# Fortran - equation of motion, astronomical units

## 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, vx=0, vy=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 vx(i+1) I use Fx, as for vy and Fy.
So for this case;
Fx = -(x+0)/(SQRT(x2 + 0)3
Fy = -(0+y)/(SQRT(0 + y2)3

Is this right?

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jedishrfu
Mentor
What you wrote doesn't seem right.

Are you familiar with polar coordinates?

SteamKing
Staff Emeritus
Homework Helper

## 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, vx=0, vy=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 vx(i+1) I use Fx, as for vy 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.

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

Mark44
Mentor

## 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, vx=0, vy=1.
My trouble is figuring out my function.
Where is the sun, at (0, 0)?
SalfordPhysics said:

## 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|.
SalfordPhysics said:

## The Attempt at a Solution

What I have been doing previously is breaking the function into x and y components, so for finding vx(i+1) I use Fx, as for vy and Fy.
What does this part -- "so for finding vx(i+1) I use Fx, as for vy and Fy." -- mean?
SalfordPhysics said:
So for this case;
Fx = -(x+0)/(SQRT(x2 + 0)3
Fy = -(0+y)/(SQRT(0 + y2)3

Is this right?

Last edited:
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.

Last edited:
Mark44
Mentor
I had another question that I didn't get the quotes right, so you might have missed it.
Mark44 said:
What does this part -- "so for finding vx(i+1) I use Fx, as for vy 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.
SalfordPhysics said:
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.

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