gravitubes.nb

Distance, velocity, and acceleration vs time on the way

Inverting the tRadial equation above...

r[t_, R_, G_, M_] := (R Tan[π/2 - (G M)^(1/2)/R^(3/2) t])/(1 + (Tan[π/2 - (G M)^(1/2)/R^(3/2) t])^2)^(1/2)

$RowBox[{Plot, [, RowBox[{RowBox[{r, [, RowBox[{t, ,, 6378140, ,, RowBox[{6.673, *, 10^(-11)}], ... e, ,, FrameLabel {"Seconds", "Meters"}, ,, AspectRatio1}], ]}]$

[Graphics:../HTMLFiles/index_32.gif]

-(G M)^(1/2)/(R^(1/2) Csc[((G M)^(1/2) t)/R^(3/2)]^2^(1/2))

vr[t_, R_, G_, M_] := -(G M)^(1/2)/(R^(1/2) Csc[((G M)^(1/2) t)/R^(3/2)]^2^(1/2))

$RowBox[{Plot, [, RowBox[{RowBox[{vr, [, RowBox[{t, ,, 6378140, ,, RowBox[{6.673, *, 10^(-11)}] ... , FrameTrue, ,, FrameLabel {"Seconds", "Meters/Second"}}], ]}]$

[Graphics:../HTMLFiles/index_38.gif]

-(G M Csc[((G M)^(1/2) t)/R^(3/2)]^2^(1/2) Sin[(2 (G M)^(1/2) t)/R^(3/2)])/(2 R^2)

ar[t_, R_, G_, M_] := -(G M Csc[((G M)^(1/2) t)/R^(3/2)]^2^(1/2) Sin[(2 (G M)^(1/2) t)/R^(3/2)])/(2 R^2)

[Graphics:../HTMLFiles/index_44.gif]

Created by Mathematica (June 17, 2004)