Question

An astronaut at rest on earth has a heart rate of 70 beats per min. When the astronaut is traveling in a spaceship at 0.90c, What will this rate be as measured by a) an observer also in the ship and b) an observer at rest on Earth

Answer 1

Inside the spacecraft, the astronaut's heart rate would be measured at 70 beats per minute. From Earth, due to time dilation, the rate would be seen as approximately 30.5 beats per minute. These estimates illustrate the effects of time dilation, where time appears to pass slower for objects moving at high speed relative to an observer.

Step-by-step explanation:

The student asked how the heart rate of an astronaut traveling in a spaceship at 0.90c would be measured by observers both inside the spaceship and at rest on Earth. This involves the concepts of time dilation and relativity in physics.

Heart Rate as Measured by an Observer in the Ship

An observer also in the spaceship would measure the astronaut's heart rate to be the same as it is on Earth, which is 70 beats per minute. This is because both the astronaut and the observer are in the same inertial frame of reference, meaning that they are both moving at the same velocity and there are no relative velocity differences between them that would affect their measurements of time.

Heart Rate as Measured by an Observer at Rest on Earth

For an observer at rest on Earth, the situation is different due to the effects of time dilation as predicted by Einstein's theory of special relativity. The astronaut's heart rate would appear to be slower. To calculate the dilated heart rate, the Lorentz factor (gamma, γ) would be used, which for a speed of 0.90c is around 2.294. Since time dilation means the events (in this case, heartbeats) would occur less frequently, you would divide the heart rate by this factor. Thus, the heart rate as observed from Earth would be approximately 30.5 beats per minute (70 / 2.294).

In both scenarios, while the astronaut experiences no difference in time passage in their own frame, an observer on Earth sees time moving slower for the astronaut due to the high velocity at which the spaceship is traveling relative to Earth. This falls in line with relativistic effects predicted by physics but not commonly noticeable except at speeds approaching the speed of light.