# Changes to the earth's orbit after mass leaves our gravity

#### MrSoftware

Joined Oct 29, 2013
2,015
So I got to thinking.. we're busy sending small bits of our planet out into space, which reduces our mass, which should change our orbit around the sun. I've long forgotten the orbital math that I learned way back in school, but for funsies would someone with a better memory calculate the difference in our orbit around the sun 1M, 2M and 1B years from now assuming we launch 10 tons of material out of our gravitational pull today? I expect that with less mass but the same orbital velocity, earth will inch closer to the sun, perhaps adding to global warming, but it would be neat to see the numbers.

#### atferrari

Joined Jan 6, 2004
4,473
So I got to thinking.. we're busy sending small bits of our planet out into space, which reduces our mass, which should change our orbit around the sun. I've long forgotten the orbital math that I learned way back in school, but for funsies would someone with a better memory calculate the difference in our orbit around the sun 1M, 2M and 1B years from now assuming we launch 10 tons of material out of our gravitational pull today? I expect that with less mass but the same orbital velocity, earth will inch closer to the sun, perhaps adding to global warming, but it would be neat to see the numbers.
In the movie "Hidden figures" the lady in charge of calculating things in NASA does mention some Euler's equations as the solution of the problem at hand and I wonder if that is what is needed in the case above.

Guessing wildly, I suspect we are, right now, much closer of 500 MT already out of the globe, floating somewhere in the space. Too many years of dogs, people, rockets, satellites, crawler rovers and who knows what else.

/EDIT
From an article in blog.wolfram.com: Where the movie mentions the solving of differential equations using Euler’s method,

EDIT/

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#### crutschow

Joined Mar 14, 2008
28,205
I agree with Albert.
The orbital distance and speed is independent of the object's mass.
Look at all the satellites in earth's orbit. For a given altitude, they orbit at the same speed.
The orbital speed is dependent only on distance, not mass.

#### WBahn

Joined Mar 31, 2012
26,398
The issue isn't the mass, it's the momemtum of the objects. Since momemtum is conserved, for the Earth to retain the same orbital parameters, the momentum of the exiting objects would have to be exactly what they were while on the planet, but that would mean that they would also be in the same orbit. So the fact that we want them to go elsewhere means that the orbital parameters of the Earth must change.

But the same is true when we use a planetary body to do a slingshot maneuver - we are performing a momentum transfer between the spacecraft and the planet, changing the momentum of both.

The Earth is a dynamic system in this regard -- it collects about 40,000 metric tons of dust and other things from space, but loses about 100,000 metric tons of stuff to space, about 95% of which is hydrogen.

The amount of mass represented by those portions of space vehicles that leave Earth's orbit (the rest doesn't make a difference since it remains part of the Earth/moon system) is tiny compared to this. As far as I know, the heaviest spacecraft to be sent beyond Earth orbit is Cassini-Huygens at less than 6 metric tons.

#### crutschow

Joined Mar 14, 2008
28,205
Okay.
I can see that if the object from earth goes out of the earth-moon orbit, then the earth's orbit must change.

#### MrSoftware

Joined Oct 29, 2013
2,015
@AlbertHall - Logically I think you are correct.. while the earth would have less mass to pull against the sun's gravity, it would also have less mass for the sun's gravity to pull on. So all other things equal, the mass should not affect the orbit, only speed and distance would affect the orbit. Good catch.

So I guess the question shifts to change in the earths momentum due to objects leaving our gravity. But going by what @WBahn says, the stuff we're sending out is almost insignificant in relation to the stuff earth collects and ejects as part of nature anyway. So maybe the sun will grow to a red giant and vaporize us long before our orbit changes due to the rockets we're sending out into space.

#### BR-549

Joined Sep 22, 2013
4,938
What about the momentum that is sideways of all the planets and the sun? This is an external force. I'm guessing much stronger and causing much more acceleration than compared to the solar system internal forces.

How much of a factor is this force on our solar system balance? Does this force only effect the sun and we follow......or is the force on all of system? What do we do and how do we explain this much stronger force effecting our system? It's a third vector....the fastest vector.

We can't measure this velocity. A six month base line would be a straight line connecting a half spiral end points. We have no idea of that length. Establishing the correct angle for reference would be hard too. Is this force incident or at angle?

Would it be possible to set and keep a spacecraft at zero acceleration? Would we detect zero acceleration at right distance between planets? Is it possible to even detect this sideways acceleration?

Could there be certain times at certain places to measure this in our system?

#### InPhase277

Joined Feb 15, 2018
23
What about the momentum that is sideways of all the planets and the sun? This is an external force. I'm guessing much stronger and causing much more acceleration than compared to the solar system internal forces.

How much of a factor is this force on our solar system balance? Does this force only effect the sun and we follow......or is the force on all of system? What do we do and how do we explain this much stronger force effecting our system? It's a third vector....the fastest vector.

We can't measure this velocity. A six month base line would be a straight line connecting a half spiral end points. We have no idea of that length. Establishing the correct angle for reference would be hard too. Is this force incident or at angle?

Would it be possible to set and keep a spacecraft at zero acceleration? Would we detect zero acceleration at right distance between planets? Is it possible to even detect this sideways acceleration?

Could there be certain times at certain places to measure this in our system?
Are you talking about the acceleration due to the sun's orbit in the galaxy? I would imagine that it is very very small because the radius of that orbit is so huge.

The sun orbits the galactic center every 280000000 years, so an angular velocity of about $$4.077x10^-7$$ degrees per second. Very small.

#### WBahn

Joined Mar 31, 2012
26,398
Are you talking about the acceleration due to the sun's orbit in the galaxy? I would imagine that it is very very small because the radius of that orbit is so huge.

The sun orbits the galactic center every 280000000 years, so an angular velocity of about $$4.077x10^-7$$ degrees per second. Very small.
If the orbital period is 280,000,000 years, then wouldn't the angular velocity be more like 4 x 10^-14 °/s ?

#### InPhase277

Joined Feb 15, 2018
23
If the orbital period is 280,000,000 years, then wouldn't the angular velocity be more like 4 x 10^-14 °/s ?
Yeah. I fudged it somehow.

#### WBahn

Joined Mar 31, 2012
26,398
We all do, from time to time. And although the number immediately struck me as incredibly large to make sense, I can't really say why. Sometimes we just don't have a feel for what is and is not a reasonable answer to question what we got. Of course, once that thought did strike me, for whatever reason, it only took a moment to look at all those zeroes and recognize that the answer would be a couple of orders of magnitude too big even if it were in degrees per year instead of per second. That's the value of estimating expected answers to see what kind of results make sense.

#### takao21203

Joined Apr 28, 2012
3,702
If dogs sent outerspace are shaved beforehand the lost mass is reduced, also if theres less paint on the rockets, like thinner layer or none.

But theres also meteorites + dust every day, as well volatile gas.

#### wayneh

Joined Sep 9, 2010
17,155
So maybe the sun will grow to a red giant and vaporize us long before our orbit changes due to the rockets we're sending out into space.
I think that's about right, at least for now. If there's any mass to worry about with regard to our orbit, it might be a bias in the direction of incoming mass. I mean for instance if the random debris is static relative to the sun, and of course we are not, then we'd be sort of plowing through this cloud of mass and there would be a net drag on us, slowing us down and sending us to a closer orbit. I have no idea if such an imbalance exists in either direction.

I believe tidal movements act as a sort of drag on rotation, also. That's probably a more significant factor than space dust.

#### BR-549

Joined Sep 22, 2013
4,938
Come on.......who here believes that the sun's orbital radius is 25 thousand light years?

Do our solar system moons orbit the sun?

It's orbits within orbits. That's how nature works. Spins within spins.

The spins go thru perpendicular steps.

#### cmartinez

Joined Jan 17, 2007
7,524
So I got to thinking.. we're busy sending small bits of our planet out into space, which reduces our mass, which should change our orbit around the sun. I've long forgotten the orbital math that I learned way back in school, but for funsies would someone with a better memory calculate the difference in our orbit around the sun 1M, 2M and 1B years from now assuming we launch 10 tons of material out of our gravitational pull today? I expect that with less mass but the same orbital velocity, earth will inch closer to the sun, perhaps adding to global warming, but it would be neat to see the numbers.
Interesting thought... but did you know that between 30,000 to 100,000 tons of meteorites hit earth each year? The earth might as well be gaining mass, rather than losing it.

A few years ago, I read that the earth's radius increases about 1mm per decade due to meteorite dust. But I can't find a reference to verify if that's an exaggeration or not... or maybe my memory fails me.

#### AlbertHall

Joined Jun 4, 2014
11,610
A few years ago, I read that the earth's radius increases about 1mm per decade due to meteorite dust. But I can't find a reference to verify if that's an exaggeration or not... or maybe my memory fails me.
How much is it shrinking due to cooling of its innards?

#### cmartinez

Joined Jan 17, 2007
7,524
How much is it shrinking due to cooling of its innards?
Another interesting question ... but the earth won't lose or gain mass because of that ...

#### AlbertHall

Joined Jun 4, 2014
11,610
Another interesting question ... but the earth won't lose or gain mass because of that ...
But the days will get shorter.

#### cmartinez

Joined Jan 17, 2007
7,524