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How to plot the Gravitational Potential vs Radius of earth plot?

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clc;
clear all;
close all;
format long g;
G=6.6743015*10^-11;
Density=5.510;
M= (4*pi*G*Density)*10^6/3;
R=[10 20 50 100 6370];
%% for the calculation for the gravitational potential
for i =1:length(R)
Gravitational_Potential(:,i) = (M*R(:,i));
i=i+1;
end
figure()
plot(R,Gravitational_Potential);
ylabel('Gravitational Potential');
xlabel('Radius of the Sphere');
title('Gravitational potential vs Radius ');
grid on
I have to plot as curve plot as attached
Hint : - consider you have a function y = x^2. And now you have points x=1,2,4,8, from this you can get the corresponding y values: y=1^2,2^2,4^2,8^2. How do you visualize these values?
Now you have the same with a function V=GM/R, and R=10k,… you got V for all these values, you can visualize your results the same way you did above.

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vimal kumar chawda
vimal kumar chawda on 17 May 2020
Thank you. Your links was one of the best explanation ever. Do you have code for all these cases?
James Tursa
James Tursa on 17 May 2020
I don't have any code for this, but the equations look farily straightforward so I don't think you should have much trouble writing this.

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Accepted Answer

Ameer Hamza
Ameer Hamza on 6 May 2020
Edited: Ameer Hamza on 6 May 2020
You are using wrong values of constants and wrong formula for Gravitational potential. Try this code
clc;
clear all;
close all;
format long g;
G=6.6743015e-11;
Density=5510;
R = 6.4e6; % radius of earth
M = 4*pi*R^3*Density/3;
r = linspace(R, 15*R);
%% for the calculation for the gravitational potential
Gravitational_Potential = zeros(size(r));
for i =1:length(r)
Gravitational_Potential(i) = -G*M/r(i);
end
figure()
ax = axes();
plot(r, Gravitational_Potential);
ax.XLim(2) = max(r);
ylabel('Gravitational Potential');
xlabel('Radius of the Sphere');
title('Gravitational potential vs Radius ');
grid on

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