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The amount of energy required to get an object in orbit is the same no mater how it is propelled. The challenge is to find a way that's more efficient than a rocket.
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In order for them to launch a rocket the skin of the rocket I think would have to be very thick to withstand the changing force vectors when spinning it just would be impractical.
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re: "The amount of energy required to get an object in orbit is the same no mater how it is propelled. "
That is almost true but not entirely. The amount of
energy added to the object is the same, but the
amount of energy expended is not the same. Like charging a battery, you consumed more AH than the AH stored in the battery.
These two entirely different ways of launching, rocket vs spinning, will be "wasting" energy differently. Take air drag for example. Air drag is proportional to V
2. So at 2x the speed, your lost to air drag is 4x.
A rocket accelerating slowly from the ground has very low V, the atmosphere is thick near ground, but V is very low. When the rocket reach high velocity, the rocket is higher in altitude where the air is thinner, so less air to create drag up there. It may waste less due to air drag, but then of course the rocket is carrying the fuel (and container) that it will burn away or discard and that is a lot of waste.
Spinlaunch is the other way around. It doesn't carry any fuel it needs to accelerate, no waste there. But on launch, it is at its highest velocity where the air is thickest, and slows down by air friction and earth's gravity - till it reach the altitude to light it's own rocket. So the launched vehicle needs to have a lot more initial energy (velocity) to deal with the lost as it goes up. While it was spinning on the ground before launch, it is wasting energy dealing with the friction of the spinning mechanism...
The other issue is the necessity to harden the payload object to deal with the 11,000g centrifugal g. Your payload object may be 1kg for a rocket launch, by the time you harden the design of that 1kg object to deal with the 11,000kg centrifugal force, your spin launch object now may be a many folds heavier 1kg. So, too complex to compare theoretically. We may well have to wait until they actually do launches to see how much efficiency it actually gained, if any.