Math Problem: How Long Until the Earth Falls Into the Sun?

Our earth has orbital motion, revolving once around the sun in about 365 days. Suppose that this orbital motion suddenly stopped completely, but everything else remained the same. How long would it take for the earth to plunge along a straight line into the sun? [...] Kepler's law applies to planetary orbits, whether they be of circular, or elliptical shape. It says that T22/T12 = R23/R13, where T is the period of an orbit and R is its semi-major axis. The semi-major axis is the average...

 Newton on the Power of Gravity

As he sat alone in a garden, he [Isaac Newton in 1666, age 24] fell into a speculation on the power of gravity; that as this power is not found sensibly diminished at the remotest distance from the centre of the earth to which we can rise, neither at the tops of the loftiest buildings, nor even on the summits of the highest mountains, it appeared to him reasonable to conclude that this power must extend much further than was usually thought: why not as high as the moon? said he to himself; an...

 Fear of Comets

When the movement of the comets is considered and we reflect on the laws of gravity, it will be readily perceived that their approach to Earth might there cause the most woeful events, bring back the deluge, or make it perish in a deluge of fire, shatter it into small dust, or at least turn it from its orbit, drive away its Moon, or, still worse, the Earth itself outside the orbit of Saturn, and inflict upon us a winter several centuries long, which neither men nor animals would be able to be...

 Stable Orbits are Impossible in More Than Three Dimensions

If one assumes that a few hundred million years in stable orbit are necessary for planetary life to evolve, the number of space dimensions is also fixed by our existence. That is because, according to the laws of gravity, it is only in three dimensions that stable elliptical orbits are possible. Circular orbits are possible in other dimensions, but those, as Newton feared, are unstable. In any but three dimensions even a small disturbance, such as that produced by the pull of the other planet...