# What if the moon was compressed to palm size?

1. Aug 4, 2013

### cyberdiver

In the recent hubbub centring on Despicable Me 2 (bear with me), I recall the first film when the protagonist stole the moon by using a shrink ray to shrink it to fit in his palm. My question is, what would happen in real life if such an absurdity was committed? For one, shrinking the moon would not make it easier for him to carry around.

I calculated that the moon's final density would exceed a neutron star's density by roughly five orders of magnitude. From what equations I could find on the internet, surface gravitational tides would reach 6*10^6 m/s^2/m; the protagonist's spacecraft would be torn to pieces in an instant. I could be wrong about the calculations, of course; mathematics was never my forte. I assumed that the final radius would be 6 cm.

2. Aug 4, 2013

### Simon Bridge

Unless he also managed to reduce it's mass. But in that case, all that energy has to go somewhere...

That's the sort of thing to expect - yes.

Mass of moon: 7x1022kg
historic size of a handful = 4in across = (approx) 0.1m or a 0.05m radius sphere.

Rs=2GM/c2 =0.009m
... roughly the same order of magnitude! So this object is very nearly a black hole.

sphere volume = 5x10-4

=> density: mass/volume = (approx) 1x1026kg/m3

Neutron stars have overall densities predicted by the APR EOS of 3.7×1017 to 5.9×1017 kg/m3
(wikipedia)

So yep - closer to a BH than a NS.
Tidal effects close to such an object would be very nasty.
OTOH: considering the energy required to do such extreme shrinkage so casually, and keep it that way without apparent concerns, cancelling out the unpleasant side effects should be easy.

3. Aug 4, 2013

### chemisttree

Of course any old super villian can shrink the Moon to palm size and retain the mass. The dangerousness (yes, I said 'dangerousness') of that experiment has always been the sticking point so nobody dared try it.

Gru's genius was in dealing with the mass the way he did. After shrinking it, he could pick it up with little effort. You will recall that after Vector stole the Moon and the temporary nature of the shrink ray began to manifest, the increasing mass of the Moon began to affect his rocket's ability to maintain course.

4. Aug 5, 2013

### Ryan_m_b

Staff Emeritus
At the moment the compressing force was released a palm sized moon would expand very rapidly. Best watched from Mars...

5. Aug 5, 2013

### cyberdiver

I imagine that it would become hot due to the compression. Very, very hot.
How hot is the question.

6. Aug 5, 2013

### SteamKing

Staff Emeritus
It's best to remember DM2 is just a cartoon. If you start thinking seriously about it, it's no longer entertainment. It's like worrying if Wile E. Coyote will suffer serious head injuries or death when the Acme Anvil drops on his head.

7. Aug 5, 2013

### davenn

Awwww steamking you have destroyed everything I ever held near and dear

Dave

8. Aug 6, 2013

### cyberdiver

It's just curiosity, really. Also, it's fun to see the ridiculous numbers piling up on the calculator.

9. Aug 12, 2013

### DHF

so going along those lines, assuming Gru didn't pick up the Moon after shrinkage but instead left it in place, how far would the gravitational threshold be? what would the effects on Earth be?

10. Aug 12, 2013

### cyberdiver

Gravitationally, nothing would change unless the moon's mass changed or there were gravity waves.

11. Aug 12, 2013

### DHF

So the Gravity would increase as the surface area shrank but the overall reach of that gravity would not extend any further then it currently does?

Last edited: Aug 12, 2013
12. Aug 12, 2013

### Bandersnatch

The only "place" where the field would be different from what it is now, is the volume below the (normal-sized) Moon's surface.

13. Aug 12, 2013

### DHF

ok now I can rest easy at night knowing that if such an event happened that the Earth wouldn't suddenly lurch out of orbit and crash into said moon.

14. Aug 12, 2013

### Simon Bridge

Just checking this:
What do you mean by "gravitational threshold"?

What do you mean by "overall reach of gravity"?

Note:
- gravity extends through all space - there is no "threshold" or limited "reach".
- gravity depends on mass - not surface area.
(You could argue that, in some situations, surface gravity is inversely proportional to surface area.)

Leave the moon unchanged, call it's unaltered radius R, and recall...

The strength of gravity at R is the "surface gravity" and it's value depends on how far the surface is from the center of mass by gR=GM/R2 and the force of gravity on a mass m close to the surface is F=mgR.

For distances >R the strength of gravity decreases quadraticly ("inverse-square law") because you are increasing your distance from the center of mass (and the total mass below you does not change).

For distances <R, the strength of gravity changes because there is less mass below you - how it changes is a bit involved because the Moon is composed of different density layers. Gravity from each layer increases as you get closer to it but decreases as you pass through.

Now shrink the moon to smaller radius r, but keep the same mass.

The strength of gravity at R is unchanged.
At distances >R - still unchanged.
The gravity decreases quadraticly ("inverse-square law") as you go from r to R, since you are getting farther from the center of mass (and the total mass below you does not change).
This means that the gravity at r must be higher than the gravity at R
i.e. the shrunken moon has a higher acceleraton of gravity at the surface because the surface is closer to the center of the same amount of mass.

That help?

15. Aug 14, 2013

### DHF

Thank you Simon,

So If the moon were shrunk to the size of a marble you wouldn't feel any difference in the gravity until you moved closer to it then R. Once you pass R the force of the gravity would continue to increase because all of the original Mass is still working on you and as you move closer you wouldn't be passing through layers and decreasing the overall mass working on you (as you would if you landed on the unaltered Moon and began drilling to the core.)

Last edited: Aug 14, 2013
16. Aug 14, 2013

### Mandelbroth

SteamKing, some of us like physics. :tongue:

I find this thread entertaining. *subscribe*

17. Aug 17, 2013

### cyberdiver

According to this website, any gravitational time dilation or redshifting should be negligible. Dang.

18. Aug 17, 2013

### Simon Bridge

Well done :)

It's a very small effect, yes.
(caveat: did not visit the link)

19. Aug 21, 2013