Periodic and Circular Motion Periodic and Circular Motion Physics Help Forum 
Sep 17th 2015, 05:03 AM

#11  Junior Member
Join Date: Sep 2015
Posts: 11

Ok.. I had defined G=6.673E11 and PI=3.14159 but forgot to paste it here.
I am trying out the modifications you have suggested. How do I calulate 'A' in A delta_t. That is, a(t) = A +Bt. Is it something to do with ax1 = (F* cos(theta1))/M1;?

 
Sep 17th 2015, 05:27 AM

#12  Physics Team
Join Date: Jun 2010 Location: Naperville, IL USA
Posts: 2,271

Originally Posted by Sangam Ok.. I had defined G=6.673E11 and PI=3.14159 but forgot to paste it here.
I am trying out the modifications you have suggested. How do I calulate 'A' in A delta_t. That is, a(t) = A +Bt. Is it something to do with ax1 = (F* cos(theta1))/M1;? 
A is equal to 'a_old.'

 
Sep 18th 2015, 05:31 AM

#13  Junior Member
Join Date: Sep 2015
Posts: 11

Ok. I have modified my code as per the changes in formula. But I am not getting a nearcircular path. The x,y coordinates are again linear. I have set ax1_new = ax2_new=ay1_new=ay2_new = 0.1 as an initial value. Maybe this is the issue(not sure what value to give for initial acceleration). Modified code is as follows: Code: //To get acceleration of M1 you divide force by its mass, leaving:
ax1_old = (F* cos(theta1))/M1;
ay1_old = (F* sin(theta1))/M1;
ax2_old = (F* cos(theta2))/M2;
ay2_old = (F* sin(theta2))/M2;
BX1 = (ax1_new  ax1_old) / delta_t;
BY1 = (ay1_new  ay1_old) / delta_t;
BX2 = (ax2_new  ax2_old) / delta_t;
BY2 = (ay2_new  ay2_old) / delta_t;
ax1_new = ax1_old + (BX1*delta_t);
ay1_new = ay1_old + (BY1*delta_t);
ax2_new = ax2_old + (BX2*delta_t);
ay2_new = ay2_old + (BY2*delta_t);
fprintf(pf1,"\nax1_new,ay1_new = %e,%e",ax1_new,ay1_new);
fprintf(pf1,"\nax2_new,ay2_new = %e,%e",ax2_new,ay2_new);
//Now for incremental movement of M1:
//v(t) = At + Bt^2/2 integrating a(T) = A + Bt
vx1_new = vx1_old + (ax1_old * delta_t) + (BX1 * (pow(delta_t,2.0)/2.0));
vy1_new = vy1_old + (ay1_old * delta_t) + (BY1 * (pow(delta_t,2.0)/2.0));
vx2_new = vx2_old + (ax2_old * delta_t) + (BX2 * (pow(delta_t,2.0)/2.0));
vy2_new = vy2_old + (ay2_old * delta_t) + (BY2 * (pow(delta_t,2.0)/2.0));
fprintf(pf1,"\nvx1,vy1 = %e, %e",vx1_new,vy1_new);
fprintf(pf1,"\nvx2,vy2 = %e, %e",vx2_new,vy2_new);
x1_new = x1_old + (vx1_old * delta_t) + ((1/2) * ax1_old * pow(delta_t,2.0))+((1/6) * BX1 * pow(delta_t,3.0));
y1_new = y1_old + (vy1_old * delta_t) + ((1/2) * ay1_old * pow(delta_t,2.0))+((1/6) * BY1 * pow(delta_t,3.0));
x2_new = x2_old + (vx2_old * delta_t) + ((1/2) * ax2_old * pow(delta_t,2.0))+((1/6) * BX2 * pow(delta_t,3.0));
y2_new = y2_old + (vy2_old * delta_t) + ((1/2) * ay2_old * pow(delta_t,2.0))+((1/6) * BY2 * pow(delta_t,3.0));
vx1_old = vx1_new;
vy1_old = vy1_new;
vx2_old = vx2_new;
vy2_old = vy2_new;
ax1_old = ax1_new;
ay1_old = ay1_new;
ax2_old = ax2_new;
ay2_old = ay2_new;
x1_old = x1_new;
y1_old = y1_new;
x2_old = x2_new;
y2_old = y2_new;
x1= x1_new;
y1 = y1_new;
x2 = x2_new;
y2 = y2_new; Do let me know if my interpretation of ax1_old and ax1_new is as you mentioned.

 
Sep 18th 2015, 06:04 AM

#14  Physics Team
Join Date: Jun 2010 Location: Naperville, IL USA
Posts: 2,271

You should not be setting initial values for acceleration, only position and initial velocity. Since you can't calculate B for the initial iteration, set it to zero.
If you are still using the same values for mass and initial velocities that you had before then I would expect the bodies to simply fly in a straight line. You have masses of only 50 and 10 Kg, initially moving a speeds of 20 m/s or so. There would be a minuscule amount of gravitational force, essentially 0, which is why you are finding the masses moving in straight lines. I suggested previously that you print out the force and/or acceleration values so you can see if the values are "reasonable." Did you try setting initial values so that the two masses start 50 meters apart with zero initial velocity to see what happens? (They should fall toward each other.) And I would also suggest that you try values that you know result in a nice orbit. For the case of a satellite orbiting the Earth you can try these values:
M1 = 6 x 10^24 Kg
M2 = 10 Kg
x1=y1 = 0
x2=7x10^6 m, y2 = 0
V1x = v1y = 0
v2x=0, v2y = 7600 m/s
Last edited by ChipB; Sep 18th 2015 at 06:08 AM.

 
Sep 21st 2015, 05:13 AM

#15  Junior Member
Join Date: Sep 2015
Posts: 11

Thanks a lot ChipB. I have got the almost circular orbit. I am trying to get a more accurate curve fitting approach. Also, the collision occurs when I set initial values so that the two masses start 50 meters apart with zero initial velocity. I am getting a presentable output compared to the output I was getting initially and am very grateful to you.

 
Sep 21st 2015, 07:23 AM

#16  Physics Team
Join Date: Jun 2010 Location: Naperville, IL USA
Posts: 2,271

Glad it's working out!

 
Sep 25th 2015, 04:28 AM

#17  Junior Member
Join Date: Sep 2015
Posts: 11

Hello ChipB,
As I have to give a demo with different values for Mass and velocity, I needed to know how to calculate suitable values for mass,initial positions and initial velocities such that the 2 satellites move in circular orbit. I get circular motion for the values you had suggested earlier.
M1 = 6 x 10^24 Kg
M2 = 10 Kg
x1=y1 = 0
x2=7x10^6 m, y2 = 0
V1x = v1y = 0
v2x=0, v2y = 7600 m/s
But when I change any parameter, I get linear motion.

 
Sep 25th 2015, 07:13 AM

#18  Physics Team
Join Date: Jun 2010 Location: Naperville, IL USA
Posts: 2,271

Try changing one value by a small amount and see what happens. If you increase the initial value of v2y by, say, 20%, while leaving all other initial values the same, what happens?

 
Sep 25th 2015, 10:21 PM

#19  Junior Member
Join Date: Sep 2015
Posts: 11

Keeping all values same and changing the value of v2y, I got the following outputs:
v2y = 9120m/s output: a nearcircular orbit.
v2y = 10944m/s output: a linear line.
v2x = 4000m/s and v2y = 6000m/s output is attached below.

 
Sep 27th 2015, 10:57 PM

#20  Junior Member
Join Date: Sep 2015
Posts: 11

Is it possible to modify the previous formulae to suit motion in 3D? That is x,y,z coordinates? The plan is to consider 2 satellites in different circular orbits as shown in attachment image. So I have consider the zplane also.

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