Tides

In reading about tides you learned that both the moon and the sun produce tidal effects on the earth.  The effects from the moon are considerably more influential than the effects produced by the sun.  However, the sun exerts a MUCH stronger gravitational force on the earth than the moon does.  

Part 1 - Convince me that the gravitational force from the sun (on the earth) is, indeed, stronger than the gravitational force produced by the moon. 

The easiest argument is simply consider that the earth orbits the sun and the moon orbits the earth.   Gravitationally, we are a pawn to the sun and the moon is a pawn to the earth.

Someone may point out that the sun is so much more massive than the moon.  This is true and this is the most important variable but there is another variable ... which is distance.  If you use this approach you need to crunch the numbers.  The sun is 27 million times more massive than the moon.  However, the sun is also 389 times farther away from us than the moon.  This would make the force drop by 389² (inverse square law) .... or 151,000.   Put the two factors together and you get 27,000,000/151,000 =  179    That is, the force of gravity from the sun is 179 times stronger than the force of gravity from the moon.

Part 2 - Resolve the apparent paradox presented in the opening paragraph.

This one is very tricky!  I will give partial credit if you simply say the moon is closer but to get the full points you need to explain why.  Tidal forces do not care how strong a force is .... the only thing that matters is the change (difference) in the force of gravity ....when compared from the closest side (A) vs. the furthest side  (B) ... see picture below (all this is in the reading material).

Now look at this graph of the inverse square law.  You can see that things change very quickly in the beginning and then taper off at the end.  This means that the strength of gravity really falls off rapidly when you are up close. Now think about tides and remember that the change in the pull of gravity is the key.

The closer you are, the larger this difference becomes.  This is why the moon produces the larger tidal forces (compared to the effects of the sun).  Stated a different way .. the sun is so far away that there is very little difference between the strength of gravity at point "A" vs. point "B".

Still not convinced?  Here are some numbers.

The chart above shows how the strength of gravity decreases according to the inverse square law (arbitrary units).  However, the important column is the last one which shows the change in gravity between successive rows.  This represents the difference in the strength of gravity.  If you had a mass (with a diameter of 1 unit) move progressively farther away from some other mass, the last column would represent the change (difference)  in the gravitational pull across the diameter of mass.  Since this is the cause of tidal effects, you can see that the closer you are, the stronger the effect becomes.

Part 3 - Find one other place where tidal effects are observed or come into play (besides the examples given in the class material)

There are several possible answers which will be graded individually.