Gravitational Field Strength and Tides


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 106 m and a mass of 5.98 x 1024 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 gCloseMoon
b. the center of the Earth gAvgMoon
c. the point on the Earth's surface farthest from the moon gFarthestMoon

Q3: What is the percentage difference between gCloseMoon and gFarthestMoon?

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 gCloseMoon , gAvgMoon and gFarthestMoon? 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 gClosestLargerand gFarthestLargeris stronger than the object's own self-gravitational 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 Shoemaker-Levy 9 did not strike the surface of Jupiter intact.



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