# Mass and gravity confuse me

1. Dec 8, 2006

### Jota

Please forgive me for how odd this question may sound. I just couldn't write it to make any more sense, and I do apologize for that.

Mass, by what I know, doesn't seem to produce the amount of gravity that it should. Take the example of Jupiter: it has a mass approximately 300 times that of earth. However, almost all of this mass is composed of two incredibly light elements; hydrogen and helium. This combination, when condensed as a liquid or solid, would probably weigh no more than 3 pounds per cubic foot, if that. That is not very dense. Earth's composition is more complex, as can be seen here: http://hyperphysics.phy-astr.gsu.edu/hbase/tables/elabund.html . Earth is approximately 50 percent hock rock that must have a much greater density than hydrogen or helium. Magma most likely weighs around 170 pounds per cubic foot (that is about the weight of granite). Half of that gives about 85 lbs per cubic foot.Therefore, earth's composition would be, approximately, over 25 times denser than Jupiters. So, Jupiter may have approximately 300 times the mass of earth, but only about 12 times the density (rough estimate).

Materials weigh more because of DENSITY, right? The denser the material the greater the gravity it produces, correct? Isn't this why mercury is around the same size as the moons of some of our gas giants, and considerably smaller than mars, yet has greater gravity than any of the former and equal gravity to the latter?

And thus I become so confused.

Jupiter's gravity well is incredibly powerful, certainly far more than just 12 times as powerful/massive/influential, as the earth. It has a surface area over 100 times greater than earth. Even at the highest cloud tops--the "surface" of this gaseous planet--it has about 2.65 times the gravity of earth. 12 times greater, over that great a surface? That is strange; that much gravity must make a gravity well bigger; MUCH bigger than it should be given its density. Why does it have much more gravity than its density should allow?

I just don't understand it. I've researched the subject considerably, but still can't figure it out. And I know that from the way I wrote it, I know it looks foolish but I can't think of a better way to phrase the question.

Thanks for any and all help given.

2. Dec 8, 2006

### HallsofIvy

Staff Emeritus
No, that's wrong. You just said earth is "over 25 times denser[\b] than Jupiter". You can't then say Jupiter has "only about 12 times the density" of earth! Mass= density times volume. If your figures are correct then 300= 25*volume so the VOLUME of Jupiter is only 12 times that of eath. Gravitational force depends only upon MASS, not upon either density or volume separately.

Yes, it's 300 times as great, assuming your "it has a mass approximately 300 times that of earth" is correct.

Surface area, like volume, is irrelevant. Gravitational force depends solely on MASS.

3. Dec 8, 2006

### SpaceTiger

Staff Emeritus
Earth's average density is about four times that of Jupiter, and both are a good bit higher than what you quoted:

Earth: ~340 lb/ft^3
Jupiter: ~80 lb/ft^3

The composition figures you quote are for the Earth's crust, which is only a very tiny fraction of its total mass. As for Jupiter, although mostly hydrogen and helium, the gas at the center is very highly condensed.

4. Dec 8, 2006

### Jota

But, planets with greater density do have greater gravity, don't they? As I pointed out, Mercury has about the same diameter as some moons of saturn and Jupiter. They all have about the same amount of matter. However, it also has far greater gravity, because the moons are composed largely of ices mixed with rock, whereas Mercury is rock and metal, which is more dense. Perhaps I haven't understood the proper context of "mass". Does mercury, with its greater density and correspondingly greater gravity, therefore have a greater MASS? I know this seems off the topic of Jupiter but it will help me better understand the crucial issue of how to define mass.

5. Dec 9, 2006

### SpaceTiger

Staff Emeritus
HallsofIvy is correct that the external gravity depends on the mass of the body, not the density.

Mercury is more than twice as massive as the most massive moon of Jupiter or Saturn, so will have a stronger gravitational field.

An object with greater average density would, at a constant size, have a greater mass. However, the planets vary in both size and density, so the density alone isn't enough to tell you the mass. For a spherical planet or moon, you can relate the average density to the mass and radius:

$$<\rho>=\frac{3M}{4\pi R^3}$$

Last edited: Dec 9, 2006
6. Dec 9, 2006

### Jota

Sorry, I feel so foolish everytime I post. I am a dunce at hard science. I wish I could make sense of that equation, but I'm terrible at math. But, I suppose what I'm trying to ask is: Does Mercury, at approximately the same volume of some gas giant's moons, have so much more density because mass?
Are mass and density the same the same thing?

7. Dec 9, 2006

### Staff: Mentor

Mass and density are not the same thing. Density = mass / volume.

Mass can literally be thought of as the quantity of material in an object (number of protons, neutrons, electrons). Density is how tightly it is packed.

Last edited: Dec 9, 2006
8. Dec 9, 2006

### Jota

So that would mean a given volume of material could have much more or much less mass than the same volume of another material. For example, one cubic foot of frozen helium, would have much less mass than a cubic foot of lead. Correct?

9. Dec 9, 2006

### kmarinas86

$Gravitational\ acceleration=GM/r^2 \propto M/r^2 \propto Mass / Surface\ Area$

10. Dec 9, 2006

### Staff: Mentor

Probably, but I'm not certain of how dense solid helium is.