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frumpydolphin
 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

 Just here to pose a question...So in a gravitational field the acceleration is defined as mG/r^2But 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.
Olinguito
 Post subject: Re: Non uniform acceleration due to gravity  |  Posted: Sat Apr 15, 2017 11:29 am

Joined: Mon Aug 19, 2013 3:56 pm
Posts: 143

 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
frumpydolphin
 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

 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?
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