TABULA/samples/Pseudogravity by rotation
This is SAMPLE3. To work with this sample, enter $3
State 1:
Pseudogravity by rotation
┌ {1} 1 min period of rotation=
┌ │ ┌ {2} @ 894.826 m length of boom
│ ├ └>{3} @ 5622.358 m circumference of circle
├ └> {4} @ 93.706 m/s pod velocity
└>┌ ┌ {5} @ 9.813 m/s² centripetal acceleration
│ ├ {6} 1 earth.g earth gravity unit=
├ │ {7} 1 mars.g mars gravity unit=
│ └>{8} @ 1 / earth pod boom -->1
└> {9} @ 2.644 / mars pod boom -->1
State 2:
Pseudogravity by rotation
┌ {1} 1 min period of rotation=
┌ │ ┌ {2} @ 338.403 m length of boom
│ ├ └>{3} @ 2126.246 m circumference of circle
├ └> {4} @ 35.437 m/s pod velocity
└>┌ ┌ {5} @ 3.711 m/s² centripetal acceleration
│ ├ {6} 1 earth.g earth gravity unit=
├ │ {7} 1 mars.g mars gravity unit=
│ └>{8} @ 0.378 / earth pod boom -->1
└> {9} @ 1 / mars pod boom -->1
Rationale
The rotating space platform Oberon described in Nida 2014 consists of a central hub for docking connected by unequal booms to a pair of pods. Rotating the space platform once every 60 s induces pseudogravity in each pod to maintain a semblance of normal life. The pods have unequal masses to constrain the platform to rotate around the hub.
NOTE: a spinning body does not rotate about the point of balance of its first moment (its centroid), but the second moment.
How long must each boom be to simulate the surface gravity of Earth and Mars respectively?
The problem is essentially solved by the line graph: Rotation Speed of Centrifuge but here we solve it with a t-table.
Try it out
SAMPLE3 loads in State 1 above. To set it to State 2…
- Select line {9} and change its value to 1
- For length of boom giving Mars gravity read item {2} length of boom
To set it back to State 1…
- Select line {8} and change its value to 1
- For length of boom giving Earth gravity read item {2} length of boom
Build this t-table
- [UNFINISHED]