osito's space research

Copernicus may have shown us that the heliocentric model was a much tidier explanation for the planetary motions as seen from Earth, but it was still just as bad as the geocentric model at predicting them. It wasn’t until Johannes Kepler altered Copernicus’ heliocentric model so that the planets orbited the sun in ellipses that we were able to accurately predict the planetary movements. Based on the data gathered from his colleague Tycho Brahe he came up with his three laws of planetary motion.

1. The Law of Orbits: All planets move in elliptical orbits with the sun at one focus.

What is an ellipse? Not to be confused with ovals, ellipses have a precise mathematical definition like circles.

(http://www.qrg.northwestern.edu/projects/vss/docs/space-environment/2-how-ellipse-is-different.html)

An ellipse is defined as the set of all points on a plane the sum of whose distances from two fixed points (foci) in the plane is a constant. A circle can be seen as a special case of an ellipse, where the two foci coincide at the origin. You can imagine the sun at one of these foci and Earth orbiting it along the ellipse.

2. The Law of Areas: A line that connects a planet to the sun sweeps out equal areas in equal time.

(https://www.pas.rochester.edu/~blackman/ast104/kepler11.html    (http://physics.weber.edu/amiri/physics1010online/WSUonline12w/OnLineCourseMovies/CircularMotion&Gravity/reviewofgravity/ReviewofGravity.html)

With this law, we see that the further a planet is from the sun the slower its movement is. From a vantage point above the Sun’s north pole, Earth appears to orbit in a counterclockwise direction around the sun. It speeds up in its passage from the aphelion to the perihelion and slows down in its passage from the perihelion to the aphelion.

3. Law of Harmonies:  The square of the period of a planet's orbit is proportional to the cube of its semimajor axis (longest radius); T² ∝ R³

(https://www.wwu.edu/skywise/a101_kepler.html)

We can use this law to find out the period of any planets orbit just by knowing the distance from it to the sun in A.U.’s (astronomical units) or vice versa. Newton would go on to develop this equation further with his Law of Gravitation.

T(Earth) = 1 year, R(Earth) = 1 A.U.

(https://www-spof.gsfc.nasa.gov/stargaze/Kep3laws.htm)

More info:

http://hyperphysics.phy-astr.gsu.edu/hbase/kepler.html#c3

The sun is the heart of our solar system. That is common knowledge today but for a long time humanity held the proud idea that they on earth were at the center. This geocentric model was based on the ideas of the ancient Greek philosophers Plato (382-322 BC) and Ptolemy (100-170 AD). They believed that the Earth was stationary at the center of everything and anything visible in the night sky orbited around it in perfect circles. But this couldn’t explain certain observations. Primarily the movement of planets, which to the Greeks were asteres planetai or wandering stars. The retrograde motion of Mars for instance, where it seems to loop back onto itself or zig-zag through the night sky about every two years.

(https://mars.nasa.gov/allaboutmars/nightsky/retrograde/)

But in order to preserve their ideal that planets orbit Earth (not yet understood to be a planet itself) in perfect circles while also accounting for the retrograde motion of Mars, Ptolemy added more circles. In this system, the planets orbited in small circles called epicycles around on a point which orbited larger circles called deferents that were centered on the stationary Earth.

 (http://homepages.uc.edu/~hansonmm/ASTRO/LECTURENOTES/F01/Lec4/Page3.html)

But even this didn’t cut it and even more circles were added; epicycles upon epicycles. This increasingly convoluted geocentric model was the accepted model of the universe for the next 1,500 years until Nicolaus Copernicus (1473-1543) came along. Copernicus pointed out that the math was a lot simpler if you placed the Sun at the center of the universe. We call this the heliocentric model.

(http://abyss.uoregon.edu/~js/ast121/lectures/lec02.html)

In the heliocentric model of Copernicus, the retrograde motion of planets is explained naturally. Retrograde motions occur naturally if planets further from the Sun move more slowly. Earths orbital radius (distance from the sun), for example is 1 A.U. (astronomical units) and its orbital speed is 30km/s. Mars’ orbital radius is 1.5 A.U. and orbital speed is 24km/s. As Earth “laps” Mars, Mars appears to go backward as seen by observers on Earth.  

(http://www.astronomy.ohio-state.edu/~depoy/Astro161/Notes/class5.pdf)