Definition, Formulas, and Example Problems

CNN Indonesia

Wednesday, 17 May 2023 13:00 WIB

CNN Indonesia —

Talking about astronomy, certainly cannot be separated from Kepler’s Laws. Kepler’s law discovered by the German mathematician and astronomer, Johannes Kepler around the 16th century.

To make it clearer, see explanations, formulas, and example questions about Kepler’s Laws.

Initially, ancient humans believed in geocentric understanding which confirmed that the earth was the center of the universe.

But then the geocentric theory was challenged after the emergence of a new theory which stated that the center of the solar system was the sun or the heliocentric theory coined by Nicolaus Copernicus.

This theory is supported by the statement of Johannes Kepler who is a mathematician and astronomer through his book entitled ‘Astronomia Nova’ in 1609.

Kepler said that the planets in the solar system revolve around the sun in accordance with their elliptical orbits. Kepler’s statement is what later became the beginning of Kepler’s Laws 1, 2, and 3.

Broadly speaking, Kepler’s Laws are laws that study the motion of planets in the solar system.

Definition and Sound of Kepler’s Laws 1, 2, and 3

The following is an explanation and the sound of Kepler’s Laws, quoted from the Class X Physics Learning Module entitled Newton’s Laws of Gravity and Kepler’s Laws (2020).

Kepler’s 1st Law

Kepler’s 1st law contains the motion of the planets in the solar system. Kepler’s 1st law states, “All the planets move in ellipses around the Sun with the Sun at one focus of the ellipse.”

Kepler’s calculations explain the orbits of the planets moving around the sun. Kepler concluded that planetary orbits are ellipses. In this orbit, there are two foci, with the sun at one focus of the ellipse.

The shape of the orbit on each planet is different, depending on the eccentricity value. This eccentricity value is from 0 to 1. If the value is closer to 0, then the trajectory of the planet will be circular. If it gets closer to number 1, then the trajectory of the planet is more elliptical.

Kepler’s 2nd Law

Kepler’s 2nd law states that the sweeps of planets are equal in the same period.

Kepler’s 2nd Law reads: “An imaginary line joining the Sun and a planet sweeps out equal areas of the arc in equal time intervals.”

Kepler’s 2nd law states that when a planet is farthest from the sun, its orbital speed will be slower. Conversely, the closer a planet is to the sun, the faster its orbital speed increases.

Kepler’s 3rd Law

Kepler’s 1st and 2nd laws were published in 1609 based on observations made by Brahe. Then Kepler looked for relationships between the motions of the different planets and calculated the motions of these planets.

Then in 1619, Kepler managed to find this relationship and poured it through Kepler’s 3rd Law.

Kepler’s 3rd law describes the ratio of the radius to the period of a planet’s orbit which reads, “The ratio of the square of the period to the cube of one half of the long axis of the ellipse is the same for all planets.”

Kepler’s Laws

Kepler’s Law formula is written with the equation: (T1/T2)² = (R1/R2)³.

With understanding:

T1 = Period planet 1
T2 = Periode planet 2
R1 = Distance of the first planet from the sun
R2 = Distance of the second planet from the sun

Examples of Kepler’s Law Problems

Planet A and planet B each orbit the sun. The ratio of the distance between planet A and planet B with the sun is 1:4. If the period of planet A is 50 days. What is the period of planet B?

Is known

RA : RB = 1:4

TA = 50 hari

Answer

TA/TB)² = (RA/RB)³

(50/TB)² = (1/4)³

TB = √(50)2 x 64

TB = 50 x 8

TB = 400 days

So the period of planet B is 400 days.

(ahd/fef)