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http://www.popsci.com/sites/popsci.com/files/styles/medium_1x_/public/import/2014/Hsu%20and%20Horanyi%20Graph%20AJP.png?itok=OSqMRad6

This graph shows the observed trajectory of lunar rover dust particles is roughly the same as in a simulated earth case. However, the earth has 6 times more gravity. Is this an accurate graph?

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    How is that roughly the same? The two earth trajectories average about two meters while the two moon trajectories average around four and a half meters. – phoog Jun 26 '17 at 03:55
  • But with six times more gravity –  Jun 26 '17 at 04:36
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    Yes, that's precisely the point, along with the air resistance. – phoog Jun 26 '17 at 04:49
  • Let me ask you this: in what respect do you find the four trajectories to be the same? Your question does not make that clear. – phoog Jun 26 '17 at 04:53
  • Like not being six times lower under six times more gravity –  Jun 26 '17 at 04:55
  • I think what the authors meant to show with green lines, is a would-be trajectory if Moon had Earth-like atmosphere. Otherwise it certainly looks wrong. – sashkello Jun 26 '17 at 05:49
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    "This graph shows the observed trajectory of lunar rover dust particles is roughly the same as in a simulated earth case." No, it shows precisely the opposite. There is nothing to investigate here. – Oddthinking Jun 26 '17 at 05:53
  • You're misunderstanding what that graph shows. In the important aspect there is a big difference between the curves! Lets examine the smallest curve (Earth simulation.) By eyeball I would say the peak is at about .8 and it falls back to zero at 1.2. Compare this to the biggest curve (Moon simulation.) The peak is at about 2.5, the zero at 5. The moon curve is symmetric, the Earth curve is not. This is what you would expect as drag does not meaningfully act upon the dust particles on the Moon. The Earth curve, however, has the peak at about 2/3 of the distance, not in the middle. This is becaus – Loren Pechtel Jun 26 '17 at 04:28
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    If you were expecting the earth trajectories to not exceed 1/6th of the moon's maximum height / distance, you should make that explicit. This kind of implicit questioning, while rampant on Skeptics, doesn't really help your question. – DevSolar Jun 26 '17 at 08:48
  • @DevSolar: I did consider whether that was his misunderstanding, but then he wouldn't have written this falsehood: "This graph shows the observed trajectory of lunar rover dust particles is roughly the same as in a simulated earth case." – Oddthinking Jun 26 '17 at 08:51
  • This shouldn't be on Skeptics. We have a whole site on Space Exploration. – DJClayworth Jun 26 '17 at 17:23
  • Obviously? Oddthinking –  Jun 27 '17 at 01:06
  • OK, so, I've looked at the paper and my comment is correct: With green lines the authors are showing the trajectories for particles with initial velocity such that without drag they would reach same distance on Earth. So, the plot serves to illustrate air resistance impact, in otherwise equivalent conditions. – sashkello Jun 27 '17 at 05:48

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I traced the graph to this paper by Hsiang-Wen Hsu and Hsiang-Wen Hsua at University of Colorado Boulder. It was published in 2012 in American Journal of Physics.

The paper is behind a paywall so I can not link to it, but I read it and it appears correct.

The authors watched video from the Apollo Moon walks looking for certain frames in which dust was kicked up by the buggy. Using those frames they measured how high and how far the dust went - that's the blue squares on the plot. This is possible because they know the frame rate and resolution of the video footage. Using the wheel of the rover as an yard stick (16 inch wheel), they can convert pixel sized to meters. Time is also know from the frame rate.

Using ballistic motion equations and accounting for linear drag they calculated 4 trajectories - 2 with Earth gravity (green dashed lines), 1 dust trajectory from the data they extracted from the video and 1 expected Moon trajectory using the actual moon gravitational constant.

Here is the paper's summary:

We have analyzed the motion of the dust clouds lofted by the Lunar Roving Vehicle of the Apollo 16 mission. Adopting a simple 2D geometry, we found that the dust followed ballistic trajectories under the influence of the lunar gravity. The gravitational constant of the moon derived from the dust trajectory is within 10% of the expected value. The images used in our analysis are available online for use as supplementary material in physics education.

ventsyv
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  • So is it legitimate –  Jun 26 '17 at 04:35
  • @James Yes, and the blue dots (the data) follow the predicted plot for the trajectory on the moon (the block line). They are about as far away from the predicted plot for Earth (the green dashed line) as they can get. How did you look at that graph and come to the opposite conclusion? – Kevin Fee Jun 26 '17 at 15:39
  • Are they six times lower in six times more gravity –  Jun 27 '17 at 01:07
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    That cannot be determined from this research. The Earth simulations appear to attempt the same initial trajectory and velocity as the observed Moon particles. Gravity isn't being investigated here - they're looking into the effects of atmospheric drag, not differing gravities. – ceejayoz Jun 28 '17 at 02:50