Math Is Fun Forum

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:

* Describe your question in the title, so people know if they can help or not ("Please help me" is not a good description).yeah changed

* make it clear what kind of help you want.  Do you want just an answer; or a hint of how to get an answer; or more detailed help on a topic.hint of answer,this is not homework so i dont want the answer and no why

*  Tell us what level you are at. It will help avoid replies that are too easy or too hard for you to understand.a bit on calculus,have learned integrals and derivatives

*  After you’'ve made a post, read it through and check it says what you intended.  Edit if necessary before we start solving the wrong problem!yeah

*  Please, oh yes PLEASE, come back and read the responses.  Then make another post either asking for more clarification or thanking the people who have given up their time freely.does subscribe to this post work?can it give me notifications?

IN SUMMARY: Use a good title, say what help you want, come back and say thanks.