Is the world getting fatter?

[entwined]

At breakfast the other day, one of our number expressed concern that if we keep sending things off into space, we will, one day, find that the mass of the Earth has been reduced to the point that it could affect it's ordit around the sun.

 

We all scoffed at this and I got into it by saying that, if anything, the opposite is true because Earth is constantly gaining mass in the form of meteorites impacting here at a much faster rate than we are losing mass due to the exportation of matter through our space program.

 

I hurried home to conduct a search to prove my point, but to no avail.

 

Two questions; Was I right in my assertion? And where can I find scientific estimations of the rate of gain--if, of course, I was right.

[Pangloss]

I don't know the answer, but you might point out to your friend that we're also losing mass due to atmospheric attrition into space.

[swansont]

The acceleration required to keep an object in a circular orbit is independent of the mass — it's v²/r, and the acceleration afforded by gravity is GM/r², where M is the sun's mass. They are independent of the earth's mass. IOW, your orbital characteristics are determined by your altitude and speed (to first order, at least). So you can e.g. have a small capsule dock with a massive space station without experiencing different accelerations.

 

What you have to worry about is mass gained/lost has a different momentum than the earth, which would change its speed.

 

If you are worried about the mass change, though, start with the fact that the earth's mass is ~6 x 10^24 kg

[Bignose]

swansont's last sentence there got me thinking and so I gathered some numbers together:

 

Given that it costs around $15,000 US to place one pound of mass in orbit (http://answers.google.com/answers/threadview?id=431680)

 

and that the 2005 US GDP was $12,455,070,000,000

(http://devdata.worldbank.org/query/default.htm)

 

It would take the US over 10 million years (at steady 2005 production) to place one one-thousandth of one percent of the earth's mass into orbit, and I am not sure that a change of 0.001% would affect the orbit of the earth too much.

 

Now, obviously, that is a little farcical since the entire US economy is not based on just putting mass into orbit, and if it was, I suspect that it would not take too long before significantly cheaper way of getting mass into orbit would be designed. Nevertheless, it just shows how large of a mass the earth really is, and at the rate of payloads of only a few thousand pounds at a time... well, your scoffing was very well justifed.

 

Edited to put the last three zeros on the GDP (good eyes entwined)

[entwined]

swansont's last sentence there got me thinking and so I gathered some numbers together:

 

Given that it costs around $15,000 US to place one pound of mass in orbit (http://answers.google.com/answers/threadview?id=431680)

 

and that the 2005 US GDP was $12,455,070,000

(http://devdata.worldbank.org/query/default.htm)

 

It would take the US over 10 million years (at steady 2005 production) to place one one-thousandth of one percent of the earth's mass into orbit, and I am not sure that a change of 0.001% would affect the orbit of the earth too much.

 

Now, obviously, that is a little farcical since the entire US economy is not based on just putting mass into orbit, and if it was, I suspect that it would not take too long before significantly cheaper way of getting mass into orbit would be designed. Nevertheless, it just shows how large of a mass the earth really is, and at the rate of payloads of only a few thousand pounds at a time... well, your scoffing was very well justifed.

 

To answer Swansont first, no, it is not I who is worried about loss of mass to the Earth, actually I think it is the other way around--though I am not worried about that either.

 

Now on your quotation of the GDP of the US, are you sure that you didn't leave off 3 zeros in that quote?