The mystery of planet 1 – Mercury dropping fast

Posted: February 7, 2012 by tallbloke in Astronomy, Astrophysics, Energy

Over on our discussion of the mysterious planet Neptune, Talkshop contributor ‘Anything is Possible’ put up a comment noting a serious inconsistency regarding Wikipedia’s entry on the planet Mercury concerning surface temperature.

Anything is possiblesays:

Hey, everyone check this out :

http://en.wikipedia.org/wiki/Mercury_(planet)

Compare the average surface temperatures given in the text :

“The mean surface temperature of Mercury is 442.5 K,[3] but it ranges from 100 K to 700 K”

with those given in the table )top RHS) :

Surface temperature
lat long min mean max
0°N 0°W 100K 340K 700K
85°N 0°W 80K 200K 380K

Explanations, anyone?

How the heck can Mercury have a “mean surface temperature of 442.5K” (a figure that has achieved wide, unthinking acceptance), when the mean temperature is 340K at the equator, and 200K at the poles?

Clearly, it can’t. Either the figures in the table are incorrect, or the figure in the text is.

If it is the latter, that represents further empirical evidence that N & Z’s application of the SB-law is far more accurate than the traditional one adopted by greenhouse theorists……

Good catch AiP! I have started a promising discussion on the talk page of Wikipedia’s entry for the planet Mercury:

Temperature

The info panel on the right of the page says the average surface temperature varies from 340K at the equator to 200K at the poles, but the main text says the overall average surface temperature is 442.5K. This is not physically possible. — Preceding comment added by tallbloke (talk) 21:49, 6 February 2012 (UTC)

Yes, I have no idea where the temperatures in the infobox come from. They need better referencing. Regards, RJH (talk) 22:21, 6 February 2012 (UTC)

Thanks. It may be that the info panel is correct and NASA’s figure is wrong. Stefan-Boltzmann has been badly misapplied to hemispheres. See https://tallbloke.files.wordpress.com/2012/01/utc_blog_reply_part-1.pdf — Preceding  comment added by tallbloke (talk) 09:19, 7 February 2012 (UTC)

While the blog apparently isn’t peer reviewed, I think the argument is strong enough to remove the inconsistent 442.5K figure from the text.agr (talk) 16:25, 7 February 2012 (UTC)

It’s only inconsistent if we have a valid reference for the infobox data. Do we? (They seem also to contradict the value of 167K maximum “on the polar plains” given (and referenced) in Geology of Mercury, and the 90K minimum claimed in the lede.) —Roentgenium111 (talk) 17:12, 7 February 2012 (UTC)

I found this, but I haven’t had a chance to check the references it cites. —agr (talk) 18:36, 7 February 2012 (UTC)

Watch this space for further updates as the discussion progresses. 🙂

Comments
  1. tallbloke says:

    Maybe this could be the start of a ‘Domino effect’. 🙂

  2. Zeke says:

    That is Venus. (:

  3. Michael Hart says:

    Don’t forget all that Holder’s-inequality stuff wrt the S-B radiation laws. I think there’s more than two ways to dice this carrot. Before making a judgement, I would want to see how this average is calculated. Is it “area-averaged” or “time-averaged [day/night/season]”, or “both”? My maths is somewhat rusty, but I think that the ‘algorithms’ may not exhibit commutativity?

    I have also just read this:
    “Extraterrestrial seasons are hardly noticeable on some planets (Venus), mindbogglingly extreme on others (Uranus) and in some cases simply impossible to define (Mercury).”
    at:
    http://science.nasa.gov/science-news/science-at-nasa/2000/interplanetaryseasons/

  4. tallbloke says:

    Informative write up about the Messenger mission here. Silent on temperature though:
    http://www.eurekalert.org/pub_releases/2011-09/ci-mnl092911.php

  5. Bill Norton says:

    Two-hemisphere model for Mercury:

    Mercury Teff = 433.8K

    MST: 307.8 to 433.8 for Tcold: 100 to 433.8K

    Read in six columns: Etot; Tcold; Ecold; Ehot; Thot; Tavg(MST)
    Ex = Energy(total surface, or cold hemisphere, or hot hemisphere)

    
       Etot       Tc      Ecold       Ehot      Thot    Tavg(MST)
    1.50191E+11   100   2.121E+08   1.500E+11   515.7   307.8
    1.50191E+11   125   5.178E+08   1.497E+11   515.4   320.2
    1.50191E+11   150   1.074E+09   1.491E+11   514.9   332.5
    1.50191E+11   175   1.989E+09   1.482E+11   514.2   344.6
    1.50191E+11   200   3.393E+09   1.468E+11   512.9   356.5
    1.50191E+11   225   5.435E+09   1.448E+11   511.1   368.1
    1.50191E+11   250   8.284E+09   1.419E+11   508.6   379.3
    1.50191E+11   255   8.967E+09   1.412E+11   508.0   381.5
    1.50191E+11   300   1.718E+10   1.330E+11   500.4   400.2
    1.50191E+11   350   3.182E+10   1.184E+11   486.1   418.0
    1.50191E+11   400   5.429E+10   9.590E+10   461.1   430.6
    1.50191E+11   433.8 7.510E+10   7.510E+10   433.8   433.8
    
    

    My Teff is 433.8K vice 442.5K, using 2007.9 avg W/m^2 from

    http://bartonpaullevenson.com/Albedos.html

    Cheers,
    Bill

  6. Bill Norton says:

    Still can’t get the column headers to line up… my

     <pre> fu is still weak. 

    Cheers,
    Bill

    [ co-mod, engineers are lazy so they invent things, go back to lazy,

    twiddle twiddle in ANSI C, okay, using mouse select your table, copy to clipboard, execute new program, edit comment, paste clipboard, have to go and see what if any improvements WordPress allows, and whether I am too lazy, next problem is how to invoke here, hotkey will probably do, don’t do GUI these days

    Etot Tc Ecold Ehot Thot Tavg(MST)
    1.50191E+11 100 2.121E+08 1.500E+11 515.7 307.8
    1.50191E+11 125 5.178E+08 1.497E+11 515.4 320.2
    1.50191E+11 150 1.074E+09 1.491E+11 514.9 332.5
    1.50191E+11 175 1.989E+09 1.482E+11 514.2 344.6
    1.50191E+11 200 3.393E+09 1.468E+11 512.9 356.5
    1.50191E+11 225 5.435E+09 1.448E+11 511.1 368.1
    1.50191E+11 250 8.284E+09 1.419E+11 508.6 379.3
    1.50191E+11 255 8.967E+09 1.412E+11 508.0 381.5
    1.50191E+11 300 1.718E+10 1.330E+11 500.4 400.2
    1.50191E+11 350 3.182E+10 1.184E+11 486.1 418.0
    1.50191E+11 400 5.429E+10 9.590E+10 461.1 430.6
    1.50191E+11 433.8 7.510E+10 7.510E+10 433.8 433.8

    –Tim]

  7. B_Happy says:

    Given that a point on the surface of Mercury will spend one “year” (88 Earth days) pointing towards the sun and the next year pointing away from the sun, then the concept of “average temperature” is probably not very meaningful.

    You can find a little cartoon of the orbit of Mercury on this page : http://www.allaboutspace.com/subjects/astronomy/planets/mercury/mercuryday.shtml

  8. tallbloke says:

    Bill N: Thanks. As far as I can see, BPL is using the ‘classical’ method of applying the S-B law, which N&Z say is wrong. See their ‘reply to comments part 1’ paper. Even Joel Shore accepts they re right about this. 🙂
    https://tallbloke.files.wordpress.com/2012/01/utc_blog_reply_part-1.pdf
    To get your column headers to line up, make the header items the same length as the items. i.e

    ___Etot____
    1.50191E+11

    use underscores either side of the label.

    B Happy: 2/3 of a year to be exact. Mercury spins thrice for each two orbits of the Sun.

  9. B_Happy says:

    “Mercury spins thrice for each two orbits of the Sun.”

    Yes, it does, but I suggest you look at the illustration in the link I gave and you will see that what I said is correct – it is to do with the difference between sidereal and solar days. For a given point on the surface sunrise to sunset takes one Mercury year, then sunset to sunrise takes the next year.

    [Reply] Quite right. Thanks.

  10. tallbloke says:

    Hmmm, reading a bit further into this, there’s an interesting timing connection between Mercury and Earth:

    For many years it was thought that Mercury was synchronously tidally locked with the Sun, rotating once for each orbit and always keeping the same face directed towards the Sun, in the same way that the same side of the Moon always faces the Earth. Radar observations in 1965 proved that the planet has a 3:2 spin–orbit resonance, rotating three times for every two revolutions around the Sun; the eccentricity of Mercury’s orbit makes this resonance stable—at perihelion, when the solar tide is strongest, the Sun is nearly still in Mercury’s sky.[76]

    The original reason astronomers thought it was synchronously locked was that, whenever Mercury was best placed for observation, it was always nearly at the same point in its 3:2 resonance, hence showing the same face. This is because, coincidentally, Mercury’s rotation period is almost exactly half of its synodic period with respect to Earth. Due to Mercury’s 3:2 spin–orbit resonance, a solar day (the length between two meridian transits of the Sun) lasts about 176 Earth days.[18] A sidereal day (the period of rotation) lasts about 58.7 Earth days.[18]

  11. adolfogiurfa says:

    There will be “mysteries” and surprises everywhere until the current paradigm does not change.
    Mercury´s orbit has an also a “surprising” high eccentricity:
    Mercury:0.21
    Venus: 0.01
    Earth:0.02
    Mars:0.09
    Jupiter:0.05
    Saturn:0.06
    Uranus: 0.05
    Neptune: 0.01
    So it “oscillates” more, to say the least. (more “energy”?)
    And Mercury´s sodium tail:

  12. adolfogiurfa says:

    @Tallbloke: Radar observations in 1965 proved that the planet has a 3:2 spin–orbit resonance
    Or: 2:3, (2/3:0.6666; Planck´s constant: 0.66252 – presumably affected by Earth´s field-) a “perfect fifth”:

  13. tallbloke says:

    @ Adolfo

    Interesting that the planets with the highest eccentricities are those with the least atmosphere..

  14. adolfogiurfa says:

    @Tallbloke: You should teach us about that “Music of the Spheres”, as you know a lot more of those relations (I know nothing really, but I dare because of that).

  15. Anything is possible says:

    Thanks for following this up, TB :

    Latest update :

    This reference from the blog might do: http://www.gps.caltech.edu/classes/ge151/references/vasavada_et_al_1999.pdf , however it makes the point that the temperature a few centimeters below the surface experiences much smaller temperature swings and converges to a constant, year round level, well above the mean surface temperature, at less than a meter depth. This was measured on the moon by the ALSEP experiments on Apollo 15 and 17. So just reporting surface temp may be misleading.–agr (talk) 16:34, 9 February 2012 (UTC)

  16. Anything is possible says:

    The text on surface temperature on the wikipedia Mercury page has been amended, and now reads thus :

    “The surface temperature of Mercury ranges from 100 K to 700 K[49] due to the absence of an atmosphere and a steep temperature gradient between the equator and the poles. The subsolar point reaches about 700 K during perihelion then drops to 550 K at aphelion.[50] On the dark side of the planet, temperatures average 110 K.[51] The intensity of sunlight on Mercury’s surface ranges between 4.59 and 10.61 times the solar constant (1,370 W·m−2).[52]”

    http://en.wikipedia.org/wiki/Mercury_(planet)

    The system works!!!!

  17. tallbloke says:

    Good result! Did you take a look at the talk page?

  18. […] temperature of airless celestial bodies. The same discrepancy has been noted on Mercury, and after a bit of prompting from the Talkshop, Wikipedia has removed the mis-estimate generated by the mis-application of the S-B law from […]

  19. Anything is possible,

    Here are my temperature estimates for the temperature at Mercury’s equator after making a few assumptions:
    1. Mercury’s regolith has the same thermal properties as the Moon’s.
    2. The rate of rotation has no effect on average temperature (Mercury day = 176 Earth days).
    3. Mercury’s bedrock is basalt at a temperature of 300 Kelvin.

    Aphelion minimum = 100 Kelvin
    Aphelion maximum = 570 Kelvin
    Perihelion minimum = 100 Kelvin
    Perihelion maximum = 695 Kelvin

    Mercury’s orbit has significant eccentricity so average temperatures (Equator) range from 335 to 380 Kelvin. I don’t give any credence to 442.5 Kelvin average challenged above.

  20. adolfogiurfa, February 8, 2012 at 5:04 pm,

    The huge eccentricity in Mercury’s orbit suggests that it was captured while the others accreted in their present positions.

  21. tallbloke says:

    GC: It’s possible that Mercury is an escaped moon of Venus
    https://tallbloke.wordpress.com/2013/04/04/tom-van-flandern-was-the-planet-mercury-once-a-moon-of-venus/
    So the capture theory is probably right.

    The temperature discussion has been vanished from the talk page. Now archived here
    http://en.wikipedia.org/wiki/Talk:Mercury_(planet)/Archive_2#Edit_request_on_13_February_2012
    Final addition was:
    I’ve added the reference to the article. I’d also like to add the actual pole’s temperature (180 K max.), but this doesn’t seem to work with the infobox’s code. Interestingly, temperatures in Mercury’s polar regions are constantly below a comfortable 310 K (37° C) from about 87°N 0°W and 85°N 90°W northward, according to Figure 5… –Roentgenium111 (talk) 21:40, 18 February 2012 (UTC)

    Mercury’s orbit has significant eccentricity so average temperatures (Equator) range from 335 to 380 Kelvin

    ~358K average for the equator then. If the dropoff to the poles is similar in character to the moon, we might expect a surface Tmean around 340K, over 100K lower than the figure originally given at wikipedia!

    I’d like to enquire at wiki why the temperature discussion was removed, so please could you write up your model so I can reference it? Thanks.

  22. oldbrew says:

    Re: ‘The mean surface temperature of Mercury is 442.5 K’

    An ‘old’ version of the wiki Mercury atmosphere page says:
    ‘during the day Mercury’s surface reaches a temperature of 420°C, while at night it dips to –180°C’

    http://web.archive.org/web/20080131111643/http://en.wikipedia.org/wiki/Atmosphere_of_Mercury#Temperature

    The current version doesn’t have a separate ‘temperature’ section, but says:
    ‘The temperature of the Mercurian exosphere depends on species as well as geographical location.’

    http://en.wikipedia.org/wiki/Atmosphere_of_Mercury#Properties

  23. I refined the precision of the Mercury calculations using two different temperatures for the basalt assumed to lie immediately below the regolith.

    Aphelion Tmax = 565.3 K (Tbase = 300 K). Add 0.1 K (Tbase = 350 K)
    Aphelion Tmin = 102.4 K (Tbase = 300 K). Add 5.4 K (Tbase = 350 K)

    Perihelion Tmax = 696.5 K (Tbase = 300 K). Add 0.1 K (Tbase = 350 K)
    Perihelion Tmin = 102.4 K (Tbase = 300 K). Add 5.4 K (Tbase = 350 K)

  24. Anything is possible says:

    @gc

    Many thanks!