USING MATLAB PROGRAM The variation of gravitational acceleration g with altitude
ID: 2083233 • Letter: U
Question
USING MATLAB PROGRAM
The variation of gravitational acceleration g with altitude y is given by: g = R^2/(R + y)^3 g_0 where R = 6371km is the radius of the Earth, and g_0 = 9.81 m/s^2 is the gravitational acceleration at sea level. The change in the gravitational potential energy, Delta U, of an object that is raised from the Earth is given by: Delta U = integral^h_0 mg dy Determine the change in the potential energy of a satellite with a mass of 500 kg that is raised from the surface of the Earth to a height of 800 km.Explanation / Answer
Matlab Program:
clc;
clear all;
close all;
R = 6371*10^3; % Radius of Earth given in Meters
g0 = 9.81; % Gravitational acceleration (Given)
m = 500; % Mass of the Satellite in Kgs(Given)
g = @(y) ((R.^2).*g0)./((R+y).^2); % Calculation of 'g' as a function of 'y' syntax for defining function is fun = @x (equation) %
dU = m*integral(g,0,800000) % dU is the change in the Potential Energy. 'integral' is the matlab inbuilt function. syntax is "integral(function, lowerlimit, upperlimit)" %
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