Gravitational Fields, Weight, Rotation, and Gravity Inside Spheres

All flashcards

What is weight?

Weight is the gravitational force acting on an object. Near Earth's surface its magnitude is approximately $W = mg$.

How is gravitational acceleration related to Earth's mass and distance?

For an object outside a spherical Earth, $g = GM_E/r^2$, where $r$ is measured from Earth's center.

How can Earth's mass be calculated from surface measurements?

Rearrange the surface-gravity relation: $M_E = gR_E^2/G$. Using standard values gives about $5.95 \times 10^{24}\ \text{kg}$.

Why do objects of different masses fall with the same acceleration near Earth?

The object's mass is both part of its gravitational force and its inertial mass; it cancels from the equations, leaving the same $g$ for each object under the same conditions.

Why are astronauts in the ISS not truly beyond Earth's gravity?

At about 400 km altitude, gravity remains roughly $8.67\ \text{m/s}^2$. Astronauts seem weightless because they and their spacecraft are in free fall together.

Quiz questions

1. What does the gravitational field at a location represent?Answer: Gravitational force per unit mass at that location.
2. For an object at the equator on a rotating Earth, what is the scale force in the idealized model?Answer: $F_s = m(g - R_E\omega^2)$
3. What is the net gravitational field inside an ideal uniform spherical shell?Answer: Zero at every interior point.
4. How does gravitational-field magnitude vary with radius inside a constant-density spherical planet?Answer: It increases in proportion to radius.
5. Why do astronauts in the ISS appear weightless despite substantial gravity?Answer: They and the station are falling together continuously around Earth.