# Newton’s Law of Universal Gravitation

## Law of Gravitation

F | gravitational force | N | |

G | universal gravitation constant = 6.67 × 10 ^{-11} N·m^{2}/kg^{2} | ||

m_{1}, m_{2} | masses of objects | kg | |

r | distance between objects | m |

## Acceleration Due to Gravity

g | acceleration due to gravity | m/s^{2} | |

G | universal gravitation constant = 6.67 × 10 ^{-11} N·m^{2}/kg^{2} | ||

m_{p} | mass of planet | kg | |

r | radius of planet | m |

## Tips to Remember

- Always remember that r is the
*center to center*distance between the two objects. For instance, if an astronaut is 2000 km above the earth—which has radius 6400 km—then the center of the astronaut is 2000 km + 6400 km from the center of the earth. That means that r is 8400 km, or 8.4 × 10^{6}m. - In the formula for the acceleration due to gravity on a planet, r actually is the radius of the planet. That’s because the center to center distance, which is what r measures, is from the center of the planet to the surface, i.e., the planet’s radius.
- When you calculate the force between two objects on earth, expect the answer to be small. Gravity is reallly a very wimpy force; you notice it only because you’re standing on something the size of a planet. You shouldn’t expect to notice the gravitational force between yourself and an object next to you.

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