Part 04 · Rotation and gravity · Card 8 of 11
Universal gravitation
Every two masses attract with a force F = G M m / r squared, where G is 6.67e-11 in SI units.
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Analogy
A very weak glue between all matter, strong only when one object is huge.
Example
Two masses
F = 6.67e-11 x 1000 x 1000 / 1^2F = 6.67e-5 N
In practice
Two 1000 kg masses 1 m apart pull each other with about 0.00007 N.
Practice
Flashcards
- How does gravitational force change if distance doubles?It falls to one quarter.
Interview questions
- Derive the speed of a satellite in circular orbit and use it to find the period of a satellite at radius r.
- Gravity equals m v^2 / r
- v = sqrt(GM/r)
- Period = 2 pi r / v
Questions people ask
Why is gravity weak between everyday objects?
The constant G is tiny, about 6.67e-11 in SI units. Two 70 kg people 1 m apart attract with about 3e-7 N, far too small to notice. Gravity only becomes obvious when one of the masses is as huge as a planet.
How do I get g = 9.8 from Newton's law?
Set weight mg equal to GMm over R squared and cancel m. This gives g = GM over R squared. With Earth's mass 5.97e24 kg and radius 6.37e6 m, the result is about 9.8 m/s squared. On a different planet you use its own mass and radius.