Homework Help is Here – Start Your Trial Now!
Science
Advanced Physics
Luna Staten is now somewhere inside that SPHERICAL SHELL. That is, r

Luna Staten is now somewhere inside that SPHERICAL SHELL. That is, r

icon
Related questions
Question

Please only do part III . The second variation!  it's in the blue box! 
please show all the work! Thanks so much!

a) Expressed as a function of given and fundamental constants, what is the Gravitational Force exerted on Luna Staten by lamnof? b) Expressed as a function of given and fundamental constants, what is the Gravitational Force exerted by Luna Staten on lamnof? 3 of 3 c) Expressed as a function of given and fundamental constants, what is the instantaneous rate at which Luna Staten will begin to accelerate toward Iamnof? II. The First Variation: Assume that the above facts remain the same EXCEPT: lamnot is nowa SPHERICAL SHELL. That is, it has the same total mass and radius as described before, but now it consists of pure vacuum--other than an infinitesimally thin and perfectly spherical surface. Funny how things change. Luna Staten Iamnot a) Expressed as a function of given and fundamental constants, what is the Gravitational Force exerted on Luna Staten by lamnof? In order to contemplate this question, think of lamnot as consisting of zillions and zillions of little point-masses, all arranged in a spherical shell. Each little point of mass pulls on Luna Staten. What is the NET result of all these little pulls? Think about this until you see why it's complicated and difficult. Explain. Think even more until you see how it might turn out to be easy to answer even though it's complicated. (The textbook reading might help) b) Expressed as a function of given and fundamental constants, what is the Gravitational Force exerted by Luna Staten on lamnof? c) Expressed as a function of given and fundamental constants, what is the instantaneous rate at which Luna Staten will begin to accelerate toward lamnof? III. The second variation:Assume that none of the above facts change EXCEPT: Luna Staten is now somewhere inside that SPHERICAL SHELL. That is, r < R. lamnot a) Expressed as a function of given and fundamental constants, what is the Gravitational Force exerted on Luna Staten by lamnof? Luna Staten HINT: Before you try to answer that, consider this simpler question: in the scenario shown in the diagram to the right, which direction will Luna Staten be pulled? To the right? To the left? Up? Down? As in the preceding variation, think of lamnot as consisting of zillions and zillions of little point-masses, all arranged in a spherical shell. Each little point of mass pulls on Luna Staten. What is the NET result of all these little pulls? b) Expressed as a function of given and fundamental constants, what is the Gravitational Force exerted by Luna Staten on Iamnof? c) Expressed as a function of given and fundamental constants, what is the instantaneous rate at which Luna Staten will begin to accelerate toward lamnof?
Transcribed Image Text:a) Expressed as a function of given and fundamental constants, what is the Gravitational Force exerted on Luna Staten by lamnof? b) Expressed as a function of given and fundamental constants, what is the Gravitational Force exerted by Luna Staten on lamnof? 3 of 3 c) Expressed as a function of given and fundamental constants, what is the instantaneous rate at which Luna Staten will begin to accelerate toward Iamnof? II. The First Variation: Assume that the above facts remain the same EXCEPT: lamnot is nowa SPHERICAL SHELL. That is, it has the same total mass and radius as described before, but now it consists of pure vacuum--other than an infinitesimally thin and perfectly spherical surface. Funny how things change. Luna Staten Iamnot a) Expressed as a function of given and fundamental constants, what is the Gravitational Force exerted on Luna Staten by lamnof? In order to contemplate this question, think of lamnot as consisting of zillions and zillions of little point-masses, all arranged in a spherical shell. Each little point of mass pulls on Luna Staten. What is the NET result of all these little pulls? Think about this until you see why it's complicated and difficult. Explain. Think even more until you see how it might turn out to be easy to answer even though it's complicated. (The textbook reading might help) b) Expressed as a function of given and fundamental constants, what is the Gravitational Force exerted by Luna Staten on lamnof? c) Expressed as a function of given and fundamental constants, what is the instantaneous rate at which Luna Staten will begin to accelerate toward lamnof? III. The second variation:Assume that none of the above facts change EXCEPT: Luna Staten is now somewhere inside that SPHERICAL SHELL. That is, r < R. lamnot a) Expressed as a function of given and fundamental constants, what is the Gravitational Force exerted on Luna Staten by lamnof? Luna Staten HINT: Before you try to answer that, consider this simpler question: in the scenario shown in the diagram to the right, which direction will Luna Staten be pulled? To the right? To the left? Up? Down? As in the preceding variation, think of lamnot as consisting of zillions and zillions of little point-masses, all arranged in a spherical shell. Each little point of mass pulls on Luna Staten. What is the NET result of all these little pulls? b) Expressed as a function of given and fundamental constants, what is the Gravitational Force exerted by Luna Staten on Iamnof? c) Expressed as a function of given and fundamental constants, what is the instantaneous rate at which Luna Staten will begin to accelerate toward lamnof?
Part 2: Non-Point Masses, aka Continuous Masses, aka Masses that have Shapes A fictional planet called 'lamnot is measured to have a mass of M, a radius of Rand a density (mass/volume) of p. Variations in both the planet's radius and density are too small to register on the measuring devices. As far as science is concerned, therefore, Planet lamnot is of essentially constant radius and uniform density. You live on a tiny far-flung satellite called 'Luna Staten. Luna Staten has a mass of m (not the same as M) but in volume is, indeed, tiny. Compared to lamnot, Luna Staten is but a particle-located at a point.. in space... and time. Luna Staten, is a distance I away from the center of lamnot. No other measurable bit of mass can be detected for parsecs and parsecs and parsecs. I. The Theme a) Expressed as a function of given and fundamental constants, what is the Gravitational Force exerted on Luna Staten by lamnof? b) Expressed as a function of given and fundamental constants, what is the Gravitational Force exerted by Luna Staten on lamnof? c) Expressed as a function of given and fundamental constants, what is the instantaneous rate at which Luna Staten will begin to accelerate toward lamnof? II. The First Variation: Assume that the above facts remain the same EXCEPT: lamnot is now a SPHERICAL SHELL. That is, it has the same total mass and radius as described before, but now it consists of pure vacuum--other than an infinitesimally thin and perfectly spherical surface. Funny how things change. Luna Staten lamnot a) Expressed as a function of given and fundamental constants, what is the Gravitational Force exerted on Luna Staten by lamnof? In order to contemplate this question, think of lamnot as consisting of zillions and zillions of little point-masses, all arranged in a spherical shell. Each little point of mass pulls on Luna Staten. What is the NET result of all these little pulls? Think about this until you see why it's complicated and difficult. Explain. Think even more until you see how it might turn out to be easy to answer even though it's complicated. (The textbook reading might help)
Transcribed Image Text:Part 2: Non-Point Masses, aka Continuous Masses, aka Masses that have Shapes A fictional planet called 'lamnot is measured to have a mass of M, a radius of Rand a density (mass/volume) of p. Variations in both the planet's radius and density are too small to register on the measuring devices. As far as science is concerned, therefore, Planet lamnot is of essentially constant radius and uniform density. You live on a tiny far-flung satellite called 'Luna Staten. Luna Staten has a mass of m (not the same as M) but in volume is, indeed, tiny. Compared to lamnot, Luna Staten is but a particle-located at a point.. in space... and time. Luna Staten, is a distance I away from the center of lamnot. No other measurable bit of mass can be detected for parsecs and parsecs and parsecs. I. The Theme a) Expressed as a function of given and fundamental constants, what is the Gravitational Force exerted on Luna Staten by lamnof? b) Expressed as a function of given and fundamental constants, what is the Gravitational Force exerted by Luna Staten on lamnof? c) Expressed as a function of given and fundamental constants, what is the instantaneous rate at which Luna Staten will begin to accelerate toward lamnof? II. The First Variation: Assume that the above facts remain the same EXCEPT: lamnot is now a SPHERICAL SHELL. That is, it has the same total mass and radius as described before, but now it consists of pure vacuum--other than an infinitesimally thin and perfectly spherical surface. Funny how things change. Luna Staten lamnot a) Expressed as a function of given and fundamental constants, what is the Gravitational Force exerted on Luna Staten by lamnof? In order to contemplate this question, think of lamnot as consisting of zillions and zillions of little point-masses, all arranged in a spherical shell. Each little point of mass pulls on Luna Staten. What is the NET result of all these little pulls? Think about this until you see why it's complicated and difficult. Explain. Think even more until you see how it might turn out to be easy to answer even though it's complicated. (The textbook reading might help)
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 2 steps with 1 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer