A consequence of these similarities is that all of the mathematical machinery we have been learning for charges should also apply to masses. Consequently, there should be a Gauss's Law for Gravity. The purpose of this exercise will be to develop Gauss's Law for Gravity: The electric field was defined as E = F/g and we used this to find the electric field а. for a point charge. Using analogous reasoning, infer the gravitational field g of a point mass. Write your answer using the unit vector f, but be careful to include the correct sign. Remember that the gravitational force between two like masses is attractive not repulsive. b. Using this same reasoning, infer an analogous Gauss's Law for Gravity. Use the symbol 4, to represent the gravitational flux, g for the gravitational field, and Min for the enclosed mass. How should the gravitational constant “big G" be included, do we need any factors of 4n? с. Consider a spherical planet of total mass M, radius R and uniform density p. Use the variable r to measure distances from the center of the planet. Using Gauss's Law for Gravity, determine the gravitational field g at points r> R. Be sure to draw a picture showing where your Gaussian surface is located in both situations and label any quantities of interest. d. Using Gauss's Law for Gravity, determine the gravitational field g at points r < R. Be sure to draw a picture showing where your Gaussian surface is located in both situations and label any quantities of interest.

A consequence of these similarities is that all of the mathematical machinery we have been learning for charges should also apply to masses. Consequently, there should be a Gauss's Law for Gravity. The purpose of this exercise will be to develop Gauss's Law for Gravity: The electric field was defined as E = F/g and we used this to find the electric field а. for a point charge. Using analogous reasoning, infer the gravitational field g of a point mass. Write your answer using the unit vector f, but be careful to include the correct sign. Remember that the gravitational force between two like masses is attractive not repulsive. b. Using this same reasoning, infer an analogous Gauss's Law for Gravity. Use the symbol 4, to represent the gravitational flux, g for the gravitational field, and Min for the enclosed mass. How should the gravitational constant “big G" be included, do we need any factors of 4n? с. Consider a spherical planet of total mass M, radius R and uniform density p. Use the variable r to measure distances from the center of the planet. Using Gauss's Law for Gravity, determine the gravitational field g at points r> R. Be sure to draw a picture showing where your Gaussian surface is located in both situations and label any quantities of interest. d. Using Gauss's Law for Gravity, determine the gravitational field g at points r < R. Be sure to draw a picture showing where your Gaussian surface is located in both situations and label any quantities of interest.