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Ranku
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If there are three bodies A, B, and C arranged linearly, and B is free falling towards C, will the gravitational presence of A affect the rate of free fall of B towards C?
Why not set up a situation and calculate it? Put B in the middle at coordinate zero, A on the left at coordinate -1 and C on the right at coordinate 1. Give them all the same mass.Ranku said:If there are three bodies A, B, and C arranged linearly, and B is free falling towards C, will the gravitational presence of A affect the rate of free fall of B towards C?
What formulas do I use and in what order?jbriggs444 said:Why not set up a situation and calculate it? Put B in the middle at coordinate zero, A on the left at coordinate -1 and C on the right at coordinate 1. Give them all the same mass.
Decide what you want to calculate. The rate at which the distance between B and C decreases?
Calculate. First with A present then with A absent.
Hint: Tides.
Newton's second law:$$F=ma$$That'll let you compute the acceleration ##a## of an object of mass ##m## when subject to a force ##F##.Ranku said:What formulas do I use and in what order?
The gravitational interaction between three bodies, also known as the three-body problem, is a complex phenomenon in which the gravitational forces between three objects affect their motion. The three bodies can either attract or repel each other, depending on their masses and distances. This interaction is governed by Newton's law of universal gravitation, which states that the force of gravity between two objects is directly proportional to their masses and inversely proportional to the square of the distance between them.
One of the main challenges in studying the three-body problem is that it has no analytical solution, meaning that there is no mathematical formula that can accurately predict the motion of three bodies under the influence of gravity. This is due to the complex and chaotic nature of the interactions between the three bodies, making it difficult to make precise calculations. As a result, scientists often use computer simulations to study the three-body problem.
No, the three-body problem cannot be solved in all cases. In some scenarios, the motion of the three bodies can be predicted with high accuracy, while in others, the interactions are too complex and unpredictable. This is known as the "n-body problem," where n represents the number of bodies involved. The three-body problem is a special case of the n-body problem, and it is still an area of active research in the field of astrophysics.
The gravitational interaction between three bodies can have a significant impact on the stability of a system. In some cases, the three bodies may form a stable orbit around each other, while in others, the interactions can cause the bodies to collide or be ejected from the system. This instability is one of the reasons why it is challenging to predict the motion of three bodies accurately.
Yes, the gravitational interaction between three bodies plays a crucial role in explaining many celestial phenomena, such as the orbits of planets around the sun, the motion of stars in a binary system, and the formation of galaxies. Understanding the three-body problem is essential in studying the dynamics of the universe and how celestial bodies interact with each other.