This is an Excel workbook containing a dynamic model of a basic binary planetary system.
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Basic Planetary Simulator
© 2024
This is an Excel workbook containing a dynamic model of a basic binary planetary system.
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I’ve been playing with this program for awhile and I’ve tried lots of different orbits. However, what I want to do is to have one object centered at a point and the other orbit around it, similar to what a satellite does around the earth. I’ve been able to produce two stable orbits – one within the other – but nothing close to a satellite orbit. Is it possible to do this with this program?
Set the mass of the first object very large or you can also go into the formula table and freeze the x/y coordinates of one object and also set the speed and accelerations of the same object to zero.
Thanks George. I had tried zeroing the initial x, y, vx and vy of one object and making its mass very large, but the orbits of both objects became wildly erratic. Zeroing the next x,y coordinates worked, and it doesn”t matter what the mass of the object is. I find it fascinating to see how changing the initial conditions of the other object, and varying the gravitational constant, affect the orbit. I haven’t gotten to the point where I can predict what will happen when I make a change in one of the parameters. Hopefully that will come with experience.
Mike, it works because the model had initially a fixed object and a moving one. It’s not experience, just plain perseverance. Let’s review:
1. Make the mass of object A large (also make sure to make the time step veeeeeeery small to start with (if mass A is 1000 times larges I expect the time step to be needed 1000 times larger to maintain convergence) after the model works increase it gradually).
2. Throw out speed formulas and coordinate formulas for object A, you don’t need them, replace them with constants as I told you in the previous reply (fixed speeds and fixed (possibly zero) coordinates). You’ll end up with a columns of constants for these.
3. The forces are calculated normally and will be placed in the same cells but they will only affect object B (since A is fixed).
It should work. Again. I believe your mistake is not decreasing the time step. Make it smaller and smaller until it works, then increase it and after that gradually while making sure the functionality is preserved.
I used some “real” numbers for the ISS and got good results. I used the semi-major axis of the ISS orbit for the initial value of x1 and the velocity at perigee for the initial value of v1y. I also “zeroed” the “next” values of x2 and y2 to keep object 2 stationary. The other initial conditions were as follows:
x1 6793172.057 m
y1 0
x2 0
y2 0
v1x 0
v1y 7660.871127 m/s
v2x 0
v2y 0
k (=G) 6.67E-11 m3kg-1s-2
dt 60 s
Zoom 354
m1 4.09E+05 kg
m2 5.97E+24 kg
Although these numbers producesd a rather boring orbit with a period of about 93 minutes, I was pleased that I got the program to work with “real” numbers. I added a chart so I could see the orbital data, since the included graph doesn’t scale enough to see the orbit. Thanks for the program and for your help.
Cool!