Tycho Brahe's detailed naked eye observations of the heavens provided the data that Kepler used to derive his laws of planetary motion. Kepler's laws of planetary made it possible for the first time for humans to understand the paths of the "wanderers" across the sky.
- Kepler's First Law Planets orbit the Sun along elliptical paths, with the Sun at one focus of the ellipse.
- Kepler's Second Law (Law of Equal Areas) The area swept out by the line joining a planet and the Sun is equal for equal intervals of time.
- Kepler's Third Law (Harmonic Law) The square of the orbital period in years equals the cube of the length of the semi major (half the longer) axis of the orbit.
A consequence of Kepler's second law is that planets orbit more slowly the more distant they are from the Sun. The third law enables the period of a planet, comet, or asteroid to be computed once observations establish the length of the semi major axis of its orbit. These laws were among the greatest quantitative achievements of the Renaissance.
Kepler also observed a supernova, only 32 years after Tycho, in 1604. The next supernova visible to the naked eye did not occur until 1987 when a star exploded in the nearby irregular galaxy known as the Large Magellanic Cloud.
Kepler and Galileo were contemporaries, though Kepler was more of a theorist and Galileo was primarily an observer. Galileo was the first to make serious scientific use of the telescope, an instrument which provided observations that challenged the Ptolemaic model of the heavens. (Kepler was unable to afford to purchase a telescope, a prohibitively expensive device at the time, though he was able to borrow one for a summer from a visiting nobleman. Galileo promised for several years to make a telescope for Kepler, but never got around to fulfilling his promise.) Galileo observed craters on the Moon, demonstrating that it was not a perfect, smooth sphere; he also gave the large lunar plains the name of "maria" (seas) because he thought they might be filled with water. He also found that the Milky Way was not a solid band of light but was filled with myriad stars, too small to be resolved by the unaided eye. Another key observation by Galileo was that Venus went through a full cycle of phases, just like the Moon; this was impossible in the Ptolemaic model but was required by the Copernican model, since Venus is between the Earth and the Sun in the latter. But one of Galileo's most important discoveries was of the four largest satellites of Jupiter, now called the Galilean moons. These bodies demonstrated that the Earth was not the only center of motion in the universe, thus refuting one of the important tenets of Ptolemaic-Aristotelian cosmology and physics.
These new observations challenged the Aristotelean notions of motion. Reconciling the new cosmology with the physics of motion required Galileo to study mechanics. From direct observation and careful reasoning, he was able to arrive at the conclusion that all bodies fall at the same rate, if air resistance is negligible. This principle, now called the equivalence principle, is one of the foundations of the general theory of relativity. Galileo also realized that motion might not be easily detectable by observers partaking of that motion, i.e., that motion is relative. This meant it was possible for us to be on a moving Earth, yet unaware of its motion. Galileo never succeeded in working out the full laws of motion. But a few months after Galileo's death, Isaac Newton was born on a farm in
In thinking about the development of life on the Earth, as well as the implications of the Copernican principle. This is discussed in greater detail in this page about the likelihood of
The laws of physics provide the foundation for a particular cosmology. By the same token, discoveries about the nature of the universe must be consistent with the laws of physics. The heliocentric cosmology of Copernicus, as clarified by Kepler, led to the need for a new theory of motion. Newtonian mechanics, in turn, created a new vision for the cosmos, the Newtonian "clockwork" universe. Discoveries made toward the end of the 19th and the beginning of the 20th centuries led to the new physics of Einstein, and, in turn, to the modern Big Bang cosmology.
A question:
Is there other life in the universe? How can we begin to answer that question, in the absence of direct evidence to answer the question in the affirmative? One way is through something known as the Drake equation, named after the astronomer Frank Drake. It is not really an equation to be solved, so much as it is a way of systematizing the unknowns. Here is how it works. Let us say we wish to estimate the quantity N, the number of technological civilizations in the galaxy. Of the n stars in the galaxy, only some fraction fp of them will have planets. Only some average number of planets per star, (H), will be potentially habitable. Of the habitable planets, there is a fraction fl that will develop life. Now of the planets that develop life, how many will develop intelligent life? Use fi for that fraction. Only some fraction of intelligent species ft will develop technology. So given all these things, we can write
N = n × fp × H × fl × fi × ft
Some of these factors are easier to estimate than others. There are about 100 billion stars in the Milky Way so we will use that for n. There now seems to be some direct evidence for planets around other stars, but as yet we still don't know what fraction of stars would have planets. If we are optimistic, then we would take a fraction near one, essentially saying that all stars have planets. What number of planets per star would be habitable? The planets would have to be located at a distance from their star that is neither too hot nor too cold. In our solar system there are three that are potentially habitable, Venus, Mars, and the Earth. Some stars would support fewer, or possibly no, habitable planets. Let's say that, on average, only one in 10 stars with planets has one planet that could support life. What have we got so far?
N = 100,000,000,000 × 1 × 0.1 × fl × fi × ft
This still leaves a lot of potentially life-bearing planets!
The next three fractions are the especially tricky ones. If life can develop, does it? Opinions differ widely on this topic. This is where the issue of whether or not there is life on Mars or on some other body in the solar system has some application. If life developed on both Mars and the Earth and it becomes much more problematic to say that life is incredibly difficult to get started on any given planet. If you believe life is inevitable, given habitable conditions, then make fl =1.
Now, if life forms, does it become intelligent? A difficult question. Life has been around on Earth for billions of years and we (modern humans) came on the scene only in the last 100,000 or so years. And any life on Mars that may have once existed (if it did) died out completely. For purposes of an estimate, let's take the ratio of 100,000 years of humans to 1 billion years of life, giving us 1 in 10,000 planets with life that develop intelligence.
Does intelligent life inevitably develop technology? Good arguments can be made either way. There doesn't seem to be anything particularly inevitable about humanity's rise to technological prowess. Although it happened rapidly once it got going, did it have to happen? Could an intelligent creature stay as a hunter/gatherer or simple tool-user for the entire length of its existence? Who knows? Let's adopt the attitude that intelligence necessarily leads to technology and say that ft = 1. So we have
N = 100,000,000,000 × 1 × 0.1 × 1 × 0.0001 × 1 = 1,000,000
One million planets with technologies!
OK, we stacked the deck by choosing all the optimistic numbers. Go back and put in some numbers of your own. You only have to insert one pessimistic number to drop the number of planets in the Milky Way down to around 1, which would be the Earth. For example, humanity has been technological for only 100 out of its 100,000 years of existence. If you find the thought of a low number of life-bearing planets depressing, that we might be alone in the Milky Way, bear in mind that there are more galaxies in the visible universe, than there are stars in our galaxy. So if there were only one life bearing planet in each galaxy there would still be trillions of life bearing planets. But we will never communicate with or visit other galaxies.
And how likely are life-bearing planets that can lead to intelligent life? Do they require a large moon, such as the Earth has? Such double planets may well be rare, particularly if the Moon formed as the result of a huge impact early in the history of the solar system. Does intelligent life require dry land as well as oceans? What are the odds that the Earth would end up with both oceans and dry land (as opposed to all oceans or all dry land)? We don't really know, but once you start thinking about it, things become rather tricky quite rapidly.
So who knows? But it does tend to make you want treat our planet and its unique inhabitants with some respect. Source : © 2005 John F Hawley
