Question

In the movie The Martian, astronauts travel to Mars in a spaceship called Hermes. This ship has a ring module that rotates around the ship to create “artificial gravity” within the module. Astronauts standing inside the ring module on the outer rim feel like they are standing on the surface of the Earth. (The trailer for this movie shows Hermes at t=2:19 and demonstrates the “artificial gravity” concept between t= 2:19 and t=2:24.)

Analyzing a still frame from the trailer and using the height of the actress to set the scale, you determine that the distance from the center of the ship to the outer rim of the ring module is 11.60 m

a)

What does the rotational speed of the ring module have to be so that an astronaut standing on the outer rim of the ring module feels like they are standing on the surface of the Earth?

b)

Astronauts standing in the ring module will experience lightheadedness and nausea if the acceleration at their feet is very different from the acceleration at their head. To avoid these adverse effects, the acceleration at their head should be no less than  96.5 %   of the acceleration at their feet. (The height of a typical astronaut is 1.52 m )

The ring module should make the astronauts feel like they are standing on the surface of the Earth without making them feel nauseated. To achieve this goal, the ring module needs to have a minimum radius. What is this minimum radius?

Answer 1