Conservation of mass incongruent with He?

[1ledzepplin1]

Hi physicists!
My name is grant and I am curious as to how helium plays into our Earth's overall mass and gravity. It's my understanding that gravity itself is functionally dependent on the quantity of mass within closed systems or objects, and it's also my understanding that helium will escape into space.
So with that all said I am wondering what the influence is on Earth's gravity that our Earth's helium supply is, I suppose, just flowing out of our closed planet system?
Also, from the perspective of you all, how is the Earth viewed from a physics standpoint with respect to gravity? Is gravity changing on Earth from the standard 9.8m/s and if not why doesn't helium loss affect this?
Thanks :)

 

[D H]

The Earth is losing a lot more hydrogen than helium. Estimates range wildly, with most estimates being a bit less than 100,000 metric tons per year. The Earth is also gaining mass from meteors. These estimates range even more wildly, from about 2,000 metric tons per year to well over 100,000 metric tons per year.

We don't even know if the Earth is losing or gaining mass.

Let's take the low number for mass gain. That means the Earth is losing about 100,000 metric tons of mass per year. That sounds like a lot, but it isn't. It's about 10^-17 of the mass of the Earth. Even the best instruments can't come anywhere close to measuring Earth's gravity to seventeen decimal places.

 

[ChrisVer]

gravity is a force, 9.8 is acceleration...
Well the acceleration g changes over the Earth's surface (not because of mass loss but because of your position/distance from the center).

9.8 is a good approximation for g on the Earth's surface... Even if Earth would lose mass it wouldn't affect the way it attracts us... this is all due to Gauss's law... Because of the form of the force, you are being attracted by the mass contained in a sphere of radius = distance of the center, and that mass is not lost... In that case you are not being attracted by the outer layers of the atmosphere where the mass loss takes place.

 

[Khashishi]

If you approximate the Earth as having spherical symmetry, then the gravity from the Earth measured at a particular point depends on the mass contained within a sphere centered at the center of the Earth which intersects the particular point. In other words, if you are standing on the surface of a spherical Earth at a particular elevation, then you feel the gravity of the Earth from all the mass below your elevation, but you don't feel the mass above your elevation. You won't feel the gravity due to helium in the upper atmosphere above your elevation. But if you were out in space, above the upper atmosphere, you do include the mass of the upper atmosphere in the gravity you feel from the Earth.

 

[ChrisVer]

I am not sure about the pressure though...I guess the pressure would have to fall if outer layers of the atmosphere are being thrown out...
since a planet with atmosphere has X value for pressure, while a atmosphere-less planet has 0 pressure...this must be true...
So how would that affect us? (expecting an answer from someone more into this kind of stuff- environmental physics) Could we measure it?

 

[mfb]

I am not sure about the pressure though...I guess the pressure would have to fall if outer layers of the atmosphere are being thrown out...

Sure it would. Luckily, no significant fraction of the atmosphere escapes to space.

So how would that affect us? (expecting an answer from someone more into this kind of stuff- environmental physics) Could we measure it?

We could certainly measure a lower atmospheric pressure.

How is that related to gravity?

 

[ChrisVer]

nothing to gravity... I guess it would be related to how much something would weight on the Earth's surface... lower pressure from above, would mean lower weight for us... (it's related indirectly to gravity)...at least that's how I think...
But the main reason I referred to the pressure is that even though we cannot measure the mass loss by our weight, we could (probably? yes) measure the pressure losing...so that we know how much is gained or loss...

 

[mfb]

lower pressure from above, would mean lower weight for us

No (you get nearly the same pressure from below as well). You have buoyancy, sure, but that is related to the density of air, not its pressure. And it reduces the number the scale shows.

 

[1ledzepplin1]

I can definitely appreciate some of the answers citing gravitational force as a function of distance AND mass and the pressure question is very interesting and I look forward to seeing more discussion on that. I feel like, however, my gravitational question was taken a bit more literally than I was looking for and I am asking something a bit more theoretical. I am thinking that different masses contribute completely unique properties to the Earth's gravitational field and that the organization with respect to the Earth's core is what truly defines it. I'm thinking that a helium atom at x distance will produce a different effect gravitationally than a boron atom at x distance, all as a function of mass distribution. Any thoughts on this? Because a potential energy difference may exist for a particular elemental mass, at a certain distance. I just don't feel like the gravitational constant should exist. I think it's proportional

 

[Nugatory]

Any thoughts on this? Because a potential energy difference may exist for a particular elemental mass, at a certain distance. I just don't feel like the gravitational constant should exist. I think it's proportional

That's why the the mass appears in the expressions for gravitational force and gravitational potential energy - because both quantities are indeed proportional to the mass. This is true for a very small object such as an atom, as well as for larger objects that are collections of atoms (for the latter, in principle we add the contribution from each individual atom, in practice we get the same results with less work by calculating with average densities and total masses).

And we know that the gravitational constant exists because we've measured the forces and potential energy with many different objects of widely varying size and composition... and we always get results that are consistent with mass multiplied by a constant. This is one of the areas where our feelings about how the universe should work are irrelevant - the universe is telling us how it does work (although it's still up to us to listen to what we're being told).

 

[1ledzepplin1]

Hahahah nugatory your sass is well received and appreciated. I asked my physics professor and she about gave me the same taste of humility in her response as well. I respect the conclusions of countless experiments that have all yielded the gravitational constant, I just can't help but poke and prod at it until I figure out exactly why that constant is as it is. This is beyond the scope of the thread and my own research though but thank y'all!

 

[ChrisVer]

So what is the problem with a constant?
We know that the force of gravity is proportional to the masses of the two attracted objects, divided by r².
The best way to write that proportionality is by a constant factor (independent of mass or distance):
$F_{(ij)}= G \frac{m_{(i)}m_{(j)}}{r_{(ij)}^{2}}$

The "nice" thing of the game is indeed $G$ was measured to be a "constant" (of course in reality it's not). One way for example, is the Cavendish experiment.
Of course it's not a constant :) (it's running)