3.1 Orbits, a Relative View 38

Last modified by MichaelBartmess on 2017/02/27 05:33
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What is an orbit?  First, we must remember that an orbit is an imaginary construct, an invisible path in space that describes the motion of one massive object relative to another.  

An orbit may not be exactly what you think it is.  In our focused existence on this planet we call Earth, we often think -- as did the ancient Greeks -- that the Earth is the center of all things.  In that picture we have, that is based on our daily experience, we think of the moon as rotating around a stationary Earth.  We think of the place we stand as a huge stationary planet and that the moon circles us.

But as the video graphic below shows, in another reality defined by the viewpoint where the center of rotation is the center of mass of the two bodies, the Earth is rotating about the moon as the moon is rotating about the Earth.

This is because gravity, the pull between the two planets is equal and opposite for both bodies.  The gravity of the Earth pulls on the moon and the gravity of the moon pulls on the Earth.

Pluto-Charon_System.gifThis file is made available under the Creative Commons CC0 1.0 Universal Public Domain Dedication

This video graphic shows the Earth and moon circling each other, where the center of the paired rotations is the center of mass of the two systems
 

If you take the logic of the discussion beyond the simple pairing of the Earth and its moon, you soon realize that the same kind of relationship exists between the Earth and the Sun, the Earth and Jupiter, the Moon and Saturn, the Earth and all the moons of Jupiter, the Earth and the planet Mars, the Earth and the closest star, and on and on and on and on ...

In reality, the true reality from the perspective of all masses in the universe, ALL stars and all planets and all specs of dust are exerting a [Could not locate page MichaelBartmess.Force of Earth's Gravity] on ALL other stars and all planets and all specs of dust.  Viewed from the center of mass of any two bodies in the universe, the two bodies can be shown to be rotating about each other.  And ALL the stars and planets and specs of dust are at the same time tugging on all the other stars and planets and specs of dust.  So, in a reality described by the most precise mathematics (beyond our abilities), all these orbits are being slightly perturbed by all the other things simultaneously pulling on each other.  The combined set of all the gravitational effects on the orbits of all things orbiting about each other results in the motions of the universe.  All this combined gravitational effect -- along with each object's momentum -- is the cause of the expansion of the universe astronomers have found in their studies.

You and gravity

An orbit is a dance between two masses, a cosmic relative interaction between all masses in our universe -- between all things -- and an orbit is caused by gravity.

NOTE: many vCalc equations are embedded throughout vCalc descriptive pages like this page.  Even though they may not stand out in the text, if you hover over the name of an equation it will likely be linked to an actual, pop-up executable equation. For example: [Could not locate page MichaelBartmess.Force of Earth's Gravity]

At this moment you, yes you, are in orbit about a distant star and that star is in orbit about my dog.  And even though she is sleeping soundly, twitching and whimpering in her puppy dreams, she is being attracted to that distant star. 

Satellites orbit over our heads providing us TV and weather radar maps and each of those satellites is in turn orbited by our Sun, our moon and the Earth itself. The Earth orbits the Sun.  The Sun orbits the center of our galaxy and the force of gravity plays the combinatorial role of making it all happen. Gravity is at the center of the phenomena we know as an orbit.

So, let's discuss orbits further below.

Contents

Orbits as Ellipses

All orbits in their basic estimation are ellipses. So, below you will find a number of links to equations and calculators related to Orbit2.gifellipses.  

The effect of many masses on a single mass cause the single selected mass to have small perturbations in its orbit.  All orbits would be pure ellipses if they were acted on by a single "other mass."  In other words if two masses were attracted to each other in empty space, they would be attracted directly toward each other. That defines a straight line path, which in this cases is the special case of an ellipse with an infinitely small semi-major axis.

** Image: By User:Zhatt (Own work) [Public domain], via Wikimedia Commons

What Causes an Orbit

In most cases, masses enter into orbits about another mass after being pulled on some trajectory by "other masses" and end up not directly impacting a second mass but passing by that second mass and being caught by that second mass's gravitational pull -- and vice versa.

Many satellites about the Earth are in very nearly circular orbits.  Circles are ellipses -- a special case of an ellipse having equal semi-major and semi-minor axes.

Earth Orbits

The better understood picture of an orbit is a car size satellite put in orbit by a rocket launch system to serve some purpose.  

Geosynchronous Orbits

A large number of satellites are crowded into a very special orbit above the Earth 


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Equations

  • Ellipse - area by vCalc
  • Ellipse - Mean Radius by vCalc
  • Orbit Period - Retrograde Orbit by MichaelBartmess
  • Orbit Period - Direct Orbit by MichaelBartmess
  • Graveyard Orbit by EmilyB
  • Orbit Period of Circular Orbit by MichaelBartmess
  • Circular Orbit Velocity using R_E by vCalc
  • Circular Orbit Velocity using `mu` by vCalc
  • Circular Orbit Velocity using r only by vCalc
  • Total Energy Circular Orbit by Billy
  • Total Mechanical Energy in a Circular Orbit by MichaelBartmess
  • Orbit Period [a] by MichaelBartmess
  • Orbit Period [a, `R_E`] by MichaelBartmess
  • Orbit Period [a, `mu`] by MichaelBartmess
  • Velocity of a Satellite by MichaelBartmess
  • Force of Gravity on Satellite by MichaelBartmess
  • vLength by vCalc
  • Astro Travel Time by vCalc

Constants

  • Earth - Eccentricity by vCalc
  • Earth - Semi-Major Axis by vCalc
  • Earth Obliquity to Orbit by MichaelBartmess