In short, Newton’s Law of Gravitation says that every object in the universe attracts every other object with a force that is directly proportional to their masses and inversely proportional to the square of the distance between them. This means that if two objects are far apart, their gravitational force will be weaker than if they were closer together. And if one of those objects is really heavy (like a planet or star), then the force between them will be even stronger. But here’s where things get interesting: this law doesn’t just apply to planets and stars! It also works for everyday objects like apples, pencils, and your favorite pair of socks. In fact, if you were to throw an apple across a room, it would follow the same path as any other object in space because they are all subject to gravity. And if you ever find yourself feeling lost or confused about this topic (or any other), just remember to take a deep breath and let the force guide you. After all, that’s what gravity is all about!

Now, let’s apply Newton’s Law of Gravitation in a real-life scenario. Imagine two nearly spherical Soyuz payload vehicles, each with mass 9000 kg and diameter 4.0 m, initially at rest relative to each other, 10.0 m from center to center. According to the law, there is an attractive force between them that can be calculated using the formula:
|F12|=Gm1m2r2=(6.67×1011Nm2/kg2)(9000kg)(9000kg)(10m)2=5.4×105N.
This force causes an initial acceleration of each payload, which can be found using Newton’s second law: a=Fm=5.4×105N9000kg=6.0×109m/s2.
The vehicles move from 10.0 m to 4.0 m apart, or a distance of 3.0 m each. A similar calculation for when the vehicles are 4.0 m apart yields an acceleration of 3.8 x 108 m/s2, and the average of these two values is used to estimate how long it takes for them to drift together and how fast they are moving upon impact.
This example demonstrates how Newton’s Law of Gravitation can be applied in real-life scenarios involving space travel and payload vehicles.