Question

The Crab Nebula (see Figure 7.41) pulsar is the remnant of a supernova that occurred in A.D. 1054. Using data from Table 7.3, calculate the approximate factor by which the power output of this astronomical object has declined since its explosion.

Short answer

The factor by which the power output of the Crab Nebula has declined since its explosion is ${10}^{-10}$.

Step-by-step solution

Definition of Concepts

Power: Power is a scalar quantity defined as how fast energy is being consumed or transformed. One watt of power is defined as one Joules of energy is being consumed per second.

Calculate the approximate factor by which output has deceased

The power output of the Crabs Nebula is,

$P_C={10}^{28}\text{W}$

The power output of the Supernova explosion is,

$P_S=5\times {10}^{37}\text{W}$

The factor by which the power output has deceased is,

$F=\frac{P_C}{P_S}$

Putting all known values,

$$\begin{gathered} F=\frac{{10}^{28}\text{W}}{5\times {10}^{37}\text{W}} \\ =2\times {10}^{-10} \end{gathered}$$

Therefore, the factor by which the power output of the Crab Nebula has declined since its explosion is ${10}^{-10}$.