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Fortran - equation of motion, astronomical units

  • #1

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?
 

Answers and Replies

  • #2
11,501
5,052
What you wrote doesn't seem right.

Are you familiar with polar coordinates?
 
  • #3
SteamKing
Staff Emeritus
Science Advisor
Homework Helper
12,798
1,666

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.
 
  • #4
Im not here no, there is no mention on my handout but could you go on anyway? regarding polar that is
 
  • #5
33,287
4,990

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:
  • #6
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:
  • #7
33,287
4,990
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.
 
  • #8
I've solved it now I just had to go from the beginning to understand things, no need for polar.
 

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