FAQ
It is currently Sat Oct 21, 2017 4:50 am


Author Message
frumpydolphin
Post  Post subject: Non uniform acceleration due to gravity  |  Posted: Sat Apr 15, 2017 12:52 am

Joined: Fri Jan 06, 2017 9:57 pm
Posts: 3

Offline
Just here to pose a question...
So in a gravitational field the acceleration is defined as mG/r^2
But r^2 can be expressed as a function of time, and uses the previous acceleration(s) to determine the new coordinates of the masses.
So then acceleration is being used to calculate acceleration. This would continue forever unless there was a way to describe acceleration in a nonuniform way, and thus the coordinates in a nonuniform way. In an example: 2 masses each 1 kg are one meter apart. Immediately they pull each other at G m/s^2. Right after, an infinitesimal amount of time after, there moving at G/(x+(1m/s^2)0.0repeating1) assuming there is only 1 axis. How can this be worked in a more logical way then multiplying by infinitesimals.


Top
Olinguito
Post  Post subject: Re: Non uniform acceleration due to gravity  |  Posted: Sat Apr 15, 2017 11:29 am
User avatar

Joined: Mon Aug 19, 2013 3:56 pm
Posts: 157

Offline
Given two object of mass $m$, the gravitational acceleration experienced by each is given by

    $ \displaystyle \frac{\mathrm d^2r}{\mathrm dt^2}\ =\ -\frac{Gm}{r^2}$
(Note the minus sign: it is because the acceleration increases as the separation between the objects diminishes.) Now $r$ is a function of $t$; if you can express $t$ as a function of $r$, you can substitute it into the RHS and analyse how acceleration varies with time.

_________________
Blog


Top
frumpydolphin
Post  Post subject: Re: Non uniform acceleration due to gravity  |  Posted: Sun Apr 16, 2017 3:44 pm

Joined: Fri Jan 06, 2017 9:57 pm
Posts: 3

Offline
So if you solve for r in that equation though, r is used in the integral on the right, so how does that math work out?


Top
Display posts from previous:  Sort by  
Print view

Who is online
Users browsing this forum: No registered users and 0 guests
You cannot post new topics in this forum
You cannot reply to topics in this forum
You cannot edit your posts in this forum
You cannot delete your posts in this forum
Jump to:   
cron

Delete all board cookies | The team | All times are UTC


This free forum is proudly hosted by ProphpBB | phpBB software | Report Abuse | Privacy