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PAstudent
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Homework Statement
Homework Equations
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The Attempt at a Solution
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Orbital Period Calculation for Binary Star Systems
- Thread starter PAstudent
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In summary, the orbital period is the time it takes for an object to complete one orbit around another object in space. It can be calculated using Kepler's Third Law, which relates the orbital period to the average distance between the objects. The orbital period is affected by the mass and distance of the objects, as well as their orbital velocities. A shorter orbital period typically results in a more stable orbit, while longer periods can lead to more chaotic orbits. The orbital period can also change over time due to various factors, and these changes can be observed and measured through careful analysis of the system.
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- #2
SteamKing
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The distance of each star from the c.o.m. of the system is not L/2. Each star in the group is located L/2 from the two stars immediately adjacent.PAstudent said:
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Mister T
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You start with the formula ##T^2=\Big( \frac{4 \pi^2}{GM} \Big)r^3## where ##M## is the mass of the attracting body.
But in your solution you use ##M## for the mass of each orbiting sun.
But in your solution you use ##M## for the mass of each orbiting sun.
1. What is the orbital period?
The orbital period is the time it takes for an object to complete one orbit around another object in space. It is typically measured in days, years, or any unit of time.
2. How is the orbital period calculated?
The orbital period can be calculated using Kepler's Third Law, which states that the square of an object's orbital period is proportional to the cube of its average distance from the object it is orbiting. This can be represented as P² = a³, where P is the orbital period and a is the semi-major axis of the orbit.
3. What factors affect the orbital period?
The orbital period is affected by the mass of the objects involved, their distance from each other, and their orbital velocities. The greater the mass and distance between the objects, the longer the orbital period will be. A faster orbital velocity will result in a shorter orbital period.
4. How does the orbital period impact the stability of a system?
The orbital period is closely tied to the stability of a system. Objects with shorter orbital periods tend to have more stable orbits, as they are constantly being pulled towards the central object. Longer orbital periods can lead to more chaotic orbits and potentially result in collisions or ejections from the system.
5. Can the orbital period change over time?
Yes, the orbital period can change due to a variety of factors such as gravitational interactions with other objects, tidal forces, and mass loss. These changes can be observed and measured through careful observation and analysis of the system over time.
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