Question

The binomial approximation is accurate only if beta<<1. Suppose you have a clock at rest in the earth's reference frame that keeps perfect time over the course of exactly one day. At what speed, in m/s, would a moving clock differ from the earth clock by ns over the course of that same exact day?

Answer 1

The student's question concerns calculating the speed at which a moving clock would differ from a stationary Earth clock by a certain time over one day, which involves the concept of time dilation from physics.

Step-by-step explanation:

The student's question relates to the concept of time dilation as described by Einstein's theory of relativity. We are given a scenario concerning the difference in time experienced by a clock moving at a certain speed compared to a clock at rest on Earth. To determine the speed at which the moving clock differs from the Earth clock by nanoseconds (ns) over the course of one day, we can use the time dilation formula:

t' = t / sqrt(1 - v^2/c^2)

where t' is the dilated time, t is the proper time, v is the relative velocity, and c is the speed of light.

The problem can be further explored by rearranging the formula to solve for v, taking into account the small time difference of nanoseconds (ns), the length of one day (24 hours), and applying approximation methods when v is much less than c.