From: alain245@videotron.ca   
      
   Le Aug/16/2020 à 16:29, JF Mezei a écrit :   
   > On 2020-08-16 11:19, Jeff Findley wrote:   
   >   
   >> The problem with the shuttle was that the penalty to launch into a   
   >> higher inclination orbit applies to all the mass put into orbit.   
   >   
   >   
   > But why is there a penalty?   
   >   
   > When you laiunch from 28°, Earth gives you 1471kmh horizontal speed vector.   
   >   
   > If you head for a 28° inclination, you add energy in the same direction   
   > as where you were going.   The resulting orbit consists of the 1471   
   > horizontal push and whatever energy you added to it to get to 25,000kmh.   
   > Right?   
   >   
   >   
   > So if you head to a 51° orbit from 28", you start with a 1471kmh   
   > eastbound vector, and instead of adding your energy in the same   
   > direction, you add diagonally. The resulting speed vector is a   
   > compnination of hoziozontal and vertical, with the horizontal being   
   > bigged than the 1471 push you got at launch.   
   >   
   > But either way, don't you get the same energy at launch, and don't you   
   > add the same acceleration amount to reach 25,000km ?   
   >   
   >   
   > If you go polar, then your horizontal component is smaller than the   
   > speed given by earth at launch, so you have to spend fuel to counter it.   
   > If you go lower than 28", then the vertical speed you got from launching   
   > at 28° has to be countered and you need to position yourself over   
   > equator. So that costs fuel.   
   >   
   > But what I don't understand is why launching from 28 to a 51°   
   > inclination would cost more fuel since the full amount of push you get   
   > at launch is used and included in your final orbit speed.   
      
   As I explained in another post it is about a lost of efficiency because   
   Earths rotation is not in the right direction. It is a little like if   
   you want to go to a position 1km east and 1 km north from where you are.   
   Because of the Pythagorean theorem, you don't need to do 2 km to get to   
   where you want to go, you use the diagonal which is of length square   
   root of 2, about 1.41 km, instead of doing 1 km east then 1 km north,   
   which would be 2 km. Now if some one gives you a lift to go to that 1 km   
   east and 1 km north position, lets say he brings you 1/2 km east, it   
   helps you but not as much as if he had brought you 1/2 km in the north   
   east direction.   
      
   It's the same for reaching orbit, Earth's rotation helps you if you are   
   heading to a 51° orbit from 28°, but not as much as if the rotation of   
   Earth was in the right direction.   
      
      
   Alain Fournier   
      
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