Brief answer: About 65 days.
Detailed answer: If what the earth stopped to you can happen on its orbit? Do not worry, this is impossible to happen actually. The earth had circled the sun to move nearly 5 billion years, without any serious destruction, and also won't stop revolution in visible future.
But if the earth is really on orbit,stop revolution how be met? Be similar to a ball that releases on tower needle to be able to bear down on quickly the ground, the earth also will begin to bear down on quickly the sun. The time that allows our computation to bump.
Direct calculative method is difficult. Because the earth leaves the sun closer and closer, the gravitational force between them is larger and larger, earthly acceleration is so rapidder, this involves integrated on the computer gravitational force, but this is more troublesome.
Contrary, here should apply general to force law. Planetary orbit is elliptical, the sun is on a focus. Current, the earth is close to a circle very much around the orbit of the sun, radius is 1 astronomical unit (it is 150 million kilometre about) .
Earthly annual won't leave the sun too close to perhaps leave the sun too far. Contrary, if we imagine the earth has the track of ellipse of a height, we can see different picture. It is slow that the object on elliptical orbit nods motion in the furthest on orbit, but the rate that they fall when be close to is rapidder and rapidder, the sidespin after be being circled finally turns, return the place that they begin afresh.
Why is this very important? Our earth (stopped on its orbit) go up in an elliptical orbit now, this is a very special elliptical orbit, what ellipse is become to cross the sun by fold is linear, but it or an elliptical orbit. This orbital radius is elliptical half, call half long axis, the half that is apart from with the sun at present namely.
Because we understand half long axis, can use general to force the 3rd law, it grows orbital partly axis and orbit cycle contact:
Go up in type, p is orbit cycle, a is half long axis, g is gravitation constant, m is the quality of the sun.
In half long axis the previous generation joins 0.5 astronomical unit, we discover orbit cycle is 129 days. This number is the time that finishs place of a whole course to need, because the half of this number will tell us,need how long to the half orbit of the sun from the earth. So the earth needs ability about 65 days to arrive at the sun.
