Kepler’s laws of planetary motion (II)

Kepler’s laws of planetary motion (II)

I will comment directly a fragment from the en.wikipedia link I gave in the previous post of this series, and then I’ll put the link itself again, along with the unedited excerpt.

Planetary acceleration

A sudden sunward velocity change is applied to a planet. Then the areas of the triangles defined by the path of the planet for fixed time intervals will be equal. (Click on image for a detailed description.)

This property for planetary motion is a direct consequence of the second law, the one that says planets must sweep equal areas at the same velocity. This can be misunderstood, because, same sweeping area velocity implies necessarily a change in BOTH linear and angular velocities, in order for the planets to scape attractive forces, as I told you in the previous post about this issue. This is so because planets’ orbits are not circumferencies, but ellipses.

Isaac Newton computed in his Philosophiæ Naturalis Principia Mathematica the acceleration of a planet moving according to Kepler’s first and second law.
  1. The direction of the acceleration is towards the Sun.
  2. The magnitude of the acceleration is inversely proportional to the square of the planet’s distance from the Sun (the inverse square law).
This implies that the Sun may be the physical cause of the acceleration of planets.

Whenever there is a change in the direction of any moving mass there has to be necessarily a change in the moving mass’s velocities (linear and angular, if the mass is moving on a straight trajectory, then the angular velocity is unchanged, and it has no angular acceleration). And a change in velocity (-ies) implies necessarily the existence of an acceleration which is greater when the change in velocity is fast, and weaker when the change in velocity is slow.

So, what happens? Is it that the Earth (let’s obviate the rest of the Solar System Planets) is changing it’s mass constantly, thus arising Lemniscatas like curves all along History since Neolitic? Is it that the Sun varies its mass? Are them both, the Earth and Sun changing constantly their masses to prevent one another from collapsing in an astrophisical crash?

What is it that gives the Earth (and the rest of the planets) the thrust to change its linear and angular velocities in order not to impact against the Sun?

I will tell you (for the sake of redundancy, because if you are reading my posts from long ago, you can anticipate what the next paragraph will be :), [no?] ) : magnetodynamics. This is what happens, magnetodynamics give planets (and their satellites) the thrust to keep dancing in ellipses of different eccentricity into space.

And this (and other astrophysic entities and events) is also why people celebrate some cultural traditional holidays along the year, because when we did not know about physics, some natural phenomena were explained by other means, not being objective, predictable or preventable, such as earthquakes peaks in intensities, or frequency, or dispersion; highest or lowest tides along the year, aroras, or other natural phenomena related to dates, stational, or periodical, as are those of equinoxes and solstices, directly related to where the planet is along its orbit, and how the difference in resulting apparent inclination of the rotation axis when compared to an ideal line orthonormal to the plane containing the Earth’s ellipsoidal trajectory.

(You know? orthonormal is a pompous way to say perpendicular, to the desperation, headache-rising and dismal of all physicists worldwide [students and teachers 🙂 ] some of whom have long ago exclaimed, ‘I resign!’ ).

Newton defined the force acting on a planet to be the product of its mass and the acceleration (see Newton’s laws of motion).
So:
Every planet is attracted towards the Sun.
The force acting on a planet is in direct proportion to the mass of the planet and in inverse proportion to the square of its distance from the Sun.
The Sun plays an unsymmetrical part, which is unjustified (pssst… until some seconds ago… when I though of the question). So he assumed, in Newton’s law of universal gravitation
One) All bodies in the solar system attract one another.
Two) The force between two bodies is in direct proportion to the product of their masses and in inverse proportion to the square of the distance between them.
ONE is because he had to explain the unsymetrical contribution of the Sun in terms of other bodies interferring.
TWO the quantitative form for this statement is based on observations and measurements Newton did in the 17th century on Earth, and also in the differential and integral ways of calculus, which comply ‘at home’, and are a fundamental for classical mechanics, but do not comply accurately in space.

As the planets have small masses compared to that of the Sun, the orbits conform approximately to Kepler’s laws. Newton’s model improves upon Kepler’s model, and fits actual observations more accurately (see two-body problem).

This is because the smaller the mass the weaker the… say ‘stationary echo’, the remnant, the inertia (in terms of kinetics, be it gravitational or magnetodynamical (believe me, that is how electric engines, such as those of mixers, work), so circumferences (which are a particular case of ellipses) prevail upon ellipses.

And the rest of this post is the link and the excerpt themselves without my (un)explanations 🙂 .

 

Kepler’s laws of planetary motions.

‘Planetary acceleration[edit]

A sudden sunward velocity change is applied to a planet. Then the areas of the triangles defined by the path of the planet for fixed time intervals will be equal. (Click on image for a detailed description.)

Isaac Newton computed in his Philosophiæ Naturalis Principia Mathematica the acceleration of a planet moving according to Kepler’s first and second law.

  1. The direction of the acceleration is towards the Sun.
  2. The magnitude of the acceleration is inversely proportional to the square of the planet’s distance from the Sun (the inverse square law).

This implies that the Sun may be the physical cause of the acceleration of planets.

Newton defined the force acting on a planet to be the product of its mass and the acceleration (see Newton’s laws of motion). So:

  1. Every planet is attracted towards the Sun.
  2. The force acting on a planet is in direct proportion to the mass of the planet and in inverse proportion to the square of its distance from the Sun.

The Sun plays an unsymmetrical part, which is unjustified. So he assumed, in Newton’s law of universal gravitation:

  1. All bodies in the solar system attract one another.
  2. The force between two bodies is in direct proportion to the product of their masses and in inverse proportion to the square of the distance between them.

As the planets have small masses compared to that of the Sun, the orbits conform approximately to Kepler’s laws. Newton’s model improves upon Kepler’s model, and fits actual observations more accurately (see two-body problem).

A deviation in the motion of a planet from Kepler’s laws due to gravitational attraction by other planets is called a perturbation.

Below comes the detailed calculation of the acceleration of a planet moving according to Kepler’s first and second laws.’ excerpt from en.wikipedia

Acerca de María Cristina Alonso Cuervo

I am a teacher of English who started to write this blog in May 2014. In the column on the right I included some useful links and widgets Italian is another section of my blog which I called 'Cornice Italiana'. There are various tags and categories you can pick from. I also paint, compose, and play music, I always liked science, nature, arts, language... and other subjects which you can come across while reading my posts. Best regards.
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