Python: Simulation of the Solar System and Total energy

[Jozefina Gramatikova]

Homework Statement

I have a project to make the Solar system on Python, which I have done, but they also require from us to calculate the total energy of the system. We don't have to make the orbits of the planets elliptical, they should be circular and I believe I made them like that. Since the orbits are circular I think the potential and kinetic energy of the planets shouldn't change. However, when I plotted both energies I noticed Mercury's potential energy oscillates. *Please tell me if Mercury's potential energy should oscillate having in mind that its orbit should be circular. Thanks*

Homework Equations

Potential energy:

where M is the mass of the Sun and m is the mass of the planet we want to calculate the potential energy of

The Attempt at a Solution

This is a piece of my code where the problem might be (if there is a problem)

 

[BvU]

You sure modr is wrt the sun ? It looks as if you overwrite body.Ep for every pass in the loop ?

 

[Jozefina Gramatikova]

You sure modr is wrt the sun ? It looks as if you overwrite body.Ep for every pass in the loop ?

what do you mean by wrt?

 

[BvU]

With respect to

Your loop is over all bodies in self.bodies. Every time body.Ep is calculated - overwriting the previous result. So the last one gets the cake.

 

[Jozefina Gramatikova]

With respect to

Do you want me to write the formula out of the loop?

 

[BvU]

Up to you. In response to your original question:

Please tell me if Mercury's potential energy should oscillate having in mind that its orbit should be circular

It should not (the potential energy wrt the sun). But I doubt Mercury.Ep is that energy.

 

[Jozefina Gramatikova]

Can I please ask you to write the line for the Potential energy the way you think it should look like. Thanks

 

[BvU]

That's your job. All I did was point out something that I noticed. Do you sgree it looks suspiious ?

 

[gneill]

I'm not particularly fluent in Python, but it appears to me that inside the outer loop each instance of $body$ will be a unique object from the set $self.bodies$. It also appears that the Jozefina is summing all of the potential energies that exist between a given body and all the others. I'd expect that to vary when other bodies are closer or farther from a given body.

@Jozefina Gramatikova , one thing you might want to check is whether the "oscillations" change if you vary the time step size in the simulation. Mercury will be the fastest moving object and will be most susceptible to errors creeping in from the integration process. These "errors" might show up as gradually changing orbits (spirals) or energy coming or going seemingly from nowhere.

 

[Jozefina Gramatikova]

I don't think I am summing all of the potential energies. I reset body.Ep to zero every time the outer for loop starts

 

[BvU]

Overlooked the +=



Suspicion is still at the same location

 

[Jozefina Gramatikova]

Can you tell me how am I summing the potential energies? I reset body.Ep to zero every time the outer for loop starts

 

[BvU]

@gneill tells you in #9
Ep should only use r wrt the sun, not do a sum

 

[gneill]

You can sum the gravitational PE's for all the bodies to obtain a net gravitational PE for the entire system. This is similar to finding the total electrical PE of a number of charges. Think of it as gravitational binding energy of the system.

When looking at a given body in orbit it is useful to look at its gravitational PE and its KE with respect the primary (Sun). The sum should be just about constant over time if the influences of other bodies in the system are negligible.

 

[Jozefina Gramatikova]

I made some changes. Does this look fine? I am a bit worried about Jupiter.

 

[BvU]

I'd be worried about Jupiter too. But I'd look in the code

 

[Jozefina Gramatikova]

 

[BvU]

So what changes over time ? Does |Jupiter.position| decrease ? And the others stay the same ?

 

[Jozefina Gramatikova]

they should all stay the same. I don't know what's wrong with Jupiter

 

[BvU]

Numerically GMm/r is around 3e35 for Jupiter ; how come you are around 3e38 ?

they should all stay the same

Well, do they ? All except Jupiter ?

 

[Jozefina Gramatikova]

I think the potential energy is fixed. However, i think i have a problem with the total energy of the system as it oscillates.

Do you think this is wrong?

 

[BvU]

Yes

 

[Jozefina Gramatikova]

I do this ^ for every planet

I gave you the sections of my code that are associated with the total energy. Could you please tell me what is wrong. Thanks

 

[Jozefina Gramatikova]

PLS TELL ME THE DEADLINE IS 5 HOURS FROM NOW. I AM DEAD

 

[BvU]

Sorry, I have I job I do want to keep, so I can't be available full time.
Can't make much sense out of what you post; no idea where the snag is
I am surprised you have circular orbits and still have the sun itself moving too. What can possibly be its Ep ?