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

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.

[James Tursa]

It is not clear to me what the actual problem is. Are you supposed to calculate the gravity potential at an interior point of the Earth? That is what your R values would indicate, as that last value looks suspiciously close to the radius of the Earth. Can you clarify this? If true, you shouldn't be using the entire mass of the Earth for your calculations, since that would give you the wrong answer. Or are those R values supposed to be altitude?

[vimal kumar chawda]

We have 3 cases interior and on the surface of the earth and outer space.

If you can calssify all three cases then it will be great.

[James Tursa]

See these discussions:

https://sciphy.in/gravitational-potential-due-to-solid-sphere/

https://sciphy.in/gravitational-field-due-to-spherical-shell/

https://sciphy.in/gravitational-field-due-to-solid-sphere/

[vimal kumar chawda]

Thank you. Your links was one of the best explanation ever. Do you have code for all these cases?

[James Tursa]

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.

Answer 1

[Ameer Hamza]

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

[vimal kumar chawda]

Thank you very much Sir:)

[Ameer Hamza]

I am glad to be of help.