Calculating the relevant variables for a rotating habitat

[DET]

1. Homework Statement

I want to calculate the rotational period and surface velocity of a Bishop Ring with a radius of 80 km and a surface 'gravity' of 0.86 G

I should note that this isn't for homework. It's for personal interest. I'm looking for a sanity check on this. The homework forum just seemed the best place for this type of question.

Homework Equations

From https://en.wikipedia.org/wiki/Artificial_gravity the formula to calculate the rotational period for a given radius and desired gravity is

t = 2 * pi * (r/a)^.5

where t is time, r is radius of the habitat, and a is desired acceleration (gravity)​

The Attempt at a Solution

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0.86 G = 8.428 m/s^2

2 * pi * (80,000/8.428)^.5 = 612 seconds

circumference = 2 * pi * 80 km = 502.65 km

linear velocity = 502.65 / 612 = 0.82 km/s = 2957 km/hrSo the habitat will rotate once every 612 seconds, and the velocity of the rim will be 2957 km/hr

Did I brain-fart anywhere in here?

 

[collinsmark]

Homework Statement

I want to calculate the rotational period and surface velocity of a Bishop Ring with a radius of 80 km and a surface 'gravity' of 0.86 G

I should note that this isn't for homework. It's for personal interest. I'm looking for a sanity check on this. The homework forum just seemed the best place for this type of question.

Homework Equations

From https://en.wikipedia.org/wiki/Artificial_gravity the formula to calculate the rotational period for a given radius and desired gravity is

t = 2 * pi * (r/a)^.5

where t is time, r is radius of the habitat, and a is desired acceleration (gravity)​

The Attempt at a Solution

[/B]
0.86 G = 8.428 m/s^2

2 * pi * (80,000/8.428)^.5 = 612 seconds

circumference = 2 * pi * 80 km = 502.65 km

linear velocity = 502.65 / 612 = 0.82 km/s = 2957 km/hrSo the habitat will rotate once every 612 seconds, and the velocity of the rim will be 2957 km/hr

Did I brain-fart anywhere in here?

It looks good to me.

There is the possibility of a very minor rounding error in your work. But given your choice of g = 9.8 m/s², which has only two significant figures, any such rounding errors would be pretty meaningless anyway.

Oh, and one last thing, the period -- the amount of time for a single rotation -- is typically denoted as capital T rather than lowercase t.

Btw, nice work!

 

[DET]

Thank you!