Gravitational Tides
Look closely at the gravitational force
acting on a moon as it orbits its planet:
If we subtract the center of mass force, we
see the differential force acting on
it:
So gravity "stretches" and
"squashes" a moon!
Let's look at this mathematically. The force of gravity
is:
So the differential
force (also called the tidal force)
across a distance dr is
Note that
- the tidal force is proportional to the mass of the primary
(M)
- the tidal force is inversely proportional to the distance
cubed.
Note also that it works both ways -- the moon also stretches the
planet!
Why is it called a tidal
force?
What is stronger on the Earth, the tidal force from the moon or
the tidal force from the Sun?
So the moon exerts a stronger force, but
the Sun's tidal force can be significant. Hence the concept of spring tides and neap
tides:
- Spring Tides: Sun and Moon in alignment; tidal forces add. Big tides!
- Neap Tides: Sun and Moon 90 degrees apart; tidal forces counteract.
Small tides.
Remember: Tides are not merely a water
effect! The Earth's surface also has tidal bulges, about 10cm in height. And the
moon has an even greater tidal bulge -- 20m high.
Thought experiment: What
happens when you keep squeezing and stretching a piece of silly putty? What
does this have to do with tides?