Answer key: Black Hole Size Worksheet

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Goal: Calculate the size of a black hole’s event horizon from its mass, and describe how the horizon grows with mass.

Completed results table

Values are the lab’s own readouts for each setting.

Answers

1. How big would the event horizon be if the Sun became a black hole without changing its mass? Compare it with the Sun’s real radius of about 696,000 km.

   Its radius would be about 2.95 km (5.91 km across), more than 200,000 times smaller than the Sun is now.

2. Compare 10 and 20 solar masses. What happens to the horizon radius when the mass doubles?

   It doubles too, from 29.53 km to 59.07 km. The Schwarzschild radius is directly proportional to mass: rₛ = 2GM/c².

3. Use rₛ ≈ 2.95 km × (mass in Suns) to estimate the horizon of Sagittarius A* (4.3 million Suns), then check with the lab.

   2.95 km × 4,300,000 ≈ 12.7 million km, about 0.085 AU, which is smaller than Mercury’s orbit.

4. Earth’s mass is about 0.000003 Suns, too small to enter in the lab. Calculate the size of an Earth-mass black hole.

   rₛ ≈ 2.95 km × 0.000003 ≈ 0.0000089 km, which is 8.87 mm. The horizon would be about 1.8 cm across, the size of a marble.

5. If the Sun were replaced by a black hole with the same mass, would Earth be pulled in? Explain.

   No. At Earth’s distance, gravity depends only on the mass, which is unchanged, so Earth would keep orbiting as before (though it would become very cold and dark).

6. The lab shows a glowing ring around the black hole. Is that ring the event horizon? Explain.

   No. The ring illustrates hot, glowing material and bent light near the black hole. The event horizon itself gives off no light that can escape.