An object falls from a height of 10,000 km towards the Earth's surface at 6,370 km. It satisfies the differential equation
h'' = -0.0098 / (h/6370)2
where h is measured in kilometers from the centre of the Earth. We plot below (in blue) the graph of the solution calculated by simple step approximations
h(t + dt) = h(t) + v(t).dt
v(t + dt) = v(t) + a(t).dt
a(t) = -0.0098 / (h(t)/6370)2
The blue graph plots the approximate solution with steps dt = 1 second. The grey graphs plot the solutions at constant g, one with the value of g at height 10,000 km and the other with the value of g at the Earth's surface.
Clicking on the black node will suspend the process, and releasing the mouse button will then resume it. Moving the black node will change its speed. Moving the blue node (the falling object) will place the falling object at different heights and restart the fall from that height.