Ah, is there anything more wonderful than being locked in the warm embrace of someone you love? The emotion, the beauty of the moment, the attraction you feel… but wait! Is that pull you feel really from your Significant Other, or is it due to… the Moon?
Just how strong is the gravity from the Moon compared to someone right next to you?
Well, listen to Q & BA Episode 4: "The Gravity of the Situation" and find out!
Viewing options:
Watch it right here, right now!
Download it directly from LibSyn.
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Show notes
The Question:
The question was sent in by Jesse C. of Doylestown, PA: "Does a person standing beside you have a greater gravitational pull on you than the Moon? I recently heard someone mention it. It sounds like a bunch of malarkey… but is it true?"
If you want to the calculations for yourself, then start with
where lower case m is your mass, upper case M is the mass of the object (the Moon, the other person, etc.), R is the distance between the two of you, and G is a constant. When you divide the force from the Moon by the force from the person, your mass and the constant divide out (your mass divided by your mass = 1). For the masses of the planets and such, go to The Nine Planets.
Images:
Mu Cephei is from Davide De Martin’s Sky Factory
Eta Carinae is from NASA/Hubble/AURA.
The Sun and Earth are from NASA (the Earth shot is from the fantabulous MESSENGER Earth flyby).
The pictures of the Flatiron/Rocky Mountains and of me fishing in Kansas are courtesy of, um, me.
And since I know people will ask: The T-shirt is available from the FSM website.
… and one more link. Guess why?
February 25th, 2007 at 9:51 pm
I like the Skepdude Calendar in the background. I always look forward to seeing what is going to be sitting there.
I found this episiode to be really interesting. That was a great question! My first response to the question was, “Of course the person has a bigger pull,” then actually thinking about it, it makes more sense that it’s the other way around. After all, the moon does have an effect on the tides.
Great show, once again. I look forward to these videos, for the info, the humor, and whatever is going to be on the table.
Just a note, I subscribed in iTunes, and I think the quality there is a lot better than youtube. I’ve also noticed that the videos appear there before they do here, haha.
February 25th, 2007 at 11:38 pm
another great video Phil.
You really should do more educational programing on a good educational channel like Discovery (TLC doesn’t count since they started doing home reno and make over shows all the time).
February 26th, 2007 at 1:23 am
no no no, you’re getting away with this too easily. The proper theory to use is General Relativity of course. And as Einstein was well aware, people do not distort space-time the same way starts or planets or moons do: “Sit with a beautiful girl for two hours and it seems like two minutes. That’s relativity”. I looked at the moon for two hours, and it really felt like two hours.
February 26th, 2007 at 2:02 am
I think that there’s another possible issue: tidal forces. After all, the gravitational influence doesn’t really affect you — you and the Earth together are essentially freely falling around the moon, right?
So, how about the tidal forces? They’re 1/R^3 so now the person (millions of times closer) easily wins over the Moon. And maybe the OB beats the Rocky Mountains, too.
February 26th, 2007 at 5:28 am
An esoteric group invited me once to talk about the moon in one of the their meetings. Beautiful place, beautiful moonshine night, interesting people. But they were a bit upset when I said the gravitational and “atomic radiation” influence of mountains were a lot bigger than the Moon’s.
Joshua have a good point about the tidal force. It is more complicated because there have to be a differential distance with respect to the center of the Earth (Moon, Sun, Jupiter etc) and the direction matters.
Thus, a person in top of another would “feel” Earth’s tidal force but not side by side. But then, gravity is not a big issue in those moments. [;)]
February 26th, 2007 at 5:56 am
Thanks, Phil, now I know of a great problem to give my students this spring when we cover gravity! And something else to think about when I’m in labor this spring.
Just a note, the sound synchronization is a bit off from the video on the version you have above.
February 26th, 2007 at 7:22 am
2 things:
First, Josh Zucker makes a good point that if you’re in free fall around an object, then you only feel tidal forces. For instance, the sun’s gravitational field causes us to accelerate towards it. But it causes our head, and our arms, and our feet, and the floor under us, and the furniture around us to accelerate towards it at almost exactly the same rates. We, and everything around us are in free fall around the sun, so by the equivalence principle, we don’t observe any change in nearby physics. This picture gets modified somewhat because there are minute differences in the strength of the sun’s gravitational field between our head and our feet. These differences cause some parts of us to accelerate at different rates than other parts, and we effectively feel tidal forces, which as Josh noted go as 1/R^3, and are quite small. The only objects we aren’t in free fall around are the earth and the obstetrician (in both cases, the floor is providing the opposing force), so their effects go as 1/R^2.
The other thing I wanted to mention is less important: calculating a gravitational field using GM/R^2, where R is the distance to the center of mass only works for far-away objects (when the distance to the object is much greater than the size of the object), or for spherically symmetric objects. Strictly speaking, to get the gravitational field from a human, you have to sum up all the little fields from each part of the human. This is complicated, but here’s a quick estimate of the size of the effect:
When you’re very close to a human, they look more like a cylinder than a sphere, so their gravitational field goes like 1/R (where R is the distance to the axis of the cylinder — the line running from the top of your head to the bottom of your feet). As your distance becomes greater than the person’s height, they look more like a sphere, and the gravitational field begins to drop off as 1/R^2. The dimensional quantity that sets the scale for this change is the person’s height, h, so the gravitational field will probably look something like
1/R(R+h)
which is about 1/Rh when R is small, and more like 1/R^2 when R is big. Regardless, 1/Rh is the relevant law for two people who are close together. Since a person’s height is about 10 times their width (which is what Phil used in the 1/R^2 law), Phil probably overestimated a nearby person’s gravitational pull by about a factor of 10.
February 26th, 2007 at 7:24 am
I haven’t seen the video yet (being at work), but I made an interesting calculation:
To feel the same pull as the moon, you’d need to be touching a 30m diameter sphere of iron.
Math involved:
Mass of iron sphere = (mass of moon) * (distance to center of iron sphere)^2 / (distance of moon)^2
Mass of iron sphere = 4/3*pi*(radius of iron sphere)^3 * 7860 kg/cubic meter (density of iron)
Solved for when distance to center of sphere is equal to radius of sphere.
I’m not taking into account that parts of the sphere are nearer than other parts. I’d need to re-study integral calculus for that. Not just now.
February 26th, 2007 at 7:26 am
I suspect it’s not actually quite 1/r^2 because a person is not a spherical body (except in certain special cases…). It’d probably approximate to a lower power of r (given that that’s what an infinite wire or infinite sheet would be) so the person would lose even more though.
February 26th, 2007 at 7:27 am
And I clearly spent too long writing that, as did ioresult who had his bit about spheres answered just before he posted.
February 26th, 2007 at 7:29 am
David SD, thanks.
Disregard my last paragraph about integral calculus! heh heh
February 26th, 2007 at 7:30 am
And thanks atr also. These posts are arriving at great speed!
February 26th, 2007 at 9:45 am
It’s generally much easier to consider a gravitational acceleration as coming from a point source. ie, consider earth as a singularity with the center of mass 6400km below your feet. That produces an acceleration of 9.8 meters/sec/sec at your feet.
Much easier to do these calcs. from this point of view,,,
GAry 7
February 26th, 2007 at 11:38 am
I worried a bit over the fact that humans are not point sources, but realized that in a 5 minute vidcast that would be hopeless to cover.
I also considered tides, but again I didn’t have time. If you work out the tides from astronomical objects, the nearby human wins easily, because you get an extra factor of distance in the denominator (1/distance3), so celestial objects get drastically reduced in their influence.
Cindy– the video/auido synching is making me crazy. It looks fine here at home, but when I upload the video it gets out of synch. That caused me many nightmares last week; the Google video was awful and I had to reupload a different version. I have to make a WMV and QT version, as well as audio, and upload it to YouTube, and and and. I would love it if I could make one version for everything, but there is no standard yet.
February 26th, 2007 at 3:37 pm
BTW, it’s another Virgin Mary sighting in Houston – this time on a baking pan. You can see the photo where they compare the pan on the left to an actual picture of a VM outlined. I think it looks like a fat bowling pin. It’s embarrassing.
February 26th, 2007 at 5:55 pm
Hey Phil, nice hairdo this time around (or was it simply masked by the cap in the last couple of episodes?). I reckon the change to you nick for that one’s gonna be miniscule, you only need to add a single L to “The Bad Astronomer.†:)
February 27th, 2007 at 12:22 am
I’m confused. Doesn’t that mean that the tides should be far more dependent on the Sun than the Moon? In other words, tides should be very dependent on day/night and the moon should have very little effect in comparison, right?
Oh wait. I just looked at wikipedia. I might as well post my comment for others to see. http://en.wikipedia.org/wiki/Tides#Tidal_physics
February 27th, 2007 at 3:28 am
[...] Bad Astronomy Blog » Q & BA Episode 4: The Gravity of the Situation ‘Just how strong is the gravity from the Moon compared to someone right next to you?’ – I found the answer surprising. via Sandwalk. (tags: astronomy moon gravity) [...]
February 27th, 2007 at 9:29 am
This topic brings to mind a great xkcd cartoon
http://www.xkcd.com/c89.html
February 27th, 2007 at 11:03 am
Who’s the guy with the fish?
February 28th, 2007 at 1:39 pm
You rock. Seriously.
Whenever I hear things like this, it reminds me that there are soooo many things to think about and learn and understand… thank goodness for teh intarwebs, so that somebody like you, who is so very good at explaining complicated things in a way that nearly everyone can understand, can teach so many people about things like this.
Your website is a science teacher’s dream. Fun, informative, relevant. Amazing.
June 14th, 2007 at 6:47 pm
[...] blobs of gas — massing as much as the Sun! — at high velocity, and was temporarily the second brightest star in the sky, even though it’s 7000+ light years [...]