Total Eclipse of the Sun: 40s Before Alignment

[Arctic Fox]

Why do total eclipses of the Sun by the Moon reach maximum eclipse about 40 seconds before the Sun and Moon's gravitational forces align?

 

[tony873004]

I've never heard that before. What do you mean by gravitational forces align? How would we know that they were aligned? By the tides?

Since gravity travels at the speed of light, I imagine that the gravitational forces should align when they appear aligned, which should lag their actual alignment by about 1 second, Light Travel Time from the Moon to the Earth.

 

[pervect]

The force of gravity is to a very good approximation a true central force - so the Earth is attracted to where the sun is now, in an inertial frame at the center of mass of the solar system (essentially equal to the inertial frame in which the sun is stationary, but not quite). This does not mean that gravity actually travels faster than light, however. See the sci.physics.faq

http://math.ucr.edu/home/baez/physics/Relativity/GR/grav_speed.html

Note that electromagnetic forces also exhibit a similar effect, this is not unique to gravity.


So draw a diagram in the center of mass of the solar system. The sun will be essentially at the origin of the diagram. Gravity pulls the Earth toward the origin.

Light, moves at a speed of 'c', so the apparent direction of light is aberrated by the Earth's orbital velocity in the center-of-mass frame.

http://64.233.187.104/search?q=cache:qOPuUq3cTaYJ:en.wikipedia.org/wiki/Aberration_of_light

So we expect .0001 radian of abberation in the direction of the light.

If we take the moon's synodic period of 29.53 days / 2 pi radians and calculate

29.53 days / (2 * Pi radians) * .0001 radians

we get 40 seconds. I'm not sure of the experimental source / observations of this number, but that's the theoretical calculation.