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Does anyone recognize the equation carved on this object?

The only hint I have is that the back side has the word "orbit" carved into it.

It may be incomplete or incorrectly copied.

enter image description here

My best interpretation in MathJax:

$U_eR_o\sqrt{\frac{2g}{(R_ôh)}}$

My grandmother carved the object. She had a hobby of carving small figures and objects out of blackboard chalk. She made (among other things) chess figures and a scene with her brother posing with his new car.

This figure was presumably carved during the space race in the 1960s.

Grandmother was a grade school teacher, so I'm pretty sure she didn't understand it and just copied it from a magazine or newspaper article.

JRE
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  • It seems to read: $v_e R_o \sqrt{2g / (R_o \frac{1}{2})}$, if that helps anyone. Doesn't immediately ring a bell. – Ludo Oct 22 '22 at 22:06
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    @Ludo: It looks more like Rôh to me. – JRE Oct 22 '22 at 22:12
  • Agreed, "oh with a hat". – Organic Marble Oct 22 '22 at 22:22
  • Maybe some kind of energy equation. U means internal energy to me, and g & h are related to potential energy. The rest I don't know. – Organic Marble Oct 22 '22 at 22:35
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    I'm getting a whiff of escape velocity $v_e = \sqrt{2\mu/r}$ but that's obviously not all of it – Erin Anne Oct 22 '22 at 23:16
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    I'm seeing that "g" as more of a greek small case rho ($\rho$ or ϱ from here). Looks a bit like this stuff which of course is related to escape velocity as well. We should use dimensional analysis here. Also, this depends on $R^{3/2}$ so look for things that have a 3/2 power law dependence. Sorry not much help. – uhoh Oct 23 '22 at 03:30
  • different but similar: What does S represent in Chris Hadfield's D = ½ ρ v² S? – uhoh Jun 11 '23 at 21:58
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    Note that it may be that the part starting with $R_0\sqrt{}\dots$ may actually be an exponent of $e$... all kinds of rocket related equations have exponential relations, that may give someone a clue. Why the $U$ that precedes that looks to be above the $e$ may just be another indication that it was copied without being fully understood... – Amit Jun 11 '23 at 23:25
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    Another possible direction: Ion thrusters... electric potential energy is many times denoted $U_e$... and perhaps we are missing an equals sign to the right of it? Perhaps this is supposed to be the electric potential energy of an ion thruster... or it is some expression where it is involved... either way, square roots of 2 also very often occurs in related expressions... see for example here, look for "ion exit velocity". – Amit Jun 12 '23 at 21:14
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    Btw, this also makes it more likely a $\rho$ rather than a $g$, that is, charge density perhaps. – Amit Jun 12 '23 at 21:17
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    Re - what @uhoh said, Child's law has application in plasma physics and has a $3/2$ power in it – Amit Jun 15 '23 at 23:31
  • for a moment I thought it might be something like this https://youtu.be/bc-OoJrrMuk – uhoh Jul 15 '23 at 04:54

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