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unscientific
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Homework Statement
Homework Equations
The Attempt at a Solution
What puzzles me is part (c), I got Vmin > Etot which suggests that the orbit is no longer bounded..
Simon Bridge said:So at some point the two new stars are inside an expanding shell of gas (etc) from the explosion so we only need to deal with the final fields of the two stars?
The second star (the one that did not blow up) may gain mass but does not change momentum from material that hits it?
What is wrong with the final system being unbound?
ehild said:Think: What does it mean that the exploding star "suffers a spherically symmetric loss of mass"? Does its momentum change in the explosion?
Just after the explosion, the the stars are still at the same place they were- The momentum of the smaller one is unchanged, what about the momentum of the bigger one? Did that symmetric mass loss change its momentum?
Calculate the energy of the two starts after the explosion, taking into account the change of volume. ehild
unscientific said:i would assume that the mass just halved instantaneously, but still retains its original speed? Not sure what volume has to do here
ehild said:What else can can you assume if the explosion is spherically symmetric?
Just after the explosion, you have the half star and a spherical shell around it. The CM of the shell coincides with the centre of the star, and travels with the initial velocity of the star, while the shell itself can expand with a high speed. You are left with two stars at distance r0 from each other, having the same velocities v1 and v2 as before the explosion. The new CM of the two-star system travels in opposite direction as the shell, but that does not influence if the starts stay bounded to each other or not.
The energy of this binary star system is 1/2 m0(v12+v22)-Gm02/r0. Substitute v1 and v2 from the solution of the original system.
ehild
ehild said:I see now that you added the angular term of KE to the potential energy, and called the sum "effective potential". Stay with the definition of KE as the sum of 1/2 mv2 of both stars, using their velocities with respect to the new centre of mass.
ehild
The Two-Body Problem is a fundamental concept in physics and astronomy that involves finding the motion of two objects, typically celestial bodies, that are gravitationally interacting with each other. It is a special case of the more general N-Body Problem and is often used to model the orbits of planets, moons, and other objects in space.
The homework statement for the Two-Body Problem typically involves finding the equations of motion, positions, velocities, and accelerations of two objects in space that are gravitationally interacting with each other. It may also involve solving for the orbital elements, energy, and angular momentum of the system.
The main equations used to solve the Two-Body Problem are Newton's Law of Universal Gravitation and Newton's Second Law of Motion. These equations, along with the equations of motion, can be used to derive the Kepler's Laws of Planetary Motion and solve for the motion of the two objects in the system.
One example of a solved Two-Body Problem is the orbit of the Earth around the Sun. By using the equations and principles mentioned above, scientists are able to accurately predict the motion of the Earth around the Sun, including its orbital period, eccentricity, and distance from the Sun at any given time.
Some common issues encountered when attempting to solve the Two-Body Problem include non-circular or non-elliptical orbits, perturbations from other celestial bodies, and the effect of relativity on the motion of the objects. These factors can make the problem more complex and require additional equations or approximations to accurately solve it.