How did Earth maintain an orbit?

[GrandMasterK]

I have two questions for yall today.

 

1. How did the earth keep an orbit as it was forming billions of years ago as it was pulling clumps of matter together and gaining mass?

 

2. If you took half the moons weight and added it to the earth, say by spreading moon rock over the surface, would we fall out of orbit and die? (ignoring the fact the moon would collide into us if that happened)

Edited April 5, 2011 by GrandMasterK

[Fuzzwood]

2) The orbit radius would increase to maintain radial velocity. The added mass "wants to travel in a straight line" more than the earth without the extra mass.

[GrandMasterK]

im confused. adding mass adjusts the orbit's position (wider) thereby allowing the more massive earth to stay in orbit at the same velocity? I would of thought packing on a lot of weight would slow us down and start pulling us towards the sun?

[mooeypoo]

I actually thought of something similar when the Japan earthquake happened. The earthquake shifted the crust a little, and as far as I understand, there were talks where it might have "pushed" the earth slightly out of orbit. Even if that's not true, it made me wonder what would happen if the Earth *was* nudged off.

 

If the earth was "nudged" off its orbit, the result would be perturbations on that orbit. That is, the Earth would "wobble" between slightly higher to slightly lower orbit.

 

I am not sure about this, but I think that this also might happen in this case. I think it might have to do with how "fast" we increase the mass of the Earth.. if it's done through a large span of time, we would probably shift to a higher orbit like Fuzz said, but if we increase the mass quickly, that should result in a perturbation.

 

I hope a more experienced physicist will be able to pitch in, though, while I try to find stuff from my mechanics books.

[swansont]

I actually thought of something similar when the Japan earthquake happened. The earthquake shifted the crust a little, and as far as I understand, there were talks where it might have "pushed" the earth slightly out of orbit. Even if that's not true, it made me wonder what would happen if the Earth *was* nudged off.

 

That's rotation. You redistribute mass and change the moment of inertia. The values given in the news reports assume that no other changes take place; my local earth orientation gurus have told me that the actual changes are not discernible in the noise.

 

 

 

As to the OP, it depends on how the mass is added. If the added mass were already in the same orbit, there would be no change at all, since the equations of motion do not depend on the satellite's mass. Otherwise there is a change in orbital speed, and then you have to recalculate what the new orbit will be.

 

For a circular orbit, GMm/r^2 = mv^/r

 

You can immediately see that m (satellite mass) cancels

 

v^2 = GM/r

 

If v decreases, r must increase. The details get messier if you go to general elliptical orbits, which is the more realistic outcome of adding some mass.

[Zant]

If the earth got more mass it would get higher gravitational pull so wouldn't we go further away from the sun in that case? If we went somewhere.

I may be wrong considering that the earth is moving at all times maybe it just works if both object remain stationary

Edited April 13, 2011 by Zant

[keelanz]

If the earth got more mass it would get higher gravitational pull so wouldn't we go further away from the sun in that case? If we went somewhere.

I may be wrong considering that the earth is moving at all times maybe it just works if both object remain stationary

 

more gravity, further away from the sun? what

stationary in physics? what

[Zant]

more gravity, further away from the sun? what

stationary in physics? what

 

What i mean is that the bigger mass something have the stronger gravitational pull it have, atleast thats how it works on objects that dont move as i said since the earth is moving i may be wrong on that part.

 

so say the earth got half the moons mass (as in the question) extra then the earth gravity get stronger so it could "fight" the suns gravity pull hence the part about moving away from the sun.

I hope it got bit clearer now, if you still dont understand what I mean feel free to comment again and ill see what I could do bout it

[Janus]

What i mean is that the bigger mass something have the stronger gravitational pull it have, atleast thats how it works on objects that dont move as i said since the earth is moving i may be wrong on that part.

 

so say the earth got half the moons mass (as in the question) extra then the earth gravity get stronger so it could "fight" the suns gravity pull hence the part about moving away from the sun.

I hope it got bit clearer now, if you still dont understand what I mean feel free to comment again and ill see what I could do bout it

 

The gravitational attraction between the Sun and the Earth is proportional to the product of thoer masses (Msun x Mearth). If either gets larger the gravitational attraction becomes stronger.

 

The amount of force that it takes to deflect a mass into a circular path (such as an orbit) agiant its natural tendency to travel in a straight line is proportional to the mass of the object.

 

Thus, if you increase the mass of the Earth by half of the Moons mass (1/162 of the Earth's mass) thne you will increase the Sun's gravitational grip on it by 0.61%, but a the same time, you will be increasing the force needed to hold the earth in its orbit by the same amount. The two effects cancel out and you see no net effect in the Earth's orbit.

Edited April 14, 2011 by Janus

[Zant]

The gravitational attraction between the Sun and the Earth is proportional to the product of thoer masses (Msun x Mearth). If either gets larger the gravitational attraction becomes stronger.

 

The amount of force that it takes to deflect a mass into a circular path (such as an orbit) agiant its natural tendency to travel in a straight line is proportional to the mass of the object.

 

Thus, if you increase the mass of the Earth by half of the Moons mass (1/162 of the Earth's mass) thne you will increase the Sun's gravitational grip on it by 0.61%, but a the same time, you will be increasing the force needed to hold the earth in its orbit by the same amount. The two effects cancel out and you see no net effect in the Earth's orbit.

 

Aha so it is because its moving/in orbit

[Moontanman]

Great explanation Janus, i was thinking along similar lines when i read yours and realized you had it. I was thinking that if the mass increased the earths orbit then as it acquired mass through meteors and dust the earth over time should be receding from the sun, i haven't read anything that would support that for sure.

[Light Storm]

Just a tidbit about earth adding on mass:

 

"While the actual amount of added material depends on which study you look at, an estimated 10 to the 8th power kilograms of in-falling matter accumulates every day. That seemingly large amount, however, IS insignificant compared to the Earth's total mass of almost 10 to the 25th power kilograms. "

Ref: http://www.physlink.com/education/askexperts/ae75.cfm

 

 

[bl4ster]

Nothing will happen cause the mass of the moon is only 1.2% mass of the earth a if we take that mass of earth is 1 then mass when we put half of the moon mass of the earth will be 1.006.And about earth moon relations, moon would get eliptic trajectory and finnaly flew away using something like gravity catapult.

 

 

Edited May 2, 2011 by bl4ster

[ewmon]

Think about it. The Earth and Moon are already a combined mass (via gravitation) orbiting the Sun at a certain distance and period, regardless of whether the two bodies are separate or together. Any which way you divide or combine the two masses, the distance and period will remain constant. What determines orbital parameters is their combined energy, which is ½mv². It also doesn't depend upon the ratio of their masses: this would hold true if the Earth & Moon were "binary planets" with a 50%/50% mass distribution.