(VPython) Can someone help me with my orbit simulator?

[CrosisBH]

Code: https://pastebin.com/5LajNBpj

So I was messing with VPython, trying to create an Earth-Moon System. I got the actual gravity to work, and can create some nice ellipical orbits. However I run into trouble trying to make the actual (almost) circular orbit of the moon.

I know that the circular orbit velocity is given by v = √(GM/r). I put the moon at <3.8e8,0,0> and Earth in the center, so natural I assigned the initial velocity to the y of the moon since the velocity is tangent to the source of the gravity. (line 27)

However when I do this, I get the right velocity (~10000 m/s), but instead of orbiting circular it shoots off in the y direction leaving the gravity well of Earth. I've been looking through this code and can't find where it went wrong. Can someone have a look at it?

 

[willem2]

However when I do this, I get the right velocity (~10000 m/s), but instead of orbiting circular it shoots off in the y direction leaving the gravity well of Earth. I've been looking through this code and can't find where it went wrong. Can someone have a look at it?

When you update the position of the moon and earth, you need to use dt as well. position = position + velocity * dt.
dt = 0.01 is really slow. dt = 10 seems to work ok. t is supposed to be seconds of real time?

Vec = Earth.pos + Moon.pos

This is wrong too, altough it doesn't make a lot of difference at the start.

 

[CrosisBH]

When you update the position of the moon and earth, you need to use dt as well. position = position + velocity * dt.
dt = 0.01 is really slow. dt = 10 seems to work ok. t is supposed to be seconds of real time?This is wrong too, altough it doesn't make a lot of difference at the start.

Well, adding the dt term to the position update did stop the moon from shooting off, so that's one problem solved, but the orbit is still highly ellipical. I also changed the vector from Earth.pos + Moon.pos to Moon.pos - Earth.pos.

 

[willem2]

I put in the following:
dt = 10 instead of dt = 0.01
Vec = Moon.pos - Earth.pos instead of Vec = Moon.pos + Earth.pos
Earth.pos = Earth.pos+Earth.v * dt instead of Earth.pos = Earth.pos+Earth.v
Moon.pos = Moon.pos+Moon.v * dt instead of Moon.pos = Moon.pos+Moon.v
And I get a circle. There's one problem still. The canvas is often not updated for a while right after the start, so the moon will skip a couple of days and the trail of th e moon will have a section of straight line. There must be some vpython reason for this.
This Earth moon system also has net momentum in the y direction, so you see the moon spiraling upwards, and if you enabled trails for the Earth you'd see it creeping upwards along a cycloid path. You might want to give an initial velocity to the Earth to counter this.

 

[CrosisBH]

I put in the following:
dt = 10 instead of dt = 0.01
Vec = Moon.pos - Earth.pos instead of Vec = Moon.pos + Earth.pos
Earth.pos = Earth.pos+Earth.v * dt instead of Earth.pos = Earth.pos+Earth.v
Moon.pos = Moon.pos+Moon.v * dt instead of Moon.pos = Moon.pos+Moon.v
And I get a circle. There's one problem still. The canvas is often not updated for a while right after the start, so the moon will skip a couple of days and the trail of th e moon will have a section of straight line. There must be some vpython reason for this.
This Earth moon system also has net momentum in the y direction, so you see the moon spiraling upwards, and if you enabled trails for the Earth you'd see it creeping upwards along a cycloid path. You might want to give an initial velocity to the Earth to counter this.

It turns out my error was forgetting to set the intial velocity. I copied it correctly but didn't save in my ide, and now it's circular. Thanks for that. As for the other problem, would any velocity be good, or do you have in mind a specific velocity?

 

[willem2]

Thanks for that. As for the other problem, would any velocity be good, or do you have in mind a specific velocity?

The total momentum of the Earth and the moon should end up 0.

 

[BvU]

You can post code clearly and more effectively, sustainably etc. using the tags [code=python] ... <source> ... [/code]
example:

from vpython import *
import numpy as np

#Earth-Moon gravity EMmulation

#IMPORTANT CONSTANTS

G = 6.67e-11    #Newton's Constant

EM = 6e24        #Earth's Mass
MM = 7e22        #Moon's Mass

ER = 6.3e6        #Earth's Radius
MR = 1.7e6        #Moon's Radius

Distance = 3.8e8Earth = sphere(pos = vector(0,0,0), radius = ER, color = color.blue)
Earth.m = EM
Earth.v = vector(0,0,0) #Velocity
Earth.p = Earth.m*Earth.v #Momentum

Moon = sphere(pos = vector(Distance,0,0), radius = MR, color = vector(0.5,0.5,0.5), make_trail=True)

Moon.m = MM
Moon.v = vector(0,np.sqrt(G*Earth.m/Distance),0)
Moon.p = Moon.m*Moon.v

dt = 0.01 

while True:
    Vec = Earth.pos + Moon.pos
    Fg = -G*Earth.m*Moon.m/mag(Vec)**3*Vec #Vector form of the Gravity Equation

    # 1. We will update the momentum according to Pf = FΔt + Pi

    Earth.p = -Fg*dt + Earth.p
    Moon.p = Fg*dt+Moon.p #-Fg becDistancese forces are equal and opposite

    #2. Update the velocites of each object, p = mv, so v = m/p

    Earth.v = Earth.p/Earth.m
    Moon.v = Moon.p/Moon.m

    #3. Update the positions
    Earth.pos = Earth.pos+Earth.v
    Moon.pos = Moon.pos+Moon.v
    print("Vector Velocity: ",Moon.v,"Magnitutde: ",mag(Moon.v))
    rate(10000)

 

[sysprog]

Code: https://pastebin.com/5LajNBpj

So I was messing with VPython, trying to create an Earth-Moon System. I got the actual gravity to work, and can create some nice ellipical orbits. However I run into trouble trying to make the actual (almost) circular orbit of the moon.

I know that the circular orbit velocity is given by v = √(GM/r). I put the moon at <3.8e8,0,0> and Earth in the center, so natural I assigned the initial velocity to the y of the moon since the velocity is tangent to the source of the gravity. (line 27)

However when I do this, I get the right velocity (~10000 m/s), but instead of orbiting circular it shoots off in the y direction leaving the gravity well of Earth. I've been looking through this code and can't find where it went wrong. Can someone have a look at it?

(emphasis added)

The center of gravity of the Earth is not the center of gravity of the Earth-Moon system.

From the Wikipedia barycenter article:

In cases where one of the two objects is considerably more massive than the other (and relatively close), the barycenter will typically be located within the more massive object. Rather than appearing to orbit a common center of mass with the smaller body, the larger will simply be seen to wobble slightly. This is the case for the Earth–Moon system, where the barycenter is located on average 4,671 km (2,902 mi) from the Earth's center, well within the planet's radius of 6,378 km (3,963 mi).​

(emphasis added)

In your Earth-Moon instance of the two body problem, your treating the Earth as the barycenter, instead of deriving the barycenter from the masses and distances and densities and momenta of the Earth and Moon (between and within) , produces an incorrect orbital result.

 

[willem2]

(emphasis added)

In your Earth-Moon instance of the two body problem, your treating the Earth as the barycenter, instead of deriving the barycenter from the masses and distances and densities and momenta of the Earth and Moon (between and within) , produces an incorrect orbital result.

Note that while the Earth starts off at 0,0 with a apeed of 0, it is not fixed. With the initial conditions here the Earth will both wobble and move slowly upwards.
I made the suggestion to give the Earth a momentum in the opposite direction of the moon, so the het momentum would be 0. The barycenter would then be at the the point (4.67*10^6, 0)
This was not the problem that made the moon fly off.

 

[BvU]

@CrosisBH : how are things ? Any favourable developments ?

 

[CrosisBH]

@CrosisBH : how are things ? Any favourable developments ?

I managed to get everything working. I got the moon to orbit in a nice circular fashion, and did what willem suggested and changed the Earth's momentum and got a nice Moon-Earth System. I'm going to try it soon with a system with multiple moons to see if I can incoorperate gravity with more than two objects, maybe like Mars