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Bonus questions can add +2 to your overall score if your answer is correct. Calculate the Schwarzschild radius for fictional planet Druidia (mass = 3.654×1025 kg ) to become a black hole.

User GhostKU
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1 Answer

2 votes

Answer:

Approximately
5.427 * 10^(-2)\; {\rm m}.

Step-by-step explanation:

For a planet of mass
M, the Schwarzschild Radius would be:


\displaystyle r_{\text{s}} = (2\, G\, M)/(c^(2)),

Where:


  • G \approx 6.674 * 10^(-11)\; {\rm m^(3)\cdot kg^(-1)\cdot s^(-2)} is the gravitational constant, and

  • c \approx 2.998 * 10^(8)\; {\rm m\cdot s^(-1)} is the speed of light in vacuum.

It is given that the mass of this planet is
M = 3.654 * 10^(25)\; {\rm kg}. Substitute this value into the expression for
r_{\text{s}} and evaluate to obtain:


\begin{aligned} r_{\text{s}} &= (2\, G\, M)/(c^(2)) \\ &\approx \frac{2\, (6.674 * 10^(-11)\; {\rm m^(3)\cdot kg^(-1)\cdot s^(-2)})\, (3.654 * 10^(25)\; {\rm kg})}{\left(2.998 * 10^(8)\; {\rm m\cdot s^(-1)}\right)^(2)}\\ &\approx 5.427 * 10^(-2)\; {\rm m}\end{aligned}.

In other words, if the radius of this planet goes below approximately
5.427 * 10^(-2)\; {\rm m}, the planet would become a black hole.

User Akansha
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7.6k points

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