8 November 2009

Last week Peter and I briefly talked about the relative contribution of the Sun and Moon to tides here on Earth. We are told that the Moon is the primary contributor because even though it is much smaller than the Sun it is much closer and the effects of gravity fall off by the inverse square law. I started reading The Tides and Kindred Phenomena in the Solar System, by George Howard Darwin (the son of Charles Darwin) again last night and was just starting the chapter on Tide-generating Force which got me to thinking about this again. I decided to plug the figures into Excel to see just how much each mass contributes to the sloshing around.

I searched the Web and found a Google Answers page on the Sun’s Gravitational Force. This tells me that

The attractive force of gravity is proportional to the mass of the two objects in question and to the square of distance.

So

            Mass
F = -------------------
    distance * distance

Next I searched the Web for the base data and plugged them into Excel.

	Sun	Moon
Mass	1,988,920,000,000,000,000,000,000,000,000	734,600,000,000,000,000,000	kg
Distance from Earth	145,597,870	384,403	km
Gravitational Pull on Earth	88,872,314,539,047.5	497,138,488,156.45

To make those huge numbers easier to understand I made a pie chart showing the relative gravitational pull of the Sun and Moon on Earth and it shows that even though the Sun is much farther away from the Moon it’s gravitational pull is still greater owing to it’s much larger mass.

So why don’t the numbers stack up against what we have been taught about the cause of the tides? Maybe as I get further into this chapter Darwin will unravel the mystery.

I found another formula on a Wikipedia page dealing with the Gravitational Constantthat uses the Gravitational Constant (which Peter mentioned last night) and the difference between the mass of the two planets. So now I needed to find and add in the mass of Earth.

      m1 – m2
F = G -------
       r * r

where

F

gravitational attraction

G

gravitational constant

m1 (m2)

mass of the planet

r

distance between the two masses

The gravitational constant is expressed as a formula that appears to change depending on what planets are involved and is higher math than I can or want to try to figure out.

I reworked the calculation ignoring the gravitational constant and that changed the relative contribution of the Moon and Sun to our tides considerably.

If I could get a simple number for the gravitational constant maybe that would be the answer to this problem.