# Orbits and oribital decay

We know that the earth's orbit is gradually becoming closer to the sun, inevitably reaching a stage where it will collide with our star.

Why shouldn't the moon behave in the same manner? Why is the moon actually moving away from the pull of the earth every year? I have come to think that it simply has to do with the mass of the earth compared to the mass of the sun. Hence why the moon is moving away from the earth and the earth is moving closer to the sun. But which law do we apply to predict such behaviour? Can Newton's or Einstein's law of gravity mathematically predict this? Could anyone quote the formula involved?

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The Earth is moving away from the Sun because there is always a small amount of energy leakage in the system. The Earth has a certain gravitational potential energy, which is negative by definition = -GMm/R. We define the zero GPE to be at the point of R=infinity. So as the system loses energy R decreases. The energy losses come from tidal interactions with the other planetary bodies, which try to push and pull the Earth in many different directions.

As for the Moon, the tidal interactions here are a bit special because they actually speed up the Moon and hence cause it to move away from the Earth. The Moon causes a significant pull on the Earth which causes tides in the oceans, as you know. The same effect rings true for the rock of the Earth which causes the whole planet to become slightly oblate. This tidal bulge then has a knock-on effect of interacting with the Moon, again through gravity. The effect is such that the Moon speeds up slightly and hence increases it's orbital radius. The equations for tidal interactions are not concise and require a lot of theory. I would recommend you read Solar System Dynamics by Murray & Dermott.

DM, as you know the Earth spins around once every 24 hours or so. The moon circles the Earth about every 28 days. The tidal bulge created by the moon's gravity on the Earth is subjected to the Earth's rotation, and hence this bulge ends up ** ahead ** of the Earth-moon centre line. The effect of this bulge position is that it not only provides a radial force, but also a small tangential one too. This small tangential force on the moon speeds it up, as natski mentioned above, and this causes the moon to move up into a higher orbit.

As for the sun - earth effect, there will be many other planets attempting to create a tidal bulge on the sun, and I don't even know if they actually exist. And if they do exist, I'm not sure if there is any rotation to the sun to create a mis alignment of the centre lines, as there is with the earth - moon, and so I'm not aware of the sun's effect on the Earth's orbit.

Perhaps Natski can explain where this "energy leakage" between the Earth and the sun comes from.

Cross your arms over your chest and spin around (sitting on a rotating desk chair or something similar) then stick your arms out. What happens? you slow down. In a simplified way, a tidel bulge connects two bodies that are gravetationally entangled. Thus, the Earth's rotation slows as it lends its energy to the moon's higher orbit.

Just incase you wanted a really simple answer.

Let me establish something first. Over the next billions of years, the earth will come closer to the Sun. And why is that? Is it because of a deviation in the earth's orbit or because the Sun is gradually becoming larger (Hydrogen converted into Helium), hence engulfing the earth?

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Let me establish something first. Over the next billions of years, the earth will come closer to the Sun.
And why is that? Is it because of a deviation in the earth's orbit or because the Sun is gradually becoming larger (Hydrogen converted into Helium), hence engulfing the earth?
If your talking about the time period from now until the death of the sun then there are many things going on.

1.
At present we are gradually moving away from the sun due to the same reasons that the moon is moving away from us

2.
The earth goes through a 100,000 year cycle (Milankovitch cycles)which changes the shape of the earths orbit.

3 Once the sun has burnt its Hydrogen and starts burning Helium in i believe 5 billion years it will expand so the earth will be closer ?

But i have also heard that the earth could actually move further away from the sun over the next 5 billion years due to less gravity from the sun due to it containing less mass.Not sure how accurate that is though.