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...

 Nemesis

But why should comets become more likely to hit us every million years? Here we launch ourselves into deep speculation. It has been suggested that the sun has a sister star, and the two orbit each other with a periodicity of about 26 million years. This hypothetical binary partner, which has never been seen but which has nevertheless been given the dramatic name Nemesis, passes, once per orbital rotation, through the so-called Oort Cloud, the belt of perhaps a trillion comets which orbits the...

 Newton's Perspective on the Universe

As all regions below are replenished with living creatures, (not only the Earth with Beasts, and Sea with Fishes and the air with Fowls and Insects, but also standing waters, vineger, the bodies and blood of Animals and other juices {49} with innumerable living creatures too small to be seen without the help of magnifying glasses) so may the heavens above be replenished with beings whose nature we do not understand. He that shall well consider the strange and wonderful nature of life and th...

 Astronomers Inventing Planets Based on Circumstantial Evi...

It happened three times in the past that theoretical astronomers invented a new planet on the basis of indirect and circumstantial evidence. The first time was in 1845 when Adams and Leverrier independently deduced the existence of the planet Neptune from the perturbations which it had produced in the motion of Uranus. One year later, Neptune was duly discovered in the predicted region of the sky. The successful prediction of the presence of an unseen planet was one {31} of the great events...

 Nemisis

Piet Hut, another Dutch astronomer fifty years younger than Jan Oort, decided to take seriously the possibility that comet showers are periodic. If they are periodic, the theory that they are caused by the random passing-by of alien stars cannot be right. If showers are periodic, they must be explained by a different theory. Piet Hut and his friend Rich Muller found an alternative theory to explain the periodicity in case it turns out to be real. The alternative theory is called Nemesis. Neme...

 The Comet Loss Cone

To understand why comet showers occur, we go back to the Oort Cloud. The theory of comet showers was worked out by Jack Hills, an American physicist now at Los Alamos. He realized that the movements of the comets in the Oort Cloud are not entirely random. Comets in the cloud are generally moving in random directions, but if a comet happens to be moving in an orbit almost exactly toward the Sun, it will not survive for long. A comet in an orbit coming close to the Sun may get boiled away and d...

 So Many Objects in Space, Why isn't it Filled with Light?

So numerous are the objects which meet our view in the heavens, that we cannot imagine a point of space where some light would not strike the eye;—innumerable stars, thousands of double and multiple systems, clusters in one blaze with their tens of thousands of stars, and the nebulae amazing us by the strangeness of their forms and the incomprehensibility of their nature, till at last, from the limit of our senses, even these thin and airy phantoms vanish in the distance.

 Astronomy affords the most extensive example of the conne...

Astronomy affords the most extensive example of the connection of physical sciences. In it are combined the sciences of number and quantity, or rest and motion. In it we perceive the operation of a force which is mixed up with everything that exists in the heavens or on earth; which pervades every atom, rules the motion of animate and inanimate beings, and is a sensible in the descent of the rain-drop as in the falls of Niagara; in the weight of the air, as in the periods of the moon.

 Hydrogen Levels in the Universe

Our Sun is significantly enriched, having formed when the Universe was more than 9 billion years old in the plane of a spiral galaxy, one of the most enriched places in the Universe. Yet, when our Sun formed, it was still made out of — by mass — 71% hydrogen, 27% helium, and about 2% “other” stuff. If we convert that into “number of atoms” and treat the Sun as typical of the Universe, that means, over the first 9.3 billion years of the Universe, the fraction of hydrogen ha...

 Dyson Spheres

The material factors which ultimately limit the expansion of a technically advanced species are the supply of matter and the supply of energy. At present the material resources being exploited by the human species are roughly limited to the biosphere of the earth, a mass of the order of 5 X 10^19 grams. Our present energy supply may be generously estimated at 10^20 ergs per second. The quantities of matter and energy which might conceivably become accessible to us within the solar system are ...