problem with differential equation and 14 degree polynomials

imcute · 2022-09-29 00:06:08

so i want to derive the O(1) algorithm of earth going around the sun(i mean a formula to calculate a smol object orbiting a large object,and only the smol object can get gravity from the large object,and i dont mean something like x²+y²=r² for circle orbits(it has to do with gravity etc,and i want to derive it not graph it and find the pattern(circle)))
so gravity is a function of position(and some constants like gravity constant and big object mass and smol object mass)
gravity sums up(∫) to velocity
velocity sums up to position
but there is a problem!(ik how to do ∫∫s)i see that the pre-integral function has something to do with its integral's integral!
i thought that for a day and did that ∫∫ so i ended up with(i used complex numbers not vectors cuz the |v| function is undifferentiable)
gravity constant*mass(smol object)*mass(big object)*(real part of position of smol object to the third power+im.p.o.p.o.s.o to the 3rd power times i)*square root of(re.p.o.p.o.s.o to the 4th power+im.p.o.p.o.s.o to the 4th power),and this should end up with re.poposo+im.poposoi
the problem is that i have no idea with how to root this(it has a degree of 3+3+4+4=14!!!)

edit:DIDNT U LISTEN TO PHYSICS CLASS THE GRAVITY FORMULA GIVES U A FORCE NOT AN ACCELERATION YOU 1/8BYTECH
---physics teacher
edit edit:oh sorry i guess that i would have to reintegral it >:C

We are happy to help! But we don't do your homework for you.this is my own question and the physics teacher scolding thing is bc i showed my calculations starting from gravity formula to him

When you post a question:

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Last edited by imcute (2022-09-29 00:11:32)

Jai Ganesh · 2022-09-29 01:30:13

Hi imcute,

What is required? Help? Suggestion? Information?

Be specific.

imcute · 2022-09-29 01:36:52

ganesh wrote:

Hi imcute,
What is required? Help? Suggestion? Information?

Help,and i have said that question

imcute · 2022-09-29 23:20:08

ganesh wrote:

Hi imcute,
What is required? Help? Suggestion? Information?
Be specific.

Hello?
I know that this isn't an ims but its not an eternity messaging service either

Jai Ganesh · 2022-09-29 23:58:00

One ought to wait. Patience!

imcute · 2022-10-09 23:49:21

ganesh wrote:

One ought to wait. Patience!

its an enternity messaging service after all ((((((

Jai Ganesh · 2022-10-10 00:31:05

imcute wrote:

ganesh wrote:
One ought to wait. Patience!
its an enternity messaging service after all ((((((

One ought to be patient.

Forum rule #1.

This is a Forum, it is not instant chat. Leave your message, and come back later (hours or days) to see what responses you got.

Bob · 2022-10-10 00:48:21

hi imcute

I've only just discovered this thread and I'm having a great deal of difficulty understanding what you are asking.

im.p.o.p.o.s.o to the 3rd power times i)*square root of(re.p.o.p.o.s.o to the 4th power+im.p.o.p.o.s.o to the 4th power),and this should end up with re.poposo+im.poposoi

Bits like this are not something I understand at all.

In 1609 Kepler published his three laws of planetary motion. Half a century later Newton used his law of universal gravitation to prove them. Is that what you are trying to do? It doesn't involve a 14 degree polynomial and the calculus is relatively straight forward.

Please start again and make it clear what you are trying to achieve. Thanks.

Bob

imcute · 2022-10-12 12:28:58

Bob wrote:

hi imcute
I've only just discovered this thread and I'm having a great deal of difficulty understanding what you are asking.
im.p.o.p.o.s.o to the 3rd power times i)*square root of(re.p.o.p.o.s.o to the 4th power+im.p.o.p.o.s.o to the 4th power),and this should end up with re.poposo+im.poposoi
Bits like this are not something I understand at all.
In 1609 Kepler published his three laws of planetary motion. Half a century later Newton used his law of universal gravitation to prove them. Is that what you are trying to do? It doesn't involve a 14 degree polynomial and the calculus is relatively straight forward.
Please start again and make it clear what you are trying to achieve. Thanks.
Bob

oohay ive redid my math
F=ma=md²r/dt²=Gmm/r²(r is an imaginary number of position)
so we get a second order differential equation d²r/dt²=Gm/r²(the two “small object mass” cancel out)
the problem is that r is a function of time which is the solve to this diff equation
then move every d²r to left and every dt² to right
r²d²r=Gmdt²
integrate both sides
∫∫r²d²r=Gm∫∫dt²
1/3∫r³dr=Gm(mysteriously,nothing is in the right integral so its a moot point and we should ignore it)
r^4/12=Gm
so r=pow(Gm/12,1/4)
what this doesn't tell us is what direction we are going,but atleast we get the linear formula
next we should actually calculate the purely complex number(i.e really complex,like no lack of any part) r
r is replaced with a+bi
<strike>(a+bi)(a+bi)d²(a+bi)=Gmd²t
integrate them
∫∫(a²+2abi-b²)d²(a+bi)=Gm(again,no thing in right integral,so ignore)
∫∫(a³+3a²bi-3ab²-b³i)d²=Gm
∫(1/4a^4+1/2a³b²i-1/2a²b³-1/4b^4i)d=Gm
1/20a^5+1/24a^4b³i-1/24a³b^4-1/20b^5i=Gm
merge likes
(1/20a^5-1/24a³b^4)+(1/24a^4b³-1/20b^5)i=Gm</strike>

whoops wrong math
(a²+b²)d²(a+bi)=Gmd²t
integrate
∫∫(a²+b²)d²(a+bi)=Gm
∫∫(a³+a²bi+b²a-b³)d²=Gm
∫(1/4a^4+1/6a³b²i+1/6b³a²-1/4b^4)d=Gm
(1/20a^5-1/20b^5)+(1/72a^4b³+1/72a³b^4)i=Gm
there it goes
but there is the problem:where is the t?im expecting the varible time in my formula!
also the original problem probably did not involve 5th powers

imcute · 2022-10-12 12:30:00

ganesh wrote:

imcute wrote:
ganesh wrote:
One ought to wait. Patience!
its an enternity messaging service after all ((((((
and come back later (hours or days)

but its weeks

Jai Ganesh · 2022-10-12 12:37:29

imcute wrote:

ganesh wrote:
imcute wrote:
its an enternity messaging service after all ((((((
and come back later (hours or days)
but its weeks

See #8 above in a related post.

Math Is Fun Forum

#1 2022-09-29 00:06:08

problem with differential equation and 14 degree polynomials

#2 2022-09-29 01:30:13

Re: problem with differential equation and 14 degree polynomials

#3 2022-09-29 01:36:52

Re: problem with differential equation and 14 degree polynomials

#4 2022-09-29 23:20:08

Re: problem with differential equation and 14 degree polynomials

#5 2022-09-29 23:58:00

Re: problem with differential equation and 14 degree polynomials

#6 2022-10-09 23:49:21

Re: problem with differential equation and 14 degree polynomials

#7 2022-10-10 00:31:05

Re: problem with differential equation and 14 degree polynomials

#8 2022-10-10 00:48:21

Re: problem with differential equation and 14 degree polynomials

#9 2022-10-12 12:28:58

Re: problem with differential equation and 14 degree polynomials

#10 2022-10-12 12:30:00

Re: problem with differential equation and 14 degree polynomials

#11 2022-10-12 12:37:29

Re: problem with differential equation and 14 degree polynomials

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