Show me the maths ... I sense poor Newtons motion laws going down
I will tell you the elements and methods you will need to know
in order to calculate it yourself but I will include an example.
1) you need to know the acceleration that is the result
of the attraction of gravity between yourself and the earth.
(9.8 ms^2)
the above 9.8 ms^2 acceleration is the force that pulls you towards the earth (980 N) if your mass is 100 kg.
2) you need to know your mass.(kg)
3) you need to know the distance from yourself to the center
of the earths gravity field.
4) I will find the needed orbital velocity.
in order to maintain a orbit around the earth all you need
to do is to match or balance the force of gravity
( the inward pull towards the center of the earths gravity field)
and the force caused by angular acceleration
( the outward force that pulls you away from the center of the earths gravity field due to the angular acceleration of
your body as it travels in a circular path around
the earth)
in essence you need to achieve a certain velocity to do this.
using the centripetal force formula you can calculate
the amount of orbital velocity that you must achieve in order to achieve a orbit with a constant altitude away from the center of the earths gravity field.
F(centripetal) = mv^2/r
if you know your mass equals = 100kg
and you know the force is 980 N ( 9.8 ms^2)
then you need to counteract the acceleration of
a force of 980 N against a mass of 100 kg
980 N will accelerate a 100 kg mass a distance of
9.8 meters in 1 second.
lets say your radius from the earths center of gravity is
in maximum low earth orbit (2000 km above surface )
adding in the 6,371 km radius of the earth you have a total
radius from the center of the earths gravity field of 8,371 km
radius = 8,371,000 meters
using the knowns to find the nedded velocity to establish a orbit.
100 kg
8,371,000 meters radius
9.8 ms^2 acceleration
find velocity
the formula results in a F (centripetal) that is the result of a division
of (mass x velocity squared / radius)
we know that the acceleration is 9.8 ms^2
so we multiply the radius by 9.8
were counteracting the acceleration caused by the force of gravity acting against a 100 kg mass with a force caused
by the resistance of an object to undergo angular acceleration
or simply put the resistance of an object to change its
direction so the result F in the centrifugal force formula
will be given as an acceleration not a force.
8,371,000 meters (radius) x 9.8 = 82,035,800
this gives us the result of mass x velocity squared
so we divide by the mass to get the velocity squared.
82,035,800 / 100 (mass) = 820,358 (velocity squared)
we then find the square root of velocity squared to get the velocity.
sqr of 820,358 = 905.73 ms (velocity)
so your orbital velocity needs to be apx 905.73 ms
in order to stay in orbit around the earth at a orbital
altitude of 2000 km.
