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# The effects of microgravity on muscle tissues

## Problem

A simple model of the effects of microgravity on astronaut’s muscles is given by “unloading,” in which reduced gravity mimics the terrestrial effects of bed rest or suspension, in which the “load” or total gravitational force acting on the muscle is reduced. Based on long-term terrestrial studies, researchers have concluded that the physiological basis of adaptation to microgravity involves a reduction in the diameter of muscle fibers, which bring about corresponding decreases in the maximum tension that can be exerted by the muscle. Due to these effects, astronauts frequently report inflammation and fatigue in their primary muscle groups upon returning to earth.
The effect of unloading on the performance of muscle tissue is shown in Figure 1, which shows examples of force-velocity relationships for hypothetical muscle tissues. The solid line indicates a standard terrestrial muscle response, the dashed line indicates the response of an astronaut who has just returned from space. The graphs were generated by terrestrial experiments in which a patient’s muscles were allowed to shorten in response a force of fixed magnitude, like a hand weight. The rate of shortening is the velocity recorded for that experiment. The experiment is then repeated by varying the load size and determining the new contraction rate, and the results are compiled to generate the force-velocity graph.
Figure 1: Force-velocity relationships for ideal muscle tissues. The solid line corresponds to a standard muscle response, but the dashed line corresponds to the muscle tissue of a recently-returned astronaut. (Adams et al. 2003)
What is the load on the muscles due to gravity of an astronaut orbiting at 2, R, start subscript, e, end subscript, where R, start subscript, e, end subscript is the radius of the earth, relative to the load she experiences on earth (F, start subscript, 0, end subscript)?