Sounds of Kepler's Law
Kepler's Law 1
Kepler's Law 1 is known as the law of elliptical trajectories. Kepler's Law I reads:
"All the planets move in an elliptical path around the sun with the sun in one of the elliptical foci"
Kepler's Law I states the shape of the planet's orbit, but cannot estimate the position of the planet at any one time. Therefore, Kepler tried to solve the problem, which subsequently succeeded in finding Kepler's II Law.
Kepler's Law 2
Kepler's Law 2 discusses the planetary motion which reads as follows.
"An imaginary gads that connect the sun with the planet sweep across the same wide area at the same time interval"
In the same time interval, Ll, Lii, and Liii. from Kepler's II law it can be seen that the speed of the biggest planetary revolution when the planet is closest to the sun (perihelium). Conversely, the smallest planet's velocity when the planet is at its furthest point (aphelium).
Kepler's Law 3
In this law Kepler describes the revolutionary period of each planet that surrounds the sun. Kepler III's Law reads:
The square period of a planet is proportional to the square of its average distance from the Sun.
Mathematically Kepler's Law can be written as follows:
Information :
T1 = Period of the first planet
T2 = Period of the second planet
r1 = distance of the first planet from the sun
r2 = distance of the second planet from the sun
This equation can be derived by combining 2 Newton's law equations, namely Newton's law of gravity and Newton's second law for regular circular motion. Decreasing the formula is as follows:
Newton II Law Equation:
Information :
m = the mass of the planet that surrounds the sun
a = centripetal acceleration of the planet
v = the average speed of the planet
r = the average distance of the planet from the sun
The equation of Newton's law of gravity:
Information :
Fg = Sun's gravitational force
m1 = mass of the sun
m2 = planet's mass
r = average distance of the planet and sun
Supporting Articles: Definition, Formula and Application of the Law of Gravity
Combined the two formulas above so that it becomes:
m2 on the left and m on the right are the mass of the planet so they can be removed.
The length of the path the planet is traveling around the planet's orbital path. The circumference of the planet's orbit can be formulated with 2 x phi x r, where r is the average distance of the planet from the sun. It is known that the average velocity of the planet is the ratio between the circumference of the orbit and the panet period, so that:
The constant k = T2 / r3 also obtained by Kepler was found by means of calculations using Tycho Brahe astronomical data. The results are also the same as those obtained using Newton's second formula above.
Examples of Kepler's Legal Questions
The time required by the earth to circle the sun is 1 year and the average distance between the earth and the center of the solar system is 1.5 x 1011 m. If it is known that the planet's orbital period of Venus is 0.615 years, what is the distance between the sun and Venus?
Known :
Earth period = Tb = 1 year
The distance from the sun to the earth Rm-b = 1.5 x 1011 m
Venus period = Tv = 0.615 years
Asked
Rm-v = ...?
Answer:
example-matter-law clerk-iii
So by using the law of Kepler III the answer is obtained the distance between the sun and the planet Venus is 1,084 x 1011 m (closer than Earth).