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It says earth is almost as old as 1/3 of the universe's age which would mean 4.5 billion years .

So how far has earth moved towards or away from the sun in these 4.5 billion years?

Now perfect balance between the centrifugal force of orbital rotation and sun's gravity is impossible so the earth's orbit should either be slowly decaying inwards or expanding outwards due to difference in magnitude of those opposing forces.

Are we still moving inwards towards the sun or are we still moving away from the sun each year?

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Now perfect balance between the centrifugal force of orbital rotation and sun's gravity is impossible so the earth's orbit should either be slowly decaying inwards or expanding outwards due to difference in magnitude of those opposing forces.

This assumption is incorrect. We could make the same argument about a weight suspended from a spring. Since the force upward from the spring and the gravitational pull on the weight can't be identical, the object must get closer or further from the earth over time.

But this isn't true because the system is in dynamic equilibrium. If the system is out of balance, the weight moves, and that changes the forces on it. The result of the changes is to push it back to the median position. The same thing happens to two objects in orbit about each other.

If an object is moving in such a path that the gravity is greater than the force necessary to maintain a circular orbit, then it will be pulled closer. But this approach increases the speed of the object so much that it will shoot back out to the original location.

Now there are many things that will be able to change the orbit over a long period of time (interactions with other bodies, changes in the mass of the objects, frictional/tidal energy loss, etc.) But without them, the energy in the orbit, and therefore the size of the orbit is stable over time.

Any long-term changes in the earth's orbit is not due to a temporary imbalance in the speed of the planet vs gravitational force, but because of these interplanetary interactions and changes in the solar mass.

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  • $\begingroup$ Ok so how much these farthest and closest distance between the earth and the sun have changed over its lifetime? $\endgroup$
    – user1062760
    Commented Apr 26, 2016 at 20:25
  • $\begingroup$ Unknown. There's no record of the early solar system to compare against. There are several hypotheses that involve the gas giants moving around quite a bit, but no consensus. You could calculate what the effect would be given only the changes in the mass of the sun, but that is expected to be dwarfed by changes from other planets. $\endgroup$
    – BowlOfRed
    Commented Apr 26, 2016 at 20:29

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