Earth's Mass: Does It Include People & Everything Else? | Simple Question

[kk727]

This is a question that was brought up in class...we were jokingly talking about if everyone in the world was transported to North America, and if all those people jumped at the same time, how the force would impact our orbit. So we estimated the mass of about 6 billion people versus Earth's mass.

But that raised this question: When they measure the Earth's mass to be about 5.97 x 10^24, is that solely the mass of the Earth, or does that number include people and everything that's on the Earth?

Probably a stupid question, but I couldn't find it when I looked online. Thanks!

 

[stevenb]

This is a question that was brought up in class...we were jokingly talking about if everyone in the world was transported to North America, and if all those people jumped at the same time, how the force would impact our orbit. So we estimated the mass of about 6 billion people versus Earth's mass.

But that raised this question: When they measure the Earth's mass to be about 5.97 x 10^24, is that solely the mass of the Earth, or does that number include people and everything that's on the Earth?

Probably a stupid question, but I couldn't find it when I looked online. Thanks!

Well, without even doing a search you can do an order of magnitude calculation. You are saying the mass of the earch is about 6x10^24 kg. The number of people on Earth is about 6x10^9 and you can estimate the mass of a human at about 100 kg (with apologies to the women who will be insulted by that overestimate). This places the mass of humans at about 6x10^11 kg. This means that the mass of the Earth is about 13 orders of magnitude greater than the mass of humans. Hence, the mass of humans is insignificant and (given how weak we are) any jumping we do in sync is not likely to generate a measurable orbital shift.

As to your specific quesiton, we probably can't estimate the mass of the Earth to 13 significant figures. The mass we measure would include humans, but we just can't resolve to that level in a measurement.

 

[FlexGunship]

Well, without even doing a search you can do an order of magnitude calculation...

Um, am I missing something here? But, if we're on the Earth, is there actually any net impact we could make even if we were hugely massive?

Imagine a single human on the surface of the Earth. This person is the same mass as the Earth. When he jumped off of the surface, the orbit of Earth would contract and it would lose angular momentum. When he landed, the Earth would get this angular momentum back and return to the previous orbit. Net energy in the system is the same. This is only true because the person must push off of the Earth to create distance, then the mutual gravitation interaction would bring them back to the exact location again.

Any amount of pushing energy exerted against the Earth the wrests free some amount of mass, must return after the masses join again. Think of it this way, if the result is to change the orbital dynamics of the Earth with your landing impact, you must also know the impact of jumping up, too.

Or else it's free energy... right?

Perhaps I've missed something.

 

[stevenb]

Um, am I missing something here? But, if we're on the Earth, is there actually any net impact we could make even if we were hugely massive?

Imagine a single human on the surface of the Earth. This person is the same mass as the Earth. When he jumped off of the surface, the orbit of Earth would contract and it would lose angular momentum. When he landed, the Earth would get this angular momentum back and return to the previous orbit. Net energy in the system is the same. This is only true because the person must push off of the Earth to create distance, then the mutual gravitation interaction would bring them back to the exact location again.

Any amount of pushing energy exerted against the Earth the wrests free some amount of mass, must return after the masses join again. Think of it this way, if the result is to change the orbital dynamics of the Earth with your landing impact, you must also know the impact of jumping up, too.

Or else it's free energy... right?

Perhaps I've missed something.

I agree. There are two aspects to the question. First, do humans have enough mass to make any difference? Then, if so, the second question is what would they need to do to affect the orbit? Simply jumping up in the air for < 1 second and coming back to Earth is not going to do anything significant. However, leaving at greater than the escape velocity will permantly change the orbit; or, jumping high enough to enter space for hours at a time might modulate the orbit. Here again, humans are not strong enough to do that with a jump.

Basically, humans don't have enough mass, nor enough jump to make a difference.

 

[FlexGunship]

However, leaving at greater than the escape velocity will permantly change the orbit;

Yes.

or, jumping high enough to enter space for hours at a time might modulate the orbit.

Don't think so. If they return, then the total energy of the event should be conserved.

Remember the Gemini rendezvous mission with the first Agena target vehicle? Conservation of angular momentum. Doesn't matter how long you wait if it's a closed system that's not influenced by outside mass or energy.

 

[stevenb]

Yes.



Don't think so. If they return, then the total energy of the event should be conserved.

Yes, but I mean that the orbit of the Earth will modulate. It may return to normal after the jump is over, but before that, it can be purturbed a measurable amount. Hypothetically, of course.

 

[FlexGunship]

Yes, but I mean that the orbit of the Earth will modulate. It may return to normal after the jump is over, but before that, it can be purturbed a measurable amount. Hypothetically, of course.

Understood. Agreed.

 

[litup]

So hypothetically, maybe it would effect the Earth's orbit by the width of one hydrogen atom in some kind of wobble but if you consider the mass jump microsecond by microsecond, the jump has to be preceded by a flexing of leg muscles, which during the jump, makes a tiny pressure wave towards the center of the Earth. Then coming down, doesn't hitting the ground produce the same wave going into the center of the Earth?
Are you saying the gravitational attraction of those 6 E9 people negates the original downwards thrust?

 

[FlexGunship]

Are you saying the gravitational attraction of those 6 E9 people negates the original downwards thrust?

Unless you think you've found a perpetual energy machine! You'd be the first.

EDIT: Actually, Earth isn't a closed system. It's always getting energy in the form of solar radiation. That radiation is being passed up the food chain until it gets to humans.

That being said, the only mechanism by which humans can exert a force on the Earth is by using the Earth as a reference (or potential energy ground). let's rephrase the question, shall we?

How hard would you have to kick the back of the driver's seat in a car, to get the car up to 60mph?

 

[kk727]

Well, I definitely didn't expect this kind of response, but it's much appreciated! I'll have to bring this up in class and perhaps we'll spend some time talking about it. I don't feel I know enough about physics to understand all of the points that were brought up, but it's interesting stuff that would be fun to research more - thanks everyone!

 

[Radrook]

Unless you think you've found a perpetual energy machine! You'd be the first.

EDIT: Actually, Earth isn't a closed system. It's always getting energy in the form of solar radiation. That radiation is being passed up the food chain until it gets to humans.

That being said, the only mechanism by which humans can exert a force on the Earth is by using the Earth as a reference (or potential energy ground). let's rephrase the question, shall we?

How hard would you have to kick the back of the driver's seat in a car, to get the car up to 60mph?

How about a nuclear blast involving all the available nuclear bombs on earth. That would be a hell of a kick on the taxi driver's back seat!

 

[FlexGunship]

How about a nuclear blast involving all the available nuclear bombs on earth. That would be a hell of a kick on the taxi driver's back seat!

Ahh, yes... you seem to have missed the point with a ninja-like precision.