Expert: Tom Whiting - 5/22/2010

Question
Dear expert,


I heard about a method for calculating mean Moon's speed (around the Earth) in a model where Sun's gravitationnal influence is 'switched-off'


(please go the following internet-links to see the illustration of this method)

http://www.speed-light.info/speed_of_light/speed_of_light_12000.gif

As we can see, a rotation of Earth-Moon system around the Sun for one synodic month is equivalent to an arc of 27° on the terrestrial orbit around the Sun. This angle (27°) is the same as the one between Moon position at 1 sideral month and synodic month according to Earth frame of reference.



http://www.speed-light.info/images/speed_of_light_12000.gif

The vector "E" (beginning from the Moon) perpendicular to the segment Earth-Sun points to a different direction every synodic month.


Thus from this "triangle" of vectors, they calculate mean Moon's speed E':



E=square root [ (E sin phi)² + (E')² ]

thus E'= E * cosine phi
      = current Moon's speed * cosine phi
      = 3680km/hour * cosine 27°

    E'=3279 km/hour


So without Sun influence on Earth-Moon system, Moon would revolve around the Earth at 3279 km/hour.

That seems MATHEMATICALLY right, but as I have some basis at mechanic, so could you explain me if this method is SCIENTIFICALLY correct?


thank you.

Answer
Hi Ed,
Sorry, but I am not a math major, so I can't help you... I'm an astronomical observer and don't get into the mathematics of it.  I do know that the moon, being in an elliptical orbit (if you artificially 'freeze' the Earth), it's velocity around the Earth is continuously changing and is variable, not fixed. (As are all the planets going around the sun... and actually the sun is moving around the galaxy, so it's not even really an elliptical orbit, but a spiral or corkscrew orbit thru space. But of course the Galaxy is moving too, so the moon's real orbit thru space is actually quite complicated, and not just a simple ellipse.)
So whatever answer you get for the current second, will not be accurate for the next second.

Plus, all velocities are all relative to some other body.  So the moon's velocity relative to the Earth is different than it's velocity relative to the sun and to Jupiter for that matter.
I leave it to the math majors to figure out all that relative velocity stuff... all I worry about is... When is the next new moon weekend so we can all go out and observe the Deep Sky Objects with a non-light polluted sky by the absent moon.  (Us DSO observers actually HATE the moon... just another light polluter of the night sky).
Clear Skies,
Tom Whiting
Erie, PA USA