How can I calculate solar intensity at Saturn

I'm trying to work out how big solar panels have to be for a Saturn probe, but can't find any data for solar energy at Saturn.

• Hint: Solar power recieved goes as $1/r^2$. You don't find any data because it really is that simple. – AtmosphericPrisonEscape Feb 18 '18 at 22:50
• +1 I think down voting of this reasonable question from a new user is just plain mean, and therefore not nice nor in keeping with SE's "be nice" policy. – uhoh Feb 24 '18 at 2:31

Saturn is about 10.1 AU from Sun, so by the inverse-square law, its solar illumination is a little less than one-hundredth that of Earth, which is also called the solar constant with a value of 1362 W/m².

$$I = I_0 \frac{1\ \mathrm{AU}^2}{R^2} \approx 1362\ \mathrm{W\ m^{-2}}\frac{1^2}{9.583^2}\approx14.83\ \mathrm{W/m^2}$$

Since Saturn's relatively large eccentricity of 0.0565 puts it anywhere between 9.041 and 10.124 AU from the Sun, $$I$$ varies from 16.66 and 13.29 W/m^2 during its 29.5 year orbital period.

• @uhoh - the question was about Saturn, not Jupiter. Details about planetary orbital characteristics are readily available online; I recommend Wiki as a first quick reference. – Professor O Sep 22 '19 at 22:29
• Ah I do that (confuse Jupiter and Saturn) about once a year, sorry about that! I've added a bit more "explanation and context" and flagged your answer to suggest that it might be okay to remove the post notice. Thanks for your comment! – uhoh Sep 22 '19 at 22:48

As a supplementary, I thought I'd include a handy table of all the major solar system bodies and their relative light exposure compared to Earth. Columns are distance to the Sun in AU, the brightness of the sun relative to Earth, and the amount of solar panels needed to get the same power output relative to earth (assuming of course, that solar panel output behaves linearly with illumination). Atmospheric effects are not accounted for.

+--------------------+-------+----------------+------------+
|                    | AU    | Sun brightness | no. panels |
+--------------------+-------+----------------+------------+
| Mercury perihelion | 0.307 | 10.61          | 0.094      |
+--------------------+-------+----------------+------------+
| Mercury aphelion   | 0.466 | 4.6            | 0.22       |
+--------------------+-------+----------------+------------+
| Venus              | 0.723 | 1.91           | 0.52       |
+--------------------+-------+----------------+------------+
| Earth              | 1     | 1              | 1          |
+--------------------+-------+----------------+------------+
| Mars perihelion    | 1.382 | 0.523          | 1.9        |
+--------------------+-------+----------------+------------+
| Mars aphelion      | 1.666 | 0.36           | 2.78       |
+--------------------+-------+----------------+------------+
| Vesta              | 2.36  | 0.18           | 5.57       |
+--------------------+-------+----------------+------------+
| Ceres              | 2.76  | 0.131          | 7.62       |
+--------------------+-------+----------------+------------+
| Jupiter perihelion | 4.95  | 0.041          | 24.5       |
+--------------------+-------+----------------+------------+
| Jupiter aphelion   | 5.25  | 0.036          | 27.6       |
+--------------------+-------+----------------+------------+
| Saturn perihelion  | 9.04  | 0.012          | 81.7       |
+--------------------+-------+----------------+------------+
| Saturn aphelion    | 10.1  | 0.0098         | 102        |
+--------------------+-------+----------------+------------+
| Uranus             | 19.2  | 0.0027         | 368        |
+--------------------+-------+----------------+------------+
| Neptune            | 30.1  | 0.0011         | 906        |
+--------------------+-------+----------------+------------+
| Pluto perihelion   | 29.65 | 0.0011         | 879        |
+--------------------+-------+----------------+------------+
| Pluto aphelion     | 49.3  | 0.00041        | 2430       |
+--------------------+-------+----------------+------------+
| Eris perihelion    | 38    | 0.00069        | 1440       |
+--------------------+-------+----------------+------------+
| Eris aphelion      | 97.4  | 0.0001         | 9490       |
+--------------------+-------+----------------+------------+
| Sedna perihelion   | 76    | 0.00017        | 5780       |
+--------------------+-------+----------------+------------+
| Sedna aphelion     | 936   | 0.000001100    | 876000     |
+--------------------+-------+----------------+------------+