Physics/Velocity through Space
QUESTION: This is not homework, I'm 30 years old.
If a moon's velocity is 300 meters/second and it's orbiting a planet whose velocity is 500 meters/second, what is its actual velocity through space, or the equation to find it ?
ANSWER: Dear Christine: Being 30 does not preclude being a student :)
This is my simple form answer, though feel free to follow up if you want exact math (you will need to know some trigonometry to follow it though):
All motion is relative. In this case, we will presume that we are talking about movement relative to the star that the planet orbits. While there will be some perturbation in a real system (not circular orbits), you can think about a swinging pendulum on top of a train. When the pendulum is swinging as fast as possible forward, its total speed in relationship to the ground will be speed(train) + speed(pendulum). When it swings back, it will be speed(train) - speed(pendulum). When the pendulum is at the end of a swing (not moving) then the total speed is just that of the train. The system keeps oscillating between these states (faster than train, same as train, slower than train, same as train etc.) in a fashion similar to a wave with high speed moments and low speed moments.
For your system, the speed of the moon will be 800 m/s at the maximum, 200 m/s at the minimum and fluctuate between the two states with an average speed equal to the planet (500 m/s).
I hope this helps, and apologies in the delay getting back to you.
---------- FOLLOW-UP ----------
QUESTION: Thanks Jeffrey, you're the best,
But isn't a moon's path through space a helix like in this video;
Pretent that the sun in the video is a planet.
So rather than the moon's velocity oscillating, isn't it just a smooth constant rate as it moves in a helix ?
Big fan of yours,
In this case, the moon orbit is not the helical spiral you are seeing in the video. This is because the direction that the sun in the video is moving is out of plane with the rotation of the planets. Instead, remember back to the the old spirograph toys (http://en.wikipedia.org/wiki/Spirograph
). For a planet circling a sun, the planet revolves in a plane around the sun. The moon, in turn, is also in the same plane. What this gives for the movement of the moon with respect to the sun is a lace fringe pattern where there is a large (planets path) loop around the sun with sub-loops (each one being a month/lunar cycle on the planet). In effect, looking at it from the top you get something that looks like lace or the patterns that the old spirographs gave you.
However, if you want to conceptually expand this to what you saw in the video, here is what you can do as a mental exercise: Imagine the same pattern you see in the video where the direction that the helix grows is the suns movement, that the bend to the helix is the the planet's orbital contribution, and then extend it to tiny loops within the helix... again going back to the lace analogy, this is much like lace fringe twisted through space. Similar to the helix you see in the movie: but subtly different with a finer, more intricate and (I think) prettier pattern on a smaller scale etched into it by the moons orbit.
As to why moons tend to orbit on the same plane as the sun, that is another can of worms, perhaps best saved for later. :)