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## 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)

## 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.