stability of the earth/moon/sun system

[l3p3r]

This has been nagging me lately:<br /><br />If the Earth is orbiting the sun, and the moon is orbiting the Earth, then how can the moon be in a stable long term orbit? Shouldn't the acceleration applied on the moon by the sun over a long period of time cause the moon's orbit to become more and more elliptical until is finally flung from the grasp of Earth's gravitational influence? <div class="Discussion_UserSignature"> </div>

 

[CalliArcale]

Given enough time, it would theoretically tend towards a situation where the Earth, Moon, and Sun are all mutually synchronous.<br /><br />A more direct answer to your question is that gravitational attraction is proportional to the inverse square of the distance between two bodies. The Sun is a lot farther away than the Earth; the Earth has far more influence on the Moon than the Sun does. So that's why the Moon orbits the Earth. The Sun does have an affect, but it's negligible compared to the Earth's effect when working out the answer to your question. <div class="Discussion_UserSignature"> <p> </p><p><font color="#666699"><em>"People assume that time is a strict progression of cause to effect, but actually from a non-linear, non-subjective viewpoint it's more like a big ball of wibbly wobbly . . . timey wimey . . . stuff."</em>  -- The Tenth Doctor, "Blink"</font></p> </div>

 

[l3p3r]

CalliArcale<br /><br />Ahh I realised the error in my reasoning late last night. Any extrusion caused to the moons orbit by the sun will be 'undone' once the Earth reaches the opposite position in its orbit! Sound sensible enough?? (Though I do recognise the effect iteself would be minute because of the relative gravitational influence) <div class="Discussion_UserSignature"> </div>

 

[contracommando]

The moon won’t be in a stable orbit forever (virtually all systems will degrade given enough time). Each time the moon orbits the Earth it recedes a very small distance (while at the same time the Earth‘s rate of rotation slows by small degree). About 2 billion years from now, the moon will be so far away (thrown out of orbit?) that it will not be able to stabilize the Earth’s axis of rotation. <br />

 

[jatslo]

The Earth is leaving the Sun too.

 

[Saiph]

actually, fun thing is when you look at the complete picture:<br /><br />The moon orbits the sun. It is perturbed by the earth however, to speed up and slow down (which according to keplars laws of orbital dynamics means it moves away from, and towards the sun as the speed is changed).<br /><br />This allows the earth to pass the moon, and then vice versa.<br /><br />The moons orbit about the sun is thus a very, very shallow sinusoidal wave (it doesn't even loop back on itself, or have any sharp bends!).<br /><br /> <div class="Discussion_UserSignature"> <p align="center"><font color="#c0c0c0"><br /></font></p><p align="center"><font color="#999999"><em><font size="1">--------</font></em></font><font color="#999999"><em><font size="1">--------</font></em></font><font color="#999999"><em><font size="1">----</font></em></font><font color="#666699">SaiphMOD@gmail.com </font><font color="#999999"><em><font size="1">-------------------</font></em></font></p><p><font color="#999999"><em><font size="1">"This is my Timey Wimey Detector.  Goes "bing" when there's stuff.  It also fries eggs at 30 paces, wether you want it to or not actually.  I've learned to stay away from hens: It's not pretty when they blow" -- </font></em></font><font size="1" color="#999999">The Tenth Doctor, "Blink"</font></p> </div>

 

[tony873004]

The acceleration due to gravity of the Sun is actually more than twice as strong as Earth's at the Moon's orbit.<br /><br />a = GM/r^2 (inverse square law)<br /><br />a(sun) = (6.67e-11 * 2e30) / (150000000000m)^2 = 0.00592888888888889 m/s^2<br />a(earth) = (6.67e-11*6e24) / (384000000m)^2 =0.00271402994791667 m/s^2<br /><br />a(sun) = 2.18 a(earth)<br /><br />The Moon receeds, yes, but Earth will tidally lock to the Moon before it has a chance to escape, and then it will actually start spiraling in towards Earth. Very, very slow process though.<br /><br />Although the Earth is receeding from the Sun for a variety of reasons, it will not receed more than a few million kilometers (compared to its hundreds of millions of km distance) over the life of the solar system. It is stable.

 

[l3p3r]

Can the stressing and warping of the Earth itself from the gravity of the moon result in a reduced orbital velocity (conservation of momentum?) Is that the same thing that you are referring to with regard to the moon receeding? <div class="Discussion_UserSignature"> </div>

 

[bonzelite]

that is extremely fascinating info. then what will happen to the earth's rotation upon the moons farthest distance from the earth? how will it affect the tides and the axis?

 

[mikeemmert]

Here, read this:<br /><br />http://en.wikipedia.org/wiki/Hill_sphere<br /><br />The Hill sphere is closely related to the Lagrange points and in fact, the L1 and L2 points are two points on the Hill sphere.<br /><br />Somewhere between the Earth and the Sun is a point where the gravitational forces of the two bodies are equal. However, since the Earth is orbiting the Sun, centrifugal force will throw anything placed there into the Earth. However, if you move closer to the Sun along the Sun/Earth line, centrifugal force will become weaker, since there is the same rpm but a shorter arm. On the other side of the Earth, the increased centrifugal force from the longer arm (same rpm) is countered by the combined force of the Sun and the Earth's gravity. These are the L1 and L2 points. The force vectors don't point anywhere, since the forces cancel and there is a net force of zero.<br /><br />Inside the Hill sphere, the force vectors point towards the Earth. Any satellite within the sphere is also orbiting the Sun. Thus, centrifugal force cancels the Sun's gravity and orbital motion around the Earth is required to cancel the Earth's gravity.<br /><br />If this confuses you, then ignore what I wrote and read the link.

 

[thalion]

The Sun's gravitational pull is stronger on the Moon than Earth's, but the mutual tides between the Earth and Moon are much greater, which is why we still have a stable satellite orbit.<br /><br />The Moon's orbital stability has its limits; if its orbit were tilted 90 degrees to the ecliptic, we'd probably lose it in a year or so.