A communications satellite with a mass of $1200 \text{ kg}$ orbits the Earth at an altitude of $800 \text{ km}$ above the Earth's surface. Determine the force of gravitational attraction exerted by the Earth on the satellite.

The gravitational force between two identical objects is $2.0 \times 10^{-6} \text{ N}$. If the mass of each object is $50 \text{ kg}$, find the distance between their centers.

A rover on Mars has a mass of $1050 \text{ kg}$. The acceleration due to gravity on Mars is $3.72 \text{ m/s}^2$. If the rover is brought back to Earth, what is the difference between its weight on Earth and its weight on Mars?

When an engineer first begins the design of a large suspension bridge, they model the entire bridge deck and the vehicles on it as a single point load (particle) acting at the center of the span to determine the maximum tension in the main cables. Why is this idealization valid in the initial stages?

A structural engineer assumes a steel I-beam is a "rigid body" when calculating the reaction forces at its supports. In reality, the steel beam will bend slightly when loaded. Discuss the justification and limitations of the rigid body assumption.