Gravitation between the Moon and the Earth: physics project

[BvU]

1018 m/s is what I get too.
On earth, g = 9.81 m/s2 So out there it should be a lot less.
Can't read you formula, but it looks as if it calculates a force ?
Keep track of R too. If you see it change very rapidly, it's a bug.
Keep track of theta too. It should evolve approximately linearly

yes you should integrate ax to get vx and ay to get vy. So you need to keep track of those.
And integrate vx to get x and vy to get y according to the

and at t = 600:
the new x is the x just above + vx * dt
the new y is the y just above + vy * dt
the new vx is the vx just above + ax * dt
the new vy is the vy just above + ay * dt
and the other ones you calculate

 

[isukatphysics69]

1018 m/s is what I get too.
On earth, g = 9.81 m/s2 So out there it should be a lot less.
Can't read you formula, but it looks as if it calculates a force ?
Keep track of R too. If you see it change very rapidly, it's a bug.
Keep track of theta too. It should evolve approximately linearly

yes you should integrate ax to get vx and ay to get vy. So you need to keep track of those.
And integrate vx to get x and vy to get y according to the

hey we just made some serious progress 1 sec

 

[isukatphysics69]

1018 m/s is what I get too.
On earth, g = 9.81 m/s2 So out there it should be a lot less.
Can't read you formula, but it looks as if it calculates a force ?
Keep track of R too. If you see it change very rapidly, it's a bug.
Keep track of theta too. It should evolve approximately linearly

yes you should integrate ax to get vx and ay to get vy. So you need to keep track of those.
And integrate vx to get x and vy to get y according to the

 

[isukatphysics69]

1018 m/s is what I get too.
On earth, g = 9.81 m/s2 So out there it should be a lot less.
Can't read you formula, but it looks as if it calculates a force ?
Keep track of R too. If you see it change very rapidly, it's a bug.
Keep track of theta too. It should evolve approximately linearly

yes you should integrate ax to get vx and ay to get vy. So you need to keep track of those.
And integrate vx to get x and vy to get y according to the

Now one thing we notice tho is that our x and y positions are increasing and not oscillating
any idea why?

 

[BvU]

Is the force attracting the moon or pushing it away ?

 

[isukatphysics69]

Is the force attracting the moon or pushing it away ?

The gravitational force is attracting the moon.. our position values are getting larger tho. we used eular integration, i was expecting the values to oscillate,
velocities here look really good tho imo. i still haven't quite made out what the position values are saying.

 

[BvU]

The gravitational force is attracting the moon..

So what about the sign of a ? If the moon leaves (R,0) with speed (0,vy) should ax and ay be > 0 ?

I'm surprised you introduce px and py if you already have a column x and y ?

(have to run: work!)

 

[isukatphysics69]

So what about the sign of a ? If the moon leaves (R,0) with speed (0,vy) should ax and ay be > 0 ?

I'm surprised you introduce px and py if you already have a column x and y ?

(have to run: work!)

ahh i see ok, have to fix that tommorow.

 

[isukatphysics69]

We screwed up our data, trying to fix. We changed the net force to a negative, not sure if everything updated

we have motion as px^2+py^2

i will close my eyes for a few minutes and then start from scratch i think starting from scratch will be a good idea but so tired

wait so the R is the sqrt(x^2 + y^2) since i have Earth centered at 0,0. so i needed the positions to calculate the acceleration with respect to time, but to get the positions i need the velocities, but in order to get the velocities i have to integrate the acceleration. this doesn't make sense. its like what came first, the egg or the chicked, well what do i need first, the position, but to get the position i need the velocity, but to get the velocity i have to integrate the acceleration. now i am confused after i thought i had it

oh wait i think it is because the velocity doesn't change it is always 1018 m/s lol.. i see nvm . i will close eyes for a few mins now then start from scratch.

when i went to graph my results the graph was not looking good. just two straight lines for the position. not sure how my professor got the circle. i used x^2+y^2 but the value was huge and didn't make sense.

 

[BvU]

i will close eyes for a few mins now then start from scratch.

Looks like you need some R&R ! (same as me, actually: 1:14 AM here and an early dentist appointment )
How did the exam go today ?

Never mind: the integration.

(added rows and columns so I can refer to them)

On line 1 there are the initial conditions 384000, 0, 0, 1018 for x, y, vx, vy.

From that you calculate (with formulas) r, theta, and a, ax, ay. (still on line 1).
​

On line 2 we are going to do our first integration step: from 0 to dt (I tried dt = 4000 sec here).

the new x is the x just above + vx * dt
the new y is the y just above + vy * dt
the new vx is the vx just above + ax * dt
the new vy is the vy just above + ay * dt
and the other ones you calculate

Or, in excel formulas:

Does that make sense to you ? If yes, then you can copy line 2 many times over
to see things go terribly wrong. We'll discuss that once you get the intgration going in a credible manner...

 

[isukatphysics69]

Looks like you need some R&R ! (same as me, actually: 1:14 AM here and an early dentist appointment )
How did the exam go today ?

Never mind: the integration.
View attachment 225349

(added rows and columns so I can refer to them)

On line 1 there are the initial conditions 384000, 0, 0, 1018 for x, y, vx, vy.

From that you calculate (with formulas) r, theta, and a, ax, ay. (still on line 1).
​

On line 2 we are going to do our first integration step: from 0 to dt (I tried dt = 4000 sec here).

​

Or, in excel formulas:

View attachment 225350

Does that make sense to you ? If yes, then you can copy line 2 many times over
to see things go terribly wrong. We'll discuss that once you get the intgration going in a credible manner...

Hi, the exam is tommorow and this is also due tommorow lol, ok i will be right back going to try to figure this out

 

[isukatphysics69]

Ok our dt is different but this is my redo of the data
here dt is 18000 seconds
i think this is looking pretty good here. i will check your post now 1 sec
my prof told me not to use trig functions so that is why i am using x/r and y/r

i can go back and change everything to 4000 seconds

 

[isukatphysics69]

 

[isukatphysics69]

 

[isukatphysics69]

Our acceleration components are looking a little different. i am refraining from trig functions because my prof advised against it.. i am trying to see if that is the only reason why
velocities differ slightly as well because of the acceleration difference, I'm pretty happy with what i am seeing right now

 

[isukatphysics69]

Looks like you need some R&R ! (same as me, actually: 1:14 AM here and an early dentist appointment )
How did the exam go today ?

Never mind: the integration.
View attachment 225349

(added rows and columns so I can refer to them)

On line 1 there are the initial conditions 384000, 0, 0, 1018 for x, y, vx, vy.

From that you calculate (with formulas) r, theta, and a, ax, ay. (still on line 1).
​

On line 2 we are going to do our first integration step: from 0 to dt (I tried dt = 4000 sec here).

​

Or, in excel formulas:

View attachment 225350

Does that make sense to you ? If yes, then you can copy line 2 many times over
to see things go terribly wrong. We'll discuss that once you get the intgration going in a credible manner...

Wait what do you mean?

 

[BvU]

Time step seems a bit big. Try 1000 --- however, I may have a bug in my stuff. ...

If the integration works and you make a scatter plot of y vs x, you should get something like a neat circle, at least initially.

prof advised against it

Prof is probably right (I can't get past x=0 without weird behaviour... (bug?)


I don't understand how you can go from x on first line to a bigger value if vx=0 ? And then on the next line to an even biger value when on line 2 vx < 0 ?

 

[isukatphysics69]

Time step seems a bit big. Try 1000 --- however, I may have a bug in my stuff. ...

If the integration works and you make a scatter plot of y vs x, you should get something like a neat circle, at least initially.

Prof is probably right (I can't get past x=0 without weird behaviour... (bug?)


I don't understand how you can go from x on first line to a bigger value if vx=0 ? And then on the next line to an even biger value when on line 2 vx < 0 ?

ohh yea i see that now.. this is where my initial confusion came in. i needed those position values to get the acceleration formulas R^2 values with respect to time.

Time step seems a bit big. Try 1000 --- however, I may have a bug in my stuff. ...

If the integration works and you make a scatter plot of y vs x, you should get something like a neat circle, at least initially.

Prof is probably right (I can't get past x=0 without weird behaviour... (bug?)


I don't understand how you can go from x on first line to a bigger value if vx=0 ? And then on the next line to an even biger value when on line 2 vx < 0 ?

I think i see the issue

 

[isukatphysics69]

So i had thought that i needed the positions with respect to time for the net force since the net force was (GMm)/(R²) and R= sqrt(px^2+py^2) since the Earth was fixed.
Edited
i will try to fix
think i see how to fix it

 

[isukatphysics69]

omg i am AN IDIOT

 

[isukatphysics69]

Omg i think its finally working i am so dumb i was changing the acceleration value now i am keeping "a" constant and only changing the ax and ay based on position currently dragging down 1 cell at a time since they all depend on each other

 

[isukatphysics69]

ok think i got it
now i have no idea how to graph this data, that's the next challenge

 

[isukatphysics69]

moon has escaped orbit

 

[isukatphysics69]

 

[isukatphysics69]

this is looking good to me, bvu thank you for all the help! i finally got it somewhat working
(the name "position y" is misleading) this is the x and y coordinates plotted

 

[isukatphysics69]

beautiful :')

 

[BvU]

In fact it shouldn't come out as a circle with the set of equations and initials we had. Has to do with reduced mass.

A physics complication. There's also a math complication: an issue with simple forward Euler for this kind of problem. But you learned a great deal which is far more important than getting the 'right' result.

Good luck with the test. I hope you did get some kip

 

[isukatphysics69]

In fact it shouldn't come out as a circle with the set of equations and initials we had. Has to do with reduced mass.

A physics complication. There's also a math complication: an issue with simple forward Euler for this kind of problem. But you learned a great deal which is far more important than getting the 'right' result.

Good luck with the test. I hope you did get some kip

Thank you, i will sleep after this report and study tommorow before the test, already went over the whole practice exam once

 

[BvU]

now i am keeping "a" constant and only changing the ax and ay based on position

Sorry for the bummer, but that isn't the idea of the exercise.

currently dragging down 1 cell at a time since they all depend on each other

in principle row n only depends on row n-1. That's forward Euler for you, the often self-quoted recipe$$x_n = x_{n-1} + v_{x, n-1} * dt \\y_n = y_{n-1} + v_{y, n-1} * dt \\v_{x, n} = v_{x, n} + a_{x, n-1} * dt \\v_{y, n} = v_{y, n-1} + a_{y, n-1} * dt$$

gotta face the drill now

 

[isukatphysics69]

Sorry for the bummer, but that isn't the idea of the exercise.
in principle row n only depends on row n-1. That's forward Euler for you, the often self-quoted recipe$$x_n = x_{n-1} + v_{x, n-1} * dt \\y_n = y_{n-1} + v_{y, n-1} * dt \\v_{x, n} = v_{x, n} + a_{x, n-1} * dt \\v_{y, n} = v_{y, n-1} + a_{y, n-1} * dt$$

gotta face the drill now

aw crap what
its not possible at this point, its 4 am and due tommorow