Fortran - equation of motion, astronomical units

[SalfordPhysics]

Homework Statement

Euler method : Plot the trajectory of a body moving under the influence of the suns gravity from initial conditions x=1, y=0, v_x=0, v_y=1.
My trouble is figuring out my function.

Homework Equations

d²r / dt² = -r/r³

The Attempt at a Solution

What I have been doing previously is breaking the function into x and y components, so for finding v_x(i+1) I use Fx, as for v_y and Fy.
So for this case;
Fx = -(x+0)/(SQRT(x² + 0)³
Fy = -(0+y)/(SQRT(0 + y²)³

Is this right?

 

[jedishrfu]

What you wrote doesn't seem right.

Are you familiar with polar coordinates?

 

[SteamKing]

Homework Statement

Euler method : Plot the trajectory of a body moving under the influence of the suns gravity from initial conditions x=1, y=0, v_x=0, v_y=1.
My trouble is figuring out my function.

Homework Equations

d²r / dt² = -r/r³

The Attempt at a Solution

What I have been doing previously is breaking the function into x and y components, so for finding v_x(i+1) I use Fx, as for v_y and Fy.
So for this case;
Fx = -(x+0)/(SQRT(x² + 0)³
Fy = -(0+y)/(SQRT(0 + y²)³

Is this right?

I wouldn't think so. Generally, for polar coordinates, r² = x² + y², thus your definitions of Fx and Fy don't make sense.

 

[SalfordPhysics]

Im not here no, there is no mention on my handout but could you go on anyway? regarding polar that is

 

[Mark44]

Homework Statement

Euler method : Plot the trajectory of a body moving under the influence of the suns gravity from initial conditions x=1, y=0, v_x=0, v_y=1.
My trouble is figuring out my function.

Where is the sun, at (0, 0)?

Homework Equations

d²r / dt² = -r/r³

Does the plain 'r' denote the magnitude of $\vec{r}$? To be clearer, you can write it as |r|.

The Attempt at a Solution

What I have been doing previously is breaking the function into x and y components, so for finding v_x(i+1) I use Fx, as for v_y and Fy.

What does this part -- "so for finding v_x(i+1) I use Fx, as for v_y and Fy." -- mean?

So for this case;
Fx = -(x+0)/(SQRT(x² + 0)³
Fy = -(0+y)/(SQRT(0 + y²)³

Is this right?

 

[SalfordPhysics]

I assume the Sun must be at (0,0) yes. And yes r = |r|.
Also, how do you do the vector notation?
Regarding your edit to the code;
I proceed as follows;
x(i+1) = x(i) + vx(i).dt
vx(i+1) = vx(i) + ax(i).dt where ax(i)=Fx i.e.; -r/|r|³
It follows as with my trajectory problem you helped with previously.

 

[Mark44]

I had another question that I didn't get the quotes right, so you might have missed it.

What does this part -- "so for finding v_x(i+1) I use Fx, as for v_y and Fy." -- mean?

Since I don't know what the above means, I can't comment on what you have for vx below.

I assume the Sun must be at (0,0) yes. And yes r = |r|.
Also, how do you do the vector notation?

# # \vec{r} # # - take out the spaces between the first and second pair of # characters.

Regarding your edit to the code;
I proceed as follows;
x(i+1) = x(i) + vx(i).dt
vx(i+1) = vx(i) + ax(i).dt where ax(i)=Fx i.e.; -r/|r|³
It follows as with my trajectory problem you helped with previously.

 

[SalfordPhysics]

I've solved it now I just had to go from the beginning to understand things, no need for polar.