MathDB

The following construction is used for training astronauts: A circle

C_2

of radius

2R

rolls along the inside of another, fixed circle

C_1

of radius

nR

, where

n

is an integer greater than

2

. The astronaut is fastened to a third circle

C_3

of radius

R

which rolls along the inside of circle

C_2

in such a way that the touching point of the circles

C_2

and

C_3

remains at maximum distance from the touching point of the circles

C_1

and

C_2

at all times. How many revolutions (relative to the ground) does the astronaut perform together with the circle

C_3

while the circle

C_2

completes one full lap around the inside of circle

C_1

Problem Statement