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Chapter 15

Q. 15.2

Calculate the Schwarzschild radius for the sun and Earth.

Strategy We use the masses of the sun and Earth in Equation (15.6) to find the Schwarzschild radius for each.

r_{ S }=\frac{2 G M}{c^{2}}=\left(1.5 \times 10^{-27} m / kg \right) M (15.6)

Step-by-Step

Verified Solution

If we substitute the mass of the sun and Earth into Equation (15.6), we obtain

 

\begin{aligned}r_{ S }(\text { sun }) &=\left(1.5 \times 10^{-27} m / kg \right)\left(2.0 \times 10^{30} kg \right)=3.0 km \\r_{ S }(\text { Earth }) &=\left(1.5 \times 10^{-27} m / kg \right)\left(6.0 \times 10^{24} kg \right)=9.0 mm\end{aligned}

 

If the Earth were a black hole, the dark spot would be very tiny indeed! Our current understanding is that neither the Earth nor the sun will ever become a black hole.