Skip to main content

What is kepler's 2nd law of planetary motion? Why is kepler's second law important?


Kepler's Second Law, The Law of Equal Areas:

Kepler's second law of planetary motion states that "a line joining a planet and the Sun sweeps out equal areas in equal time intervals". This means that the planet moves faster when it is closer to the Sun and slower when it is farther away. To understand Kepler's second law, it is helpful to think about the concept of angular momentum. Angular momentum is the product of an object's mass, its velocity, and the distance from the object to the center of rotation. In the case of a planet orbiting the Sun, the angular momentum of the planet is constant.

Kepler's second law of planetary motion.


Angular momentum = Mass*Velocity*Distance from Sun to celestial body.

L = MVR

Now, angular momentum is constant (as angular momentum is conserved). Therefore, L and M are constant. R is a variable as the orbit is elliptical in shape (from the first law of Kepler). So, to compensate for the variable R, the velocity V of the planet changes, As R increases V decreases, and vice versa. Hence, keeping the angular momentum constant.

The change in the planet's velocity is what allows it to sweep out equal area in equal time intervals. When the planet is closer to the Sun, it has high velocity and travels a greater orbital distance. When the planet is farther away from the Sun, It has lower velocity and travels a smaller orbital distance in a particular time but the area swept is equal in both cases for that particular time

Kepler's second law has a number of important implications. First. it shows the planets do not move with constant speed throughout their orbits. Second, it shows that the angular momentum of the planet orbiting the sun is constant. Third it shows that the closer the planet is to the sun, the faster it moves.

Kepler's second law is one of the three laws of planetary motion that was first published by Johannes Kepler in 1609. The other two laws are Kepler's first law and Kepler's 3rd law of Planetary motion.

Kepler's law of planetary motion was a major breakthrough in the understanding of the solar system. It provided a mathematical description of the motion of the planet that was consistent with observation. Kepler's law also confirmed the heliocentric model of the solar system, which places the Sun at the center of the solar system and planets orbit around the sun. Kepler's laws of planetary motion are still used today to study the motion of planets, moons, comets, and other objects in the solar system. They are also used to study the motion of stars and galaxies in the other part of the universe.

Geocentric and Heliocentric Model.



Nuances and subtleties to Kepler's second law.

There are a few nuances and subtleties to Kepler's second law that are worth noting.

  •  First, the law only applies to closed orbits and open orbits such as the orbit of a comet does not sweep out equal areas in equal time intervals. 
  • Second. the law only applies to the orbits that are not perturbed by the other objects. The orbits of the planet in the solar system is perturbed by the gravitational pull of other objects or planets. This perturbation causes the planets to move at a slightly varying speed throughout their orbits.
  •  Finally, the law only applies to orbits that are relativistic The effect of special relativity must be taken into account. This causes the planet to move at slightly different speeds throughout its orbits 
Despite these nuances and subtleties, Kepler's second law is a remarkably accurate description of the motion of planets in the solar system. It is a testament to Kepler's genius that his laws of planetary motion are still used today to study the motion of objects in the solar system and beyond.



Labels:

Comments

Post a Comment

Popular Posts

You can never be satisfied if you are not satisfied NOW.

You can never be satisfied if you are not satisfied NOW. One reason for this is that there is no future, no past, no present just NOW, And every feeling, emotion, and dissatisfaction is just the changes in NOW. So if you're not satisfied now, you can never be satisfied ever again. Another reason is that our life will not change as drastically as we think in our imagination, even after we achieve whatever we want, or whatever we think will change our life. There will be changes, but they seem tiny and small over a period of time. So, learning to be completely satisfied with now and not relying on your hopes for the changes in now is the most important skill. And understand this, that there might be a kind of FOMO (fear of missing out) we will always have, and it's not an unrealistic one. Like, if we choose to do business, we are automatically negating all the other possible career options, And it can be applied to any other aspect of life, like marriage. If you get married to on...
Post a Comment
Read more

Gyroplane, A fascinating plane that can become your Taxi.

The aviation industry is full of fascinating and interesting machines with unique designs, capabilities, and mechanisms. Among these Gyroplane or Autogyro holds a unique place as it bothers some features of fixed-wing planes and some features of helicopters and becomes a perfect blend for a low-speed aircraft with high fuel efficiency and better stability and control. using very interesting phenomena like auto rotation to spin its top rotor and produce lift. So in this blog, we will be discussing what is autogyro? how does an autogyro work? and the future of autogyro. What is AutoGyro or Gyroplane? A gyroplane or autogyro (from the Greek word meaning ('self turning'), is a heavier-than-air aircraft that uses a rotor usually to the rare of the fuselage called pusher configuration to produce thrust. Autogyro uses an engine to power its rare rotor, which creates the forward motion of the airplane by pushing the air backward. To produce lift it uses another rotor, which, unlike a h...
Post a Comment
Read more

Heat Engine!

  Heat Engines! Engines are machines designed to convert one form of energy into mechanical energy. But commonly machines that acquire heat from the combustion of fuel and transform a part of this heat energy into mechanical energy are called heat engines or simply engines. One of the greatest advantages of a heat engine is that most forms of energy can be easily converted into heat by different processes than heat engine converts it into mechanical energy. Heat engines can be classified into two major types, as follows: ·      External Combustion Engines. ·      Internal Combustion Engines. External Combustion     Internal Combustion
1 comment
Read more