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Old Sep 17th 2015, 04:03 AM   #11
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Ok.. I had defined G=6.673E-11 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;?
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Old Sep 17th 2015, 04:27 AM   #12
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Originally Posted by Sangam View Post
Ok.. I had defined G=6.673E-11 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.'
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Old Sep 18th 2015, 04:31 AM   #13
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Ok. I have modified my code as per the changes in formula. But I am not getting a near-circular 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.
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Old Sep 18th 2015, 05:04 AM   #14
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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 05:08 AM.
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Old Sep 21st 2015, 04:13 AM   #15
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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.
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Old Sep 21st 2015, 06:23 AM   #16
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Glad it's working out!
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Old Sep 25th 2015, 03:28 AM   #17
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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.
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Old Sep 25th 2015, 06:13 AM   #18
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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?
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Old Sep 25th 2015, 09:21 PM   #19
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Arrow

Keeping all values same and changing the value of v2y, I got the following outputs:
v2y = 9120m/s output: a near-circular orbit.
v2y = 10944m/s output: a linear line.
v2x = 4000m/s and v2y = 6000m/s output is attached below.
Attached Thumbnails
What is the formula to find distance between two satellites in space?-spiral.png  
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Old Sep 27th 2015, 09:57 PM   #20
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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 z-plane also.
Attached Thumbnails
What is the formula to find distance between two satellites in space?-2orbits.png  
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