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Orbital simulation  Calculate object position over time in a 2d plane 
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#1
Apr914, 04:20 PM

P: 9

Hi
Im busy creating an application to simulation a rocket in orbit. Im having trouble as the results im getting are incorrect. Could someone please check if im using the correct method as stated below. Everything works on a 2d plane, and has a x and y coordinate and a x and y velocity and a mass coordinates are in meters and the mass is in kg. Method: Calculate the distance between the rocket and the planet using the distance formula distance = sqrt[ ( x2  x1)^2  (y2  y1)^2 ] calculate the force earth exerts on the rocket using the The Universal Law of Gravitation where G is the Gravitational constant m is the mass of an object and r is the distance between them force = (G*m1*m2) / distance^2 Using the inverse of tan get the angle to calculate the the x and y components ( I know for a fact im getting this is correct, its a bit tricky to explain) I calculate the angle for each quadrant going from the x axis to the y axis Calculate the acceleration of the rocket acceleration = force / mass Calculate velocity change over timer ( this is usually 0.01 seconds ) deltaVelocity = acceleration * time Calculate the x velocity component deltaXvelocity = deltaVelocity * cos(angle) Calculate the y velocity component deltaYvelocity = deltaVelocity * sin(angle) Calculate the new x velocity newXvelocity = currentXvelocity + deltaXvelocity Calculate the new y velocity newYvelocity = currentYvelocity + deltaYvelocity set the new position of the rocket newXposition = currentXposition + ( newXvelocity * time ) newYposition = currentYposition + ( newYvelocity * time ) Something is wrong with this method and i do know what. I know for a fact that a an object in orbit round about 420km travelling at round about 7700 m/s should be in a roughly circular orbit and one that has a high eccentricity. Currently with the results im getting to obtain a roughly circular orbit at 420km i need to have a velocity of round about 5500m/s Thanks for taking the time 


#2
Apr914, 04:25 PM

P: 886

It sounds like you are using the Euler method, which is numerically unstable.
You should try Verlet integration https://en.wikipedia.org/wiki/Verlet_integration or a RungeKutta method https://en.wikipedia.org/wiki/Runge%...93Kutta_method both of which have better stability properties. Or try https://en.wikipedia.org/wiki/Leapfrog_method which is almost as simple as the Euler method. This page has a decent description of why Euler method fails. https://en.wikipedia.org/wiki/Euler_integration 


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