Mathematics and Astronomy
Mathematics is the language in which God has written the Universe -Galileo Galilei
Ever thought how meteorologists calculate the dates of meteor shower? or how future rovers and missions are planned? Like c’mon it can’t be like a meteor texting it’s arrival date nor is there someone to sit on another extra-terrestrial object who’s giving the updates(sorry for my hopeless and wild imaginations). Yes, you guessed it right! It’s maths!! Thanks to this Queen(read Mathematics)even extraction of oxygen from moon rocks is possible. Yaaaaaa!!
Calculations in a nut-shell
•SIZE CALCULATIONS: The SUN has a diameter of 1,392,000km whereas that of EARTH is about 12,742km. Hence the SUN’S diameter is about 109 times greater than the earth’s diameter. Whereas the moon is about a quarter of EARTH’S diameter.
•DISTANCE CALCULATIONS: The SUN is about 149 million km away from the EARTH. The MOON is about 384,403km away from EARTH.
•The SUN’S diameter is about 400 times that of EARTH & it is also about 400 times farther away. At this particular period in EARTH’S history, the sun is about 400 times larger than that of moon. Hence the sun and moon seem to be of same size from EARTH.
An important quantity in planetary exploration is the distance to the horizon. It is a application of “Geometry” It’s calculation depends on the diameter of a planet and the height of the observer above the ground. Helps in determining the height of a transmission antenna for proper reception to a specified distance. It’s an important feature for lunar explorers as moon has no ionosphere for bouncing the radio signals over the horizon
•The MOON is slowly pulling away from EARTH at the rate of 3.8cm per year. The following formula predicts the distance of the moon after a period of 2 billion years (approx.)
• D(T) = 38T + 385,000; where T is the elapsed time from today in millions of years. D is the distance in km
•The diameters of sun and moon are very different. Inspite of that they appear almost the same size( as we have discussed before). Hence the astronomers for their convenience use the concept of angular measures of arcseconds.
v1 degree= 60 arc minute
v& 1 arc minute= 60 arc seconds. Hence this formulation also helps in finding the approximate sizes.
•CRATER FORMATION is another important issue for Lunar Mathematics worth mentioning. Any source energy in any direction is not worthy enough for forming a crater! Physicists-Mathematicians have been working on this for years and they’ve come across this following formulation (an approximate answer)
• E = 4.0 * 1015 D3 Joules ; where D is the crater diameter in km ;
•A crater can easily be assumed as a cylinder. Hence the volume of water present in each crater can be derived using the formula of volume of a cylinder i.e V=R2h; V,R,h being the usual parameters
- Total Solar Eclipses occur when the angular sizes of sun and moon becomes the same. We know (discussed earlier) the moon is moving farther away with time. Hence there will eventually be a time when the angular sizes of moon,earth and sun will no longer match. Hence no Total Solar Eclipse!
Wanna look at some AMAZING calculations on Astronomy by some famous name?
#HIPPARCHUS’S CALCULATION: Hipparchus gave an approximate value for the distance between Earth and Moon during an eclipse ( A Total Solar Eclipse at Syrene and a partial eclipse at A lexandria) He also measured the precession of Earth’s rotation axis, precession of equinoxes. Using his knowledge of sperical angles to the problem denoting location of Earth.
#ARISTARCHUS’ CALCULATION :He (around 270 BC) derived the lunar distance from the duration of a lunar eclipse (It was mainly accepted that the Earth was a sphere at that time). He got the lunar distance as 19 Re. Aristarchus’s work on the motion of the Earth has not survived, but his ideas are known from references of Greek mathematician Archimedes, Greek biographer Plutarch and many others.
#CLAUDIUS PTOLEMY’S CALCULATION (150AD) : Ptolemy knew about Moon’s parallax. He invented the “Parallastic Instrument”. He used geocentric positions of Moon and used them in observations for the lunar distance determination. This parallax technique was known to Hipparchus but he didn’t use it in his calculation. He got the lunar distance to be 59Re.
***GEOCENTRIC or Earth-centred. Ptolemy thought all objects including the planets, Sun, Moon and Stars orbited Earth.
Well, it’s not even near the END.
Mathematics also helps to reveal the Size and distance calculations of sun earth and moon. Examples of some applications and questions which may arouse readers are as follows
•Why the sun and moon seem to be of same size from earth?
•Calculating the distance to the horizon
•Slope-Intercept Graphing: The Moon’s Orbit
•Assumption of sizes through angles
•Crater formation
•Amount of water present on a surface
- Is it possible to calculate The LAST TOTAL SOLAR ECLIPSE?
I’ll cover them in my upcoming stories till then SAYONARA!!
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Information credit: Google, www.wikipedia.in
Image credit: ImageSearchMan
