Out of this world calculations

Using the artificial gravity equation yields some interesting possibilities. First the equation:

If we want to solve for R ( for radius ), then use this:

R equals 9.81 times g divided by the quantity: 3.14 times rpm divided by 30 ( which is then squared)

To simplify a bit, let g = 1 and rpm = 1, then the denominator becomes a constant, which is 3.14/30 squared. That equals 0.011 rounded. This yields a radius of approx 892 meters at 1 rpm, which will give you 1 Earth gravity. The spinning around a center point will give the sense of gravity needed.

That's a big number. But you can manipulate the rpms and the gravitation field that you previously set to 1. The numbers can get more reasonable that way.

Could you spin up a Starship then and get an approximation of Mars gravity? If not, then could you could dock two together and spin up somewhat more than 2 rpm and get an Earth gravity?

Let's say the crew is at 50 meters ( length of Starship) from the center. To calculate g's at 2.5 RPM, we get close to 1 Mars gravity. If you want an Earth gravity, you need to spin a bit faster.

A little over 4 rpm would do it. But humans generally cannot tolerate higher numbers. That high may be a problem. You have to go at least 2 to get to a little more than lunar gravity. Most folks can tolerate that, or so I recall. If memory serves, then two docked together and spun up to 2 rpm will get you maybe a half Martian gravity. Is that enough? If not, you have to spin up a bit more. To get an Earth gravity, you half to spin up to a point that could be a real problem.

If all that is unsatisfactory, another solution will have to be found. Perhaps 4 Starships lined up together? Six or even eight? The more Starships, the longer the radius is, and the easier an Earth's gravity will be reachable. If his plan to make a thousand ship fleet, he's gonna need every one of them.

It would take 18 Starships lined up in a line and spun up to 1 rpm in order to approximate 1 Earth gravity. Er, maybe not what you want to do. Fewer Starships and more rpm may be the ticket.

I think eight @ 2 rpm would be a fair number. How to do all this is another problem for another time.