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I would like to know where on Mars the least lowest daily temperatures depending on the time of year will be.
At first glance one might think, as I did, that it has to be along its equator, but because the intensity of the solar radiation varies from 492 W/m² at aphelion to 715 W/m² at perihelion and aphelion happens in northern summer, the northern latitudes at about 20⁰ will probably have the least lowest daily temperatures.

But to know the local temperatures varying with latitude and time of year the first thing one needs is the daily incoming global solar radiation.
Of course there are other factors that also determine the surface temperature, like local albedo and the atmosphere, but this calculation will be the first and most important step.

Question:
What will be the calculation for the local maximum solar radiation from day to day, throughout the martian year ?

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The solar radiation can be calculated knowing the distance from the Sun, the subsolar latitude, and the latitude of the place of interest. Knowing those three values, the calculation would be as follows:

$$ I_{solar} \approx = 717 \ \text{W/m}^2 \left(\frac{1.38138027 \text{AU}}{r}\right)^2 \cos(lat -lat_{ss})$$

where $lat_{ss}$ is the sub-solar latitude.

The term $(1.38138027 \text{AU}/r)^2$ corrects for the distance, and the cosine term corrects for the zenith angle of the sun; that is, how close the Sun passes to the zenith from the observing location.

The values can be obtained from the JPL Horizons website using output quantities of 15 (subsolar latitude) and 19 (distance from the Sun).

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  • $\begingroup$ Sorry for the confusion and the deletion of former comments. Your answer is not wrong i think, but I ask for a time dependent equation (radiation intensity from day to day, depending on the distance from the Sun). $\endgroup$ – Cornelis Aug 12 '20 at 17:16
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    $\begingroup$ @Cornelisinspace. Yes, step 1 is to calculate the position of Mars from the orbital parameters. Do you want to do that? Or use a website to get representative numbers? (Step 1 is an entire question and answer in itself.) Step 2 is to compute the subsolar point, or the "declination" of the Sun as seen from Mars. That is another series of equations. Then step 3 is what I provide. There may be a simple series of equations that approximate both of those, with only 1 or 2 dozen terms in them. I will see what I can find. $\endgroup$ – JohnHoltz Aug 12 '20 at 21:16
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    $\begingroup$ The pdf titled "Accurate analytic representations of solar time and seasons on Mars with applications to the Pathfinder/Surveyor missions" located at agupubs.onlinelibrary.wiley.com/doi/pdfdirect/10.1029/97GL01950 gives the equation for the distance r (in my equation, rm in the PDF) and subsolar point (declination in the PDF), and only requires 5 equations, and 29 terms. Not bad! Plus the calculation of the date from J2000, so more equations and terms. $\endgroup$ – JohnHoltz Aug 12 '20 at 21:23
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    $\begingroup$ @uhoh The numerical values are for the moment when Mars is at perihelion. If you use the JPL Horizons website with output quantities 15 and 19 you can find that on June 22, 2022 the distance from Mars to the Sun is 1.3813 AU, and the 717 W/m² is at the object data page. $\endgroup$ – Cornelis Aug 15 '20 at 8:44
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    $\begingroup$ @Cornelisinspace ah, okay I got it now, thanks! $\endgroup$ – uhoh Aug 15 '20 at 8:45
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This is a supplement to the accepted answer from @JohnHoltz to show an example of the maximum solar radiation in Jezero crater (18.38⁰N) throughout a full martian year.

Feb. 18, 2021 (planned landing date Perseverance): r = 1.57021553, lat.= 2.243093 -------------------------------->......................................................717 x 0.773941 x cos(18.38 - 2.243093)⁰ = 533 W/m².
May 19, 2021 (the Sun is at the zenith in Jezero crater): r = 1.65106961, lat. = 18.341973 -------------------------> .. ................................................717 x 0.836657 x cos(18.38 - 18.341973)⁰ = 502 W/m².
July 13, 2021 (Mars is at aphelion): r = 1.66595504, lat. = 24.008276 ---------------------------------------------------> ....................................................717 x 0.687543 x cos(18.38 - 24.008276)⁰ = 475 W/m².
Aug. 25, 2021 (northern summer solstice): r = 1.65683720, lat. = 25.456249 ------------------------------------------> ....................................................717 x 0.695131 x cos(18.38 - 25.456249)⁰ = 495 W/m².
Nov. 26, 2021 (the Sun is at the zenith again): r = 1.58079433, lat. = 18.433113 -------------------------------------> ....................................................717 x 0.763617 x cos(18.38 - 18.433113)⁰ = 547 W/m². Feb. 24, 2022 (fall equinox): r = 1.46695298, lat. = 0.143556 ---------------------------------------------------------------> .....................................................717 x 0.886735 x cos(18.38 - 0.143556)⁰ = 604 W/m².
June 22, 2022 (Mars is at perihelion): r = 1.38130590, lat. = -24.056784 -----------------------------------------------> ...................................................717 x 1.000108 x cos(18.38 + 24.056784)⁰ = 529 W/m².
Juli 21, 2022 (winter solstice): r = 1.38752975, lat. = -25.456143 --------------------------------------------------------->....................................................717 x 0.991156 x cos(18.38 + 25.456143)⁰ = 513 W/m².
Dec. 26, 2022 (spring equinox): r = 1.55688141, lat. = -0.093208 --------------------------------------------------------->......................................................717 x 0.787255 x cos(18.38 + 0.093208)⁰ = 535 W/m².

So based on these results only, despite Jezero crater being well north of the equator, wintertime would be warmer there than summertime !

For comparison, some results throughout a year for Gale crater (5.4⁰S).

Juli 13, 2021 (Mars is at aphelion):............. 429 W/m².
Aug. 25, 2021 (northern summer solstice):. 428 W/m².
Feb. 24, 2022 (northern fall equinox):..........633 W/m².
June 22, 2022 (Mars is at perihelion):......... 679 W/m².
Juli 21, 2022 (northern winter solstice):.......667 W/m².
Dec. 26, 2022 (northern spring equinox):.....562 W/m².

And here are the results for McLaughlin Crater (21.9⁰N), once considered a candidate landing site.

Juli 13, 2021 (Mars is at aphelion):............. 493 W/m².
Aug. 25, 2021 (summer solstice):................ 497 W/m².
Feb. 24, 2022 (fall equinox):.........................590 W/m².
June 22, 2022 (Mars is at perihelion):..........498 W/m².
Juli 21, 2022 (winter solstice):......................481 W/m².
Dec. 26, 2022 (spring equinox):....................523 W/m².

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  • $\begingroup$ Would not goiing underwater be the best practical solution for the main problems facing a settlement on Mars ? $\endgroup$ – Cornelis Oct 9 '20 at 14:52

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