the gravitaitonal constant is only constant at one specific height in the gravitaitonal field. But the gravitaitonal force is reducing, the further away from earth you get. So what you actually have to do is calculate U1 = -GMm/r1 for the LEO and U2 = -GMm/r2 for surface level. leaving out the objects mass already you get as difference
(U1-U2)/m = 6.67e-11 x 5.97e24 x (1/6,73e6-1/8,73e6) = 13,555 Now that is your specific energy from the starting velocity = 1/2 v² from the kinetic energy. So at ground level you actually need 5,206 m/s ignoring air friction.
Also your length of the railgun exceeds the atmosphere, so not only for the friction, but also for the distance to earth you will need much less speed at the end of that railgun. Furthermore g will get less as it gets higher, so you can accelerate faster towards the end of it.
I’m not claiming the concept is viable by default, but your calculation is not including crucial aspects of how gravitaitonal force changes in a gravitaitonal field.
How did you calculate 8200 m/s?
the gravitaitonal constant is only constant at one specific height in the gravitaitonal field. But the gravitaitonal force is reducing, the further away from earth you get. So what you actually have to do is calculate U1 = -GMm/r1 for the LEO and U2 = -GMm/r2 for surface level. leaving out the objects mass already you get as difference
(U1-U2)/m = 6.67e-11 x 5.97e24 x (1/6,73e6-1/8,73e6) = 13,555 Now that is your specific energy from the starting velocity = 1/2 v² from the kinetic energy. So at ground level you actually need 5,206 m/s ignoring air friction.
Also your length of the railgun exceeds the atmosphere, so not only for the friction, but also for the distance to earth you will need much less speed at the end of that railgun. Furthermore g will get less as it gets higher, so you can accelerate faster towards the end of it.
http://hyperphysics.phy-astr.gsu.edu/hbase/gpot.html
I’m not claiming the concept is viable by default, but your calculation is not including crucial aspects of how gravitaitonal force changes in a gravitaitonal field.
I looked at a delta-v chart, which mostly list 9000-10000 for 250km orbits. I subtracted 10% from the one on Wikipedia for an absolute minimum.
That rather speaks against the concept, wouldn’t you say?