The vertical pressure distribution in the Earth's lower atmosphere can be modeled using the Barometric Law: P = P_surf exp [GMm/kT (1/r - 1/r_surf)] where: P_surf is the surface pressure (in units of Torr) G is the universal gravitational constant (in units of N m^2 kg-^2) M is the mass of the Earth (in units of kg) m is a mean molecular mass (in kg per particle) k is Boltzmann's constant (in units of JK^-1) r is the height (in meters, from the center of the Earth) corresponding to P(r): and r_surf is the height (in meters, from the center of the Earth) corresponding to P_surf: (1) Write a Matlab program by hand, that computes P using the values for r given in the first line of the table below (table is located on the next page) (2) Run your program in Matlab, to compute each P value using the corresponding value for r in the below table (table locate on the next page). For example, to compute P in the second line of the table below, use the r value in the second line, etc.) (3) For both (1) and (2), use the following numerical values for G, M, m, k, T, r_surf and P_surf: G 6.672 times 10^-11 M = 5.97 times 10^24 m 4.8149 times 10^26 k 1.3807 times 10^-23 T = 300 r_surf = 6.371 times 10^6 P_surf = 760 The vertical pressure distribution in the Earth's lower atmosphere can be modeled using the Barometric Law: P = P_surf exp [GMm/kT (1/r - 1/r_surf)] where: P_surf is the surface pressure (in units of Torr) G is the universal gravitational constant (in units of N m^2 kg-^2) M is the mass of the Earth (in units of kg) m is a mean molecular mass (in kg per particle) k is Boltzmann's constant (in units of JK^-1) r is the height (in meters, from the center of the Earth) corresponding to P(r): and r_surf is the height (in meters, from the center of the Earth) corresponding to P_surf: (1) Write a Matlab program by hand, that computes P using the values for r given in the first line of the table below (table is located on the next page) (2) Run your program in Matlab, to compute each P value using the corresponding value for r in the below table (table locate on the next page). For example, to compute P in the second line of the table below, use the r value in the second line, etc.) (3) For both (1) and (2), use the following numerical values for G, M, m, k, T, r_surf and P_surf: G 6.672 times 10^-11 M = 5.97 times 10^24 m 4.8149 times 10^26 k 1.3807 times 10^-23 T = 300 r_surf = 6.371 times 10^6 P_surf = 760