carrier has greater volume than its perfect mass sphere
measure on carrier surface has greater radius from mass centre than a measure taken from the surface of the perfect mass sphere.
take into account the earth-point model, shrunk to equivalent mass of a carrier.
we both looked at this mass situation.
*mine treated it as a scaled geometric relationship.
*yours treated it as a scaled point to point relationship.
+mine was wrong because the point of measure was off by the difference of a carrier 1/2 length vs perfect mass sphere radius
+yours was off by the difference of a perfect mass sphere vs the original earth radius.
both + are off, because the calculated distance is greater than the perfect mass sphere radius would have been.
distance is critical here.
although field decreases with distance, at close distances the relationship is tricky, because any change in distance sways results a lot.
the distance in question here is 1 radian from the center, the surface.
imagine moving 1 radian towards the center. now all forces are gone
move 1 radian out. the force weakens with distance, but not that much because the force lines that once were spread out flat are coming together and becoming more parallel.
move 2 radians out and the lines are even more parallel. the force weakened, but in a more regular fashion.
in your model, the move would have had only a regular relationship between points. i.e. going to the center of the mass would have actually increased gravity, rather than decrease.
in my model there is no room for motion at all. the relationships are kept static. it becomes less accurate as distance increases since it relates less and less to the original value.
ALTHOUGH, because the force drop, in actuality, during surface takeoff doesnt fall off like in a regular relationship (lines becoming more parallel, increasing their effectiveness, even though losing force, sort of making a null change zone), slight variations in distance, paricularly away from the surface, have only a small force variation. like a ladder sliding down a wall. you can slide the base away form the wall a good amount before the top starts sloding down the wall with good speed.
my point of measure is only a small distance from the perfect sphere. meaning that even though the force falloff in the field exists, it is just leaving its irregular ladder-like phase, so its only skewed a little.
your formula used distances.
it compared the force of attraction earth at a distance of 1 radian (surface)
it compared the force of attraction carrier at 1 earth radian.
but there never was a fighter launched at that radius. it was launched at the carriers 1/2 length, which you could cionsider its pseudo-radius-albeit-larger
if you choose to scale mass, you should scale distance too (or at least use the new one), since that is your point of measure. measure from there to the mass center.
you were finding falloff at a position that was irrelevant to the whole problem. thats why you
were off by a factor of 7.
-schehearzade