Sunday, March 29, 2015

Thinking About Motion

The last section of my daily Jupiter Today podcasts is a summary of the position of Jupiter relative to the Earth and the Sun.  One of the values I report is the daily change in velocity (in km/hour).  What I've noticed after these few months is that the change in velocity itself is changing.

So I decided to finally look into this a little more.

Below are six plots.  The x-axis in every case is the number of days past 2015-Mar-22.  The y-axis is the value of the parameter in the units described below.

The 1st plot is the distance from Jupiter to Earth (in km) over the course of ten years, sampled every day.

The 2nd plot is the difference in distance over the course of that day.

The 3rd plot is the radial velocity between Jupiter and Earth (in km per day).

The 4th plot is the change in the change in that radial velocity.

The 5th plot is the radial acceleration between Jupiter and Earth (in km per day per day)

The 6th plot (the one I'm most interested in) is the change in that radial acceleration.

To put this into language, what this last plot is showing is that not only is the change in velocity changing, but that change is changing too!!!! Confused?????  So am I.

I've been trying to figure out a way to describe what this would feel like in our ordinary life.  The best I can come up with is that we're driving a car over bumps that are changing their shape over time.  So the amplitude (and frequency????) of the bumping is changing as we drive over them.

Looking at the plot itself, what do the maxima and minima represent?  My best guess is superior conjunction and opposition.  But which is which ... and why?  Why does this plot have a "sawtooth" shape and not a sine wave shape?  I'm fairly certain that the smaller wiggles are caused by Jupiter's moons.

For sure I need to look at this closer and in as many perspectives as I can.

If any of you have any ideas on how to interpret these plots, please comment!

1 comment:

  1. Because Jupiter and Earth orbit in the same direction, they move parallel to each other during every opposition and conjunction. Speed, acceleration are zero then. Change in acceleration is zero every half time between an opposition and conjunction. The asymmetry comes from the distance Earth-Jupiter being shorter at opposition than at conjunction, 5 vs 6 AU. Since Jupiter's orbital period is 12 times that of Earth, so for sake of intuition, imagine Earth with constant speed and Jupiter as a fixed point. Around opposition, Earth changes its speed relative Jupiter faster than when on the other side of the Sun. Just like a circle with small radius (5 AU) is more curved than one with large radius (6 AU).

    The small wiggles could be caused by Earth's Moon, they look as if they could be monthly. Jupiter is too massive to move in any relevant amount compared with our own tidal force. Variations in amplitude (and tiny dito in frequency) however depends on Jupiter's eccentricity of almost 0.05 which is a distance change from the Sun of ½ AU every 6 years. Earth eccentricity of 0.017, or 0.03 AU change per half year is probably not visible in the diagrams.