Physics / Unit 4: Circular Motion and Gravity
4.5 Gravitational Field Strength
Notes
The gravitational field strength at a distance $r$ from the center of a planet of mass $M$ is $\displaystyle g = \frac{GM}{r^2}$.
- At Earth's surface, $g = 9.8 \text{ N/kg} = 9.8 \text{ m/s}^2$.
- At twice Earth's radius from the center, $\displaystyle g = \frac{9.8}{4} = 2.45 \text{ m/s}^2$.
- Astronauts in orbit feel weightless because they and their spacecraft are in free fall together, not because gravity is zero. At the space station's height, $g$ is still about 90% of its surface value.
Practice
A satellite is 3 Earth radii from Earth's center. What is $g$ there?
$\displaystyle g = \frac{9.8}{3^2} = \frac{9.8}{9} \approx 1.09 \text{ m/s}^2$.
Why do astronauts float inside the orbiting space station?
Gravity is still strong there; everything is in free fall at the same rate.
Planet X has the same radius as Earth but twice the mass. What is $g$ on its surface?
$\displaystyle g = \frac{GM}{r^2}$; doubling $M$ doubles $g$.
Ready for more? Take the Unit 4 test.