# Fictitious force in a binary stars

• Rikudo
In summary, a fictitious force in a binary stars is a force that appears to act on objects in a rotating frame of reference, but is not actually present in the system. It can cause objects to experience acceleration or change in direction, and is also known as a "centrifugal force." This force cannot be directly measured, but its effects on the motion of objects can be observed and measured. The Coriolis force, a type of fictitious force, may also be present in a binary stars system. In most cases, the fictitious force can be ignored in calculations, but in some cases, it may need to be taken into account.
Rikudo
Homework Statement
Two planets with mass M1 and M2 revolve around each other in circular orbits. The distance between them is r. A mass m that is located on the surface of M1 with radius R feels fictitious force that modifies the mass's acceleration. Assume that mass m is very small and ignore the effect from M1's rotation. (see figure)

Write down the vector of the fictitious force in m, M2, r, gravity constant G, and unit vector!
Relevant Equations
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I have a difficulty in understanding the question.
Fictitious force is a force whose motion is described using a non-inertial frame of reference. Which frame is the question referring to?

Rikudo said:
Which frame is the question referring to?
Excellent question!
I suggest m's frame of reference, i.e. find that force which, added to the normal force, results in m's instantaneous acceleration.

Rikudo

## 1. What is a fictitious force in a binary stars?

A fictitious force in a binary stars is a force that appears to act on objects in a binary star system, but is actually a result of the objects' motion in a non-inertial reference frame. This force is not a real physical force, but rather a mathematical construct used to explain the observed motion of objects in the system.

## 2. How does a fictitious force affect the motion of objects in a binary star system?

A fictitious force can affect the motion of objects in a binary star system by causing them to appear to accelerate or change direction, even though there is no actual force acting on them. This is because the objects are moving in a non-inertial reference frame, which creates the illusion of a force.

## 3. What causes a fictitious force to occur in a binary star system?

A fictitious force in a binary star system is caused by the rotation of the system itself. Since the objects in the system are moving in a curved path due to their mutual gravitational attraction, they are technically in a non-inertial reference frame. This rotation creates the appearance of a force acting on the objects.

## 4. Can a fictitious force be measured in a binary star system?

No, a fictitious force cannot be directly measured in a binary star system because it is not a real physical force. However, its effects can be observed and measured through the motion of objects in the system.

## 5. How does the magnitude of a fictitious force in a binary star system compare to other forces?

The magnitude of a fictitious force in a binary star system is typically much smaller than other real physical forces, such as gravity or electromagnetic forces. This is because it is a mathematical construct used to explain the observed motion of objects, rather than a real force acting on the objects.

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