Two \(140-\mathrm{kg}\) satellites collide at an altitude where \(g=8.7 \mathrm{m} / \mathrm{s}^{2}\) and the collision imparts an impulse of \(1.8 \times 10^{5} \mathrm{N} \cdot\) s to each. If the collision lasts \(120 \mathrm{ms}\), compare the collisional impulse to that imparted by gravity. Your result should show why you can neglect the external force of gravity.

Impulse in physics is a key concept that helps us understand the change in momentum of an object when a force is applied over a specific time period. It's given by the product of the force (\( F \)) and the time duration (\( t \)) during which the force acts, mathematically represented as Impulse (\( J \)) = Force (\( F \)) \times Time (\( t \)).

Idealizing, this can be understood as a push or a pull that acts on the object briefly, causing it to speed up, slow down, or change direction. In our satellite collision case, the impulse imparted on each satellite significantly affects its velocity. Since the impulse is high (\(1.8 \times 10^{5} \text{N} \text{s}\)), it indicates a considerable change in momentum, far outweighing the gradual influence of gravitational force over the brief period of collision.

This can be better grasped if we visualize it in terms of a soccer ball being kicked — the foot's impact transfers an impulse, deciding the ball's subsequent path over a short time.

Gravitational force is a fundamental interaction that pulls two masses towards each other. Newton's law of universal gravitation states that every mass exerts an attractive force on every other mass. This force is directly proportional to the product of their masses and inversely proportional to the square of the distance between their centers.

For objects near the Earth's surface, this force can be simplified as the weight of the object where the force (\( F \)) is the product of mass (\( m \)) and the acceleration due to gravity (\( g \)). In our exercise, we were asked to calculate this force for each satellite, yielding a force that's constant over the short duration of the collision. On Earth, this force is what keeps us grounded and dictates how objects fall.

Satellite collision physics involves understanding the dynamics when two satellites crash in orbit. The forces involved during impact can be vastly different from what we experience on Earth due to microgravity conditions. In our example, the impulse is the variable of interest. When two satellites collide, they exchange momentum through the impulsive force, which acts over a brief period.

Determining the gravitational impulse during this interval gives insights into whether gravity's effect is significant compared to the collisional impulse. In most cases, during the very short span of a collision, the change in momentum due to the satellite's mutual impacts dwarfs the relatively gentle pull of gravity. This is why in practical scenarios, engineers often neglect gravitational influence when calculating collision outcomes in space.