Calculating Energy, Angular Momentum & Period for Binary Stars in ZMF

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In summary, the conversation discusses the calculation of total energy, angular momentum, and period of a binary star system before the explosion of one of the stars. The two stars have equal mass after the explosion and are in circular orbit around their common center of mass. The individual stars have masses of mo and 2mo, and are separated by a distance of ro. The person asking the question is unsure of how to calculate the total energy and angular momentum, and questions whether the total angular momentum will be zero due to the equal and opposite masses. They also ask for clarification on what ZMF stands for.
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Homework Statement



Two individual stars in a binary system (m1=mo, m2=2mo) are in circular orbit about their common centre of mass and are separated by a distance ro. At some stage, the more massive star explodes - resulting in the two stars having equal mass after the explosion

(a)Calculate the total energy, angular momentum and period of the binary star as viewed in the ZMF before the collision.

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The Attempt at a Solution



Not sure how to do this...For energy, do I find the energy of each inidividually and add? How about for angular momentum? Surely that is just zero in total because the two are equal and opposite?
thanks
 
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What is the ZMF?
 

1. How do you calculate the energy of a binary star system in the zero momentum frame (ZMF)?

To calculate the energy of a binary star system in the ZMF, you can use the equation: E = (1/2) * μ * v^2 * a^2, where μ is the reduced mass of the system, v is the relative velocity of the stars, and a is the separation between the stars. This equation takes into account both the kinetic and potential energies of the system.

2. What is the formula for calculating the angular momentum of a binary star system in the ZMF?

The angular momentum of a binary star system in the ZMF can be calculated using the equation: L = μ * v * a, where μ is the reduced mass of the system, v is the relative velocity of the stars, and a is the separation between the stars. This equation takes into account the mass, velocity, and distance of the stars in the system.

3. How do you determine the period of a binary star system in the ZMF?

The period of a binary star system in the ZMF can be determined using the equation: P = 2π * √(a^3 / G * (m1 + m2)), where a is the separation between the stars, G is the gravitational constant, and m1 and m2 are the masses of the stars. This equation takes into account the mass and distance of the stars, as well as the gravitational force between them.

4. What is the significance of calculating energy, angular momentum, and period in the ZMF for binary star systems?

Calculating energy, angular momentum, and period in the ZMF allows us to better understand the dynamics and stability of binary star systems. It also allows us to make more accurate predictions about their future evolution and potential outcomes, such as the formation of a new star or the merging of the two stars.

5. Are there any limitations or assumptions when using the ZMF to calculate energy, angular momentum, and period for binary star systems?

Yes, there are limitations and assumptions when using the ZMF to calculate energy, angular momentum, and period for binary star systems. One limitation is that it assumes the system is isolated and not influenced by any external forces. Additionally, it assumes that the stars have circular orbits and that their mass and distance remain constant over time. These assumptions may not always hold true in real-world scenarios and can affect the accuracy of the calculations.

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