, so average radius may not be accurate enough.
And Mercury has that issue with General Relativity.
 
  • #5
Charles Link said:
Please show your calculations, especially for mercury. I think your arithmetic must be off, or else their number is incorrect. ## \\ ## Edit: See: https://nssdc.gsfc.nasa.gov/planetary/factsheet/mercuryfact.html They give 9082.7 for Solar irradiance on about line 15.
Well, I'm just using Wolfram Alpha to do the calculations:
Mercury: 1376 W/m^2 * (Earth average orbit radius)^2 / (Mercury average orbit radius)^2 - Wolfram|Alpha
Mars: 1376 W/m^2 * (Earth average orbit radius)^2 / (Mars average orbit radius)^2 - Wolfram|Alpha

So you're saying my calculations are more right than the values in Wolfram-Alpha?
 
  • #6
  • #7
The values reported by W-A when you type in e.g. 'Mercury solar irradiance' are (as noted) based on time-dependent distance from the Sun. I.e., these are not the average values, but values at this particular moment.
This simply means that for planets whose current position in their elliptical orbits is significantly different than the average distance, the current solar irradiance will also differ significantly from what you get from calculations which assume circular orbit.

If you scroll down the results page, you'll see an entry along the lines of X * average solar irradiance of Y. Those should be closer to what you're calculating.
 
  • #8
These are the values I get, along with bbbl67's:

values are watts/meter^2
\begin{matrix}
Planet & peri & ave & aph & current & wolf & bbbl67\\
Mercury & 14600 & 9187 & 6309 & 6452 & 9183 & 6283\\
Venus & 2669 & 2632 & 2596 & 2629 & 2630 & 2600\\
Earth & 1424 & 1376 & 1323 & 1392 \\
Mars & 720 & 591 & 493 & 718 & 593 & 711 \\
Ceres & 210 & 179 & 155 & 204 \\
Jupiter & 56.2 & 50.8 & 46.2 & 47.9 & 50.8 & 47.4\\
Saturn & 16.8 & 15.0 & 13.5 & 13.7 & 15.1 & 13.5\\
Uranus & 4.11 & 3.73 & 3.41 & 3.50 & 3.74 & 3.47\\
Neptune & 1.55 & 1.52 & 1.50 & 1.54 & 1.52 & 1.53\\
Pluto & 1.56 & 0.88 & 0.57 & 1.22
\end{matrix}

"current" values are based on data from 3 different sources. All of them were a tad bit different.
Sources:
 
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  • #10
Charles Link said:
@OmCheeto Thank you=that explains it. Mercury must have a very elliptical orbit.

Almost as elliptical as Pluto.

distances in AU
\begin{matrix}
planet & aph & perih & aph/perih \\
Mercury & 0.467 & 0.307 & 1.52 \\
Venus & 0.728 & 0.718 & 1.01 \\
Earth & 1.02 & 0.983 & 1.04 \\
Mars & 1.67 & 1.382 & 1.21 \\
Ceres & 2.98 & 2.56 & 1.16 \\
Jupiter & 5.46 & 4.95 & 1.10 \\
Saturn & 10.1 & 9.04 & 1.12 \\
Uranus & 20.1 & 18.3 & 1.10 \\
Neptune & 30.3 & 29.8 & 1.02 \\
Pluto & 49.3 & 29.7 & 1.66
\end{matrix}

Btw, I had everything locked and loaded from a HW problem from last December.
When I looked at the equation for "watts/m2 = 1376 / r2", it really confused me. It was missing all manner of values, π's and squares. What kind of voodoo math was I up to that day? Then I realized those all dropped out because Earth is at 1 AU.
 
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  • #11
Bandersnatch said:
The values reported by W-A when you type in e.g. 'Mercury solar irradiance' are (as noted) based on time-dependent distance from the Sun. I.e., these are not the average values, but values at this particular moment.
This simply means that for planets whose current position in their elliptical orbits is significantly different than the average distance, the current solar irradiance will also differ significantly from what you get from calculations which assume circular orbit.

If you scroll down the results page, you'll see an entry along the lines of X * average solar irradiance of Y. Those should be closer to what you're calculating.
Ah, I didn't realize that Wolfram-Alpha used real-time values for those!
 

1. How is solar irradiance calculated at each planet?

Solar irradiance is calculated by taking into account the distance between the sun and the planet, the tilt of the planet's axis, and the planet's atmosphere. The formula used to calculate solar irradiance is: S = L / 4πd², where S is the solar irradiance, L is the luminosity of the sun, and d is the distance between the sun and the planet.

2. What is the unit of measurement for solar irradiance?

The unit of measurement for solar irradiance is watts per square meter (W/m²). This measures the amount of solar energy that falls on a specific area of the planet's surface.

3. How does solar irradiance vary between different planets?

The solar irradiance at each planet varies depending on its distance from the sun, its tilt, and its atmospheric conditions. For example, planets closer to the sun, such as Mercury, receive more solar irradiance than those farther away, like Neptune. Additionally, planets with thicker atmospheres, like Venus, will have lower solar irradiance compared to planets with thinner atmospheres, like Mars.

4. Why is calculating solar irradiance important?

Calculating solar irradiance is important because it helps us understand the amount of solar energy that is available at each planet. This information is crucial for studying the planet's climate, atmosphere, and potential for sustaining life. It also helps us in designing solar panels and other solar-powered technologies for different planets.

5. Can solar irradiance be affected by other factors besides distance and atmosphere?

Yes, solar irradiance can also be affected by other factors such as solar activity, which can cause fluctuations in the amount of radiation emitted by the sun. Changes in a planet's orbit or rotation can also affect its solar irradiance. Additionally, human activities such as deforestation or pollution can alter a planet's atmosphere and thus, impact its solar irradiance.

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