Force is proportional to m1 * m2 / r^2, so your weight as a percentage of your surface weight is equal to (radius of earth / (radius of earth + height above surface))^2.
this post was submitted on 23 Jan 2024
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Okay, that was way simpler than I thought it might be, lol. Thanks!
~~Mass~~ weight of object on earth = g(mass of object * mass of earth)/(earth radius)^2
Weight of object in orbit= g(mass of object * mass of earth)/(earth radius + distance from earth)^2
Dividing the two equations gives us:
(1/(earth radius + distance from earth)^2)
---------------------------------------
(1/earth radius)^2
Which yields:
(Earth radius)^2
-----------------------------------------
(earth radius + distance from earth)^2
Multiplying the fraction above by 100 will give a percentage.
To check if the equation makes sense imagine if the object was very far from earth. Then the weight (earths gravity) would be small and thus the percentage would be small. This checks with our equation
We can try it for the ISS and see we get:
((6378)^2) ÷(408+6378)^2 = .88
Or 88%
This was helpful... I appreciate you taking the time to write it all out~