The Earth's moon has a mass approximately 1/81 that of the Earth,
and the moon's center of mass is on average approximately 60 Earth
radii away from the center of mass of the Earth. We will use this
information to try and develop a very simplified explanation for
oceanic tides upon the Earth.
Q1: Sketch
this situation as two circles, including a line from center to center
from Earth to moon, extending the line on through the Earth to both
surfaces of the Earth. Label objects and the points on the Earth's
surface closest and farthest from the moon.
Q2: The
Earth has an average radius of 6.37 x 10^{6} m and a mass
of 5.98 x 10^{24} kg. Calculate the gravitational field
strength of the moon at these points on the Earth:
a. the nearest point on the Earth's
surface to the moon g_{CloseMoon}
b. the center of the Earth g_{AvgMoon}
c. the point on the Earth's surface
farthest from the moon g_{FarthestMoon}
Q3: What
is the percentage difference between g_{CloseMoon} and g_{FarthestMoon}?
Q4: Imagine
our model Earth is a perfectly smooth sphere initially covered with
a uniform, thin layer of water. How would this water eventually
be distributed due to the differing values of g_{CloseMoon}
, g_{AvgMoon} and g_{FarthestMoon}?
Sketch the water distribution and explain this in your own words.
Hint: where does water fall fastest, average and slowest towards
the moon? Where does it pile up?
Q5: Imagine
our model Earth is now rotating about its center of mass once every
24 hours. Use this to explain in your own words the water tides
experienced by a stick person rotating with the earth at a point
on the Earth's surface. How many high and low tides each should
the person see in 24 h?
If any astronomical object is so close to a much larger body such
that the difference between g_{ClosestLarger}and g_{FarthestLarger}is
stronger than the object's own selfgravitational field and stronger
than it's own material strength it is pulled apart. The maximum distance
at which this occurs is called the Roche limit; it is the distance
within which an object is pulled apart by tidal stress, or where satellites
cannot form by accretion.
Q6: From
elementary school astronomy examples, describe a situation where
the Roche limit plays a role in preventing a moon from forming.
Q7: Use
the above information to hypothesize why the comet ShoemakerLevy
9 did not strike the surface of Jupiter intact.
