Space
Explainer
When escape velocity hits light speed
Squeeze the Sun to about 3 km wide radius and light can't escape.
Quick check · tap an answer to continue
Lesson notes
Key points
- Set escape velocity equal to the speed of light and solve for radius to get the Schwarzschild radius.
- This Newtonian shortcut happens to match general relativity's exact result for a non-rotating black hole.
- Because r_s scales linearly with mass, one solar mass gives about 3 kilometres, ten solar masses about 30.
Takeaway: r_s = 2GM/c², growing in direct proportion to mass.
Quick check: Tripling a black hole's mass makes r_s?
- 3 times larger
- 9 times larger
- √3 times larger
Schwarzschild radiusEvent horizonLinear scaling
Lessons like this, for your syllabus.
Short narrated study videos written for your course, level and exam. Free to start.
Get lessons for your own syllabus