WTF: Orbital Mechanics/Celestial Mechanics, Newton and Kepler’s Laws

image Apparently this cartoon was all to true with respect to the Mars Climate Orbiter.  However, for some reason I am certain that there were no women wearing sexy pantsuits on the navigator team for the MCO.  If I am wrong leave a comment.

Hi ho: Well like Tim Buxton said at the Mix09 keynote today, the transition is the important part of a design.  MCO didn’t make the transition well.  Let’s start with an analysis of the back story.  Gravity and it’s impact on your life.

It all starts a long time ago, a really long time ago when gravity was created in our universe, which although most people think that I was around when that happened but I wasn’t.  To start with my convoluted effort to pull in F# to simulating the orbital boo-boo that was the MCO, then we might do the Mars Polar Lander, likely though I will get bored with it all and move on to something else.  So stick with me.

Gravity sucks.

The primary laws we will using are the Newton Laws of Motions and Kepler’s Laws

Newton formulated his laws for all objects, Kepler’s Laws were created for celestial bodies.  So this is an example of the specialized laws such as Kepler’s Laws were passed on to someone else to create the generalized solutions.  Of course, prior to Newton’s writing down of the laws, people had noticed things like a wagon rolling down hill was harder to stop than a wagon moving on flat land.  Newton’s Laws of Motion quantified the observation in a way that was measurable and repeatable.  There was something missing though, and that missing part was to be solved by Einstein, and won’t be discussed in this series of blogs, just because it is hard enough to do the simple stuff like planetary motion.

The laws are as follows:

Kepler Laws.

  1. The Law of Orbits: All planets move in elliptical orbits, with the sun at one focus.

  2. The Law of Areas: A line that connects a planet to the sun sweeps out equal areas in equal times. (Also known as Conservation of Angular Momentum)

  3. The Law of Periods: The square of the period of any planet is proportional to the cube of the semimajor axis of its orbit. Also known as the Harmonic Law

Newton’s Laws of Motion

First Law of Motion

    • Every object in a state of uniform motion tends to remain in that state of motion unless an external force is applied to it

Second Law of Motion

  • The relationship between an object's mass m, its acceleration a, and the applied force F is F = ma. Acceleration and force are vectors (as indicated by their symbols being displayed in slant bold font); in this law the direction of the force vector is the same as the direction of the acceleration vector.

Third Law of Motion

  • For every action there is an equal and opposite reaction.


Gravity, it’s the law!

Tomorrow, getting started with coding…

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