TYCHO BRAHE'S UNIVERSE

Tycho Brahe was considered the last and the greatest astronomer prior to the invention of the telescope. At the age of 30, he was able to establish his own astronomical observatory in Hven,located between Denmark and Sweden under the patronage of Danish King Frederick the II.

​He accurately measured and recorded the positions of the sun, the moon, and the planet for 20 years. realizing that his data did not fit into the models of Ptolemy and Copernicus, he proposed his own model of the universe. In his universe, the sun orbited Earth, while the other planets orbited the sun.

Kepler's third law is known as the Law of Harmonies. It states that the squares of the periods of the planets are proportional to the cubes of their mean distances from the sun.

Period is the time it takes to make one complete revolution around the sun. In symbols,

(T1/T2)²=(d1/d2)³

where T1 and T2 are the periods, and d1 and d2 are the mean distances of planets 1 and 2 from the sun.

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​Planetary distances from the sun are normally expressed in astronomical units, AU. One AU is equal to the mean distance between Earth and the sun.

1 AU= 149597871 kilometers

= 150000000 kilometers

​The period of other planets is usually compared to that of Earth, which is a year. a year is equal to 365.25 days.

​SELF-TESTS: What are the three laws of Kepler on Planetary Motion?

​SAMPLE PROBLEM 1.1

The mean distance of Mercury from the sun is o.3871 times that of Earth. Find the Ratio of Mercury's period to Earth's p eriod.

SOLUTION: Let subscripts 1 & 2 refer to Mercury and Earth respectively. Using Kepler's Law of harmonies.

(T1/T2)² =(d1/d2)³

T1/T2 =(d1/d2)^3/2

(0.3871/)^3/2

^=0.2408

​PRACTICE EXERCISES 1.

The planet Vulcan was postulated to exixt in an attempt to explain the precession of Mercury. How long will Vulcan make one complete revolution around the sun if its distance from the sun is two-thirds that of Mercury? You may use data from sample problem 1.1