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Does cumulative mass of Mercury, Venus, Earth's moon and Mars total 99% of Earth's mass ?

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    $\begingroup$ Show your sources and your work. That'll make a better question. $\endgroup$
    – RonJohn
    Apr 23, 2023 at 5:10
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    $\begingroup$ it would certainly be close - Venus is a bit lighter than Earth and the rest are basically loose change. Before getting too golden ration on the topic you need to work out how the moon's formation as an ejected chunk of earth fits into things. $\endgroup$ Apr 23, 2023 at 5:28
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    $\begingroup$ This page ssd.jpl.nasa.gov/astro_par.html has planetary system masses in the form of GM (gravitational parameter), which is known to much higher precision than the mass. $\endgroup$
    – PM 2Ring
    Apr 23, 2023 at 13:05
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    $\begingroup$ Interesting related fact: If you just look at planets, each one is larger than all the smaller ones combined, and Earth is actually the one where that comes closest to being false. This is because Venus is so massive relative to Earth. When you look at all bodies ordered by mass, that pattern no longer holds, as other answers and your own calculation indicate. $\endgroup$ Apr 23, 2023 at 18:59
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    $\begingroup$ I, for one, welcome the human desire to find meaning in coincidence. I hadn't considered this kind of question before and had fun my writing my sort-of-related answer, so I've upvoted. Welcome to Space SE! $\endgroup$
    – Erin Anne
    Apr 24, 2023 at 2:45

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According to Wolfram Alpha, your calculation is correct. (The masses of Phobos and Deimos are negligible here.)

It's not a particularly remarkable coincidence; glancing at a list of solar system bodies ordered by mass, it didn't take me long to find that the mass of Mercury is 99.8% of the combined masses of Ganymede, Titan, and Europa.

Screen shot of Wolfram Alpha, showing the sum of the masses of Mercury, Venus, the Moon, and Mars is 5.91 x 10^24 kg, or 0.99 Earth masses

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    $\begingroup$ "(The masses of Phobos and Deimos are negligible here.)": in fact, adding the entire asteroid belt makes virtually no difference. Occasionally someone suggests dropping asteroids on Mars to add to its gravity, but all the asteroids together are only a few percent of the mass of the moon. $\endgroup$ Apr 23, 2023 at 17:34
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Russell Borogove's answer got me wondering how one might best successively approximate the mass of the Earth by using other solar system bodies (say, if you wanted to balance a scale). My every interaction with Wolfram Alpha causes it to choke so I've instead referred to Wikipedia's List of Solar System objects by size.

Venus, Mars, and Mercury are good first choices; they're the next three-most-massive bodies in the solar system. Those alone get you 97% of the way there.

The next choices are critical.

  • Adding Titan seems to put you slightly over (don't make the same mistake I did; the precision of the table in Earth masses is slightly lower, so stick with the $10^{21} \text{kg}$ column).

  • Adding the Moon instead leaves you at about 0.99 of Earth's mass, as the OP indicates.

  • Instead adding Callisto, Triton, and Haumea seems to put you just under an Earth mass, with the error bars overlapping those of Earth's mass as given in the table.

Link to the spreadsheet where I played with the numbers

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    $\begingroup$ Per PM 2Ring's comment on the question this would be significantly improved by using $\mu$ or GM for the bodies, because part of my motivation was approximating Earth's mass to within our current measurements. $\endgroup$
    – Erin Anne
    Apr 24, 2023 at 2:48
  • $\begingroup$ How about adding in Planet 9;) $\endgroup$ Apr 24, 2023 at 18:22
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Using the gravitational parameters of JPL: DE430/431 (the most accurate I could find), the discrepancy between the cumulative sum and the mass of the Earth is about five magnitudes higher than the uncertainty, so this clearly checks out.

 22.03178E+12     Mercury
324.858592E+12     Venus
  4.902800066E+12  Moon
 42.828375214E+12  Mars

394.621547280E+12  Sum

398.600435436E+12  Earth

The ratio is thus indeed very close to 99%, 0.9900179

The similarity is a bit less striking when one considers that the missing mass is about 80% of a Moon mass.

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    $\begingroup$ Pluto is about 17.7 % of a Moon mass, the total mass of the asteroid belt is calculated to be 3% that of the Moon. The mass of Eris is 22.4 %, Haumea is about 5.5 %, Makemake 4.2 %, Gonggong 2.4 %, Quaoar 1.9 % and Sedna about 1 %. Together about 58 % of the Moon. So still 22 % missing. $\endgroup$
    – Uwe
    Apr 24, 2023 at 9:29
  • $\begingroup$ The GM values I linked in my 1st comment on the question come from DE 440. Horizons body data has GM for numerous bodies, including many of the larger asteroids, eg, here's Vesta, but they aren't of high precision, and the Horizons docs are rather vague on the sources for the body data pages. $\endgroup$
    – PM 2Ring
    Apr 24, 2023 at 9:55
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    $\begingroup$ But if we also look at the moons of the gas giants, we get Ganymede 202 %, Titan 183%, Callisto 146 % and Io 122 % of the Earth's Moon. $\endgroup$
    – Uwe
    Apr 24, 2023 at 10:53
  • $\begingroup$ What units are these masses in? $\endgroup$ Apr 25, 2023 at 18:54
  • $\begingroup$ @JasonGoemaat They're GM values, in units of $m^3/s^2$. See en.wikipedia.org/wiki/Standard_gravitational_parameter $\endgroup$
    – PM 2Ring
    Apr 25, 2023 at 19:41

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