Kepler’s laws for solar system.  Explain astronomy really very interesting.  Because  You will learn. About Earth motion elliptical orbit. planetary motion in this topic.

Solar System

Kepler's laws | elliptical orbit astronomy solar system

How does planets,  motion around the Sun ? Why planet motion,  around the Sun ? Why every planet motion,  in different elliptical path ? What do you think,  about the Sun Motion.  All hidden concepts,  for planets motion, I will discuss in this topic. In simple way , So lets start .


Great astronomer mathematician Kepler


 

Kepler Astronomer German

Kepler a German mathematician.  He was assistant astronomer Tycho Brahe.  Kepler lived in an era.  when there was no clear distinction,  about Astronomy and Astrology . But there was a strong,  division between astronomy (mathematics) and Physics (Natural philosophy).

Kepler also incorporated religious arguments.  And reasoning into his work,  Motivated by the religious conviction, and belief that God has created the world.  According to an intelligible plan,  that is accessible,  through the natural light of reason.


Astronomy for planet motion


When Kepler described his new astronomy.  About celestial Physics. Then Kepler first major astronomical work.  Demonstrating the periodic conjunction of Saturn and Jupiter planets.  He realized that regular polygons,  bound one inscribed and one circumscribed,  circle at definite ratios.

He provided information, about the universe  on the basis of geometry . Kepler found that,  the spheres of planet is placed,  an intervals according to the relative sizes of each planet’s .  Assuming the planets is moving around the Sun.

Kepler was thinking . he had revealed,  God’s geometrical plan for the universe. Kepler provided,  three beautiful law’s,  for planets motion . One the observation done.  i will discuss these laws in this post . It was ancient believe,  that Earth is centre of the Universe,  and all other planets,  including the Sun . Moves around the Earth.

But later ,  Galileo declared that Sun is the Center,  of the universe.  And all other planets,  including the Earth moves around the Sun.

Why all Planets moves around the Sun ?

The mass of the Sun,  is very very large,  in the solar system.  in other words,  you can say,  Sun has 99% of  solar mass system.  And  rest 1%,  of mass is for other planets. 

Due to Sun heavy mass .  its gravitational force,  attraction is very very large.  So all other planets, are moving around the Sun.  All planets are bounded. with negative energy to Sun.  Now you can ask,  due to large gravitational force attraction,  of the Sun,  all planets should attracted towards the Sun.  And collapse with the Sun . But this does not happen .


Centripetal force rotate planets

Well this does not happen. Due to centripetal force,  balanced by gravitational force attraction. Just like,  moon does not fall on the Earth.  Actually moon falls, towards the Earth.  But due to centripetal force attraction.  And Earth motion, Moon goes into circular motion.  Around the Earth.  for hidden concept of satellite orbital.  You can refer,  previous post satellite orbital velocity


Why all planets move in different elliptical path ?


The reason for elliptical path,  depends  mainly on three factors.  Mass, velocity and distance.  Then Gravitational influence is determine.  take an example,  for the Sun and the Earth.  since mass of the Sun , is very very large.  than mass of the Earth.

So the common centre of mass . for these two bodies,  is called barycentre.  Which will be near,  to the heavy mass. And both body,  will move  around this barycenter, as a centre point.


Elliptical orbit is due to barycenter

Earth and Sun moving velocity is different.  So sometime,  gravitational influence,  between these two bodies , will be more . due to different velocity,  then Earth will go closer,  to the barycentre.  That is near the Sun.

Sometime gravitational influence,  will be less,  then Earth will far,  from the barycentre.  So here barycentre,  is the distance for these two bodies.  which is changing,  according to time changes,  and hence every planets,  moves in an elliptical path.

If both object,  mass and velocity , become same.  then it will move in a circle . rather than elliptical path.

Every planets have different path . Due to different barycenter,  for all planets .  in the solar system,  and every planet will move around,  its own barycentre.  Hence every planets , have different elliptical path.  In the solar system.


What does the Sun revolve around ?


This is Very interesting,  in Solar system.  All planets move around the Sun.  But do you know.  what does the Sun revolve,  around ?  Well you will know,  this question answer.  in this topic.  see the below picture.

 

super massive black hole

First you should know, where is the Sun stable,  in this universe.  see the above picture,  moving Galaxy,  is spread in one lakh light year distance .

And Sun is,  about 30 thousand light year , from the super massive black hole.  centre in the Galaxy.  as shown in the picture,  at this location.  the Sun is stable.


Super massive hole of Solar system

Super massive black hole,  is biggest black hole.  it is in every Galaxy.  its mass is very very huge . million times of the Solar system.  All the element present,  in the Galaxy,  including Sun,  stars moves , around the super massive black hole.

And one day , every element of the Galaxy,  will be consumed.  by this super massive black hole.  and will be compress,  all element in this hole . But it will take,  billion of years.

Hence the Sun is moving,  around the super massive black hole,. it is important to know,  that not only the Sun,  but whole solar system . moves around the super massive black hole.

The Sun rotate,  about its own axis , time taken 25 days, relative to Earth.  means one day at Sun,  will be equal to 25 days of the Earth.


Kepler’s Laws of planetary motion


Kepler was the first scientist, who does foundation for gravitational force , action between two massive bodies, on the basis of mathematical data observation,  for planets position and motion in the universe. data collected from Tycho Brahe observation done.

Actually Kepler was not able to explain,  the cause of planetary motion, means why planets do motion in such a way, he was having the mathematical data proof,  but unable to explain the cause.

So later this law’s of gravitation  published by Newton . with cause and proof. But you should remember, gravitational force foundation given by Kepler. Hence you will learn all three Kepler’s laws .

First Law of Kepler’s

First law of Kepler’s explain, about law of orbits. Which state that any planets or stars moves,  in which path, Kepler told that it moves in a closed path,  then closed path may be circle, ellipse, square . close path is such that, which starting from one initial point,  and finally reached at initial point, that is closed path.

Hence Kepler told that, planets moves around the Sun, in a closed path .and that shape is ellipse, not a circle so the path is elliptical orbit.

 

Kepler's first law

Orbit law

See the above picture of ellipse, you know ellipse has two foci as shown in picture, A simple property of ellipse is the sum of the distance r1 and r2 from any point on ellipse is always remain a constant value.

Which is (r1+r2) = constant now where will be the Sun ? Kepler told Sun may be either of foci 1 and foci 2 not at ellipse centre and planets are moving around this as shown in elliptical path.


Kepler’s first law statement : All planets moves in elliptical orbit, with Sun at one foci of ellipse .


Kepler’s second law

Kepler’s second law is about, law of Area,  see the below picture.  planet is moving in elliptical path here r1 ,r2 and r3 are called position vector. The area covered in one second is called areal velocity v1, v2 and v3 are areal velocity.  

                                                                              Kepler second laws

Kepler’s law told that, area covered in one second,  at any point of path is equal. So three area shown in figure in one second are equal.


Kepler’s Second law statement : Areal velocity of planet, around the Sun remains constant.


Areal velocity = Area swept by position vector in one second = 1/2*v1*r1  ( for small angle r1 is taken as height ) here base of triangle is taken in one second so using formula s = vt = V1*1 = v1 . According to this law if the areal velocity is same in one second then you can write.

1/2*v1*r1 = 1/2*v2*r2 = 1/2*v3*r3  = constant 


Areal velocity concept

v1*r1 = v2*r2  or v1/v2  = r2/r1 or  V is inversely proportional to r , Hence it gives a conclusion that if radius will be small then velocity will be large and if radius is large then velocity of planet will be slow. this is very important conclusion.

Now you can tell which velocity is fast in v1 and v2, Well i hope your answer will be v1 because radius is small r1 than radius r2. Hence you can think when planets moves around the Sun then which time velocity is fast ?

well when planet is nearest to the Sun it moves fast and when far away from the Sun the moves slow.

Kepler’s third law    

Kepler’s third law is law of time, now till you were studying about only one planet, but many planets moves around, the Sun in different orbit, and all have different orbit time. So Kepler established a relation between orbital time and distance from the Sun. 


Kepler’s third law statement :  For different planets in motion, square of time is proportionate cube of distance . 


T²/r³  = constant, where T is orbital time, of planet and r is distance from the Sun. It is a very important number.

Kepler’s Constant 

All the planets, which are moving around the Sun . if you will calculate T²/r³ it will give you a same value.  

T²/r³ = 2.95×10⁻³⁴ y²m⁻³  so from this value, you can calculate, any planet orbital time period .if distance is given or if distance is given , then you can calculate orbital time period of that planet.


I will continue in next post, with more hidden concepts of Physics topic. I hope that ,you have enjoyed learning Kepler’s laws. I want your feedback, comments, and share on social media . Learn more and grow, Thanks for sharing.