- #1

Will Flannery

- 120

- 36

The freefall wiki entry wiki Freefall has an analytic solution for freefall distance in a gravitational field, but ... it doesn't seem to work ... at least i can't get it to work ... here is my MATLAB program to test it ...

clear

G=6.7e-11; % gravitational constant m^3/(kg*s^2)

mEarth = 5.9742e24; % mass of Earth in kg

rEarth = 6.378e6; % radius of Earth in m

% drop a 1kg ball from 100m above the surface of the earth

mu = G*(mEarth + 1);

y0 = rEarth + 100;

t = 1;

x = (3/2*(pi/2-t*sqrt(2*mu/y0^3)))*2/3;

y1 = y0*(x - x^2/5 - 3*x^3/175 - 23*x^4/7875 - 1894*x^5/3931875 - 3293*x^6/21896875 - 2418092*x^7/62077640625);

y0-y1

ans =

9.5639e+04

So, the apple fell 95000 m in the 1st second ... (or I made a mistake)

I tried to check the references, the first has a lot of formulas but not the one above, and the second is behind paywall (The Physics Teacher) and the abstract does not look promising.

Is there an analytic formula anywhere ?

clear

G=6.7e-11; % gravitational constant m^3/(kg*s^2)

mEarth = 5.9742e24; % mass of Earth in kg

rEarth = 6.378e6; % radius of Earth in m

% drop a 1kg ball from 100m above the surface of the earth

mu = G*(mEarth + 1);

y0 = rEarth + 100;

t = 1;

x = (3/2*(pi/2-t*sqrt(2*mu/y0^3)))*2/3;

y1 = y0*(x - x^2/5 - 3*x^3/175 - 23*x^4/7875 - 1894*x^5/3931875 - 3293*x^6/21896875 - 2418092*x^7/62077640625);

y0-y1

ans =

9.5639e+04

So, the apple fell 95000 m in the 1st second ... (or I made a mistake)

I tried to check the references, the first has a lot of formulas but not the one above, and the second is behind paywall (The Physics Teacher) and the abstract does not look promising.

Is there an analytic formula anywhere ?

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