Chapter 1.3, Problem 26E

To determine

To find: The functionthat defines the brightness of the star Delta Cephei in terms of time.

Answer to Problem 26E

The brightness of Delta Cephei is given by the function $M\left(t\right)=4.0+0.35\sin \left(\frac{2\pi }{5.4}t\right)$.

Explanation of Solution

Given:

Time period of the maximum brightness of the star Delta Cephei is $5.4$ days with the average brightness 4.0 and it varies by $\pm 0.35$.

Calculation:

As the maximum period of brightness is 5.4 days consider total time period for Delta Cephei as 5.4 days.

Since the time period is of 5.4 days, the time period in terms of time t is given by $\sin \left(\frac{2\pi }{5.4}t\right)$.

Note that the average amplitude of the star is 4.0 with variation of $\pm 0.35$ in the magnitude.

Use the above information to construct a function to calculate the brightness of the starDelta Cephei as shown below,

$M\left(t\right)=4.0+0.35\sin \left(\frac{2\pi }{5.4}t\right)$.

Therefore, the function that models the brightness of star in Delta Cephei as function of time is $M\left(t\right)=4.0+0.35\sin \left(\frac{2\pi }{5.4}t\right)$.