Thursday, November 17, 2022

➖ The Laws of Planetary Motion ➕

Tycho Brahe’s accurate observations of planetary positions provided the data used by Johannes Kepler to derive his three fundamental laws of planetary motion.
Kepler’s laws describe the behavior of planets in their orbits as follows:

(1) planetary orbits are ellipses with the Sun at one focus;

(2) in equal intervals, a planet’s orbit sweeps out equal areas; and

(3) the relationship between the orbital period (P) and the semimajor axis (a) of an orbit is given by 
P2 = a3 
(when a is in units of AU and P is in units of Earth years).

Thursday, November 3, 2022

✂ The Search for Extraterrestrial Intelligence

Some astronomers are engaged in the search for extraterrestrial intelligent life (SETI). Because other planetary systems are so far away, traveling to the stars is either very slow or extremely expensive (in terms of energy required). Despite many UFO reports and tremendous media publicity, there is no evidence that any of these are related to extraterrestrial visits. Scientists have determined that the best way to communicate with any intelligent civilizations out there is by using electromagnetic waves, and radio waves seem best suited to the task. So far, they have only begun to comb the many different possible stars, frequencies, signal types, and other factors that make up what we call the cosmic haystack problem. Some astronomers are also undertaking searches for brief, bright pulses of visible light and infrared signatures of huge construction projects by advanced civilizations. If we do find a signal someday, deciding whether to answer and what to answer may be two of the greatest challenges humanity will face.

Sunday, September 11, 2022

Gravity

 Once Newton boldly hypothesized that there was a universal attraction among all bodies everywhere in space, he had to determine the exact nature of the attraction. The precise mathematical description of that gravitational force had to dictate that the planets move exactly as Kepler had described them to (as expressed in Kepler’s three laws). Also, that gravitational force had to predict the correct behavior of falling bodies on Earth, as observed by Galileo. How must the force of gravity depend on distance in order for these conditions to be met?

The answer to this question required mathematical tools that had not yet been developed, but this did not deter Isaac Newton, who invented what we today call calculus to deal with this problem. Eventually he was able to conclude that the magnitude of the force of gravity must decrease with increasing distance between the Sun and a planet (or between any two objects) in proportion to the inverse square of their separation. In other words, if a planet were twice as far from the Sun, the force would be (1/2)2, or 1/4 as large. Put the planet three times farther away, and the force is (1/3)2, or 1/9 as large.

Wednesday, August 24, 2022

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➖ The Laws of Planetary Motion ➕

Tycho Brahe’s accurate observations of planetary positions provided the data used by Johannes Kepler to derive his three fundamental laws o...