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/sci/ - Science & Math

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5818847 No.5818847 [Reply] [Original]

Acceleration is the rate of change of velocity, which is in turn the rate of change of displacement, so displacement can be calculated by integrating acceleration twice. Acceleration due to gravity varies as the inverse square of distance, which is affected by the displacement. So is distance then defined in terms of itself?

Like, say for the sake of argument you have a particle 1 meter away from a fixed attractor with mass of 1 kilogram. The particle has initial velocity 0. How do you find its position after 1 second?

Mathematica gives me a max recursion depth error.

>> No.5818853

d = v*t + (a*t^2)/2

>> No.5818857

>>5818853
That assumes constant acceleration. In this, acceleration is given by g(m)/r^2

>> No.5818878

It's a second order differential equation that can't be naively solved by integrating twice. It's also a two-body problem, so unless one of the masses is much larger than the other you can't simply neglect the motion of the other body. I made a semi-detailed post on stack exchange where the asker wanted to know how to calculate the time it would take for two masses to come together under gravity. You can use the same approach to find r(t).

>> No.5818886

>>5818878
Forgot the link:
http://physics.stackexchange.com/questions/55278/distance-traveled-in-a-simple-two-body-problem/55284