Calculating Energy of Separating Stars: Potential vs Kinetic Energy

In summary, during an exercise to calculate the energy required to separate stars to an infinite distance, both the potential and kinetic energies must be taken into account. This is because the initial state of the system includes both types of energy, and separating the stars requires work to be done against their potential energy. However, it is possible for the kinetic energy to remain the same even after the stars have been separated by an infinite distance. The assignment explicitly asks for the total energy needed for this separation.
  • #1
zezima1
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I recently did an exercise where I had to calculate the total energy needed to separate the stars completely from each other - i.e. make the distance between them infinity.
One then had to calculate the potential energy between them as well as their kinetic energies. But there's something I don't get here - why do you have to use the kinetic energy in the calculations too. Couldnt you imagine a situation where the kinetic energy was the same after they had been separated by a distance of infinity.
 
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  • #2
Work needed to separate the stars to infinity is the potential energy of the system in it's initial state. The total energy of the system is the potential energy and the kinetic energy.

Check the wording of the problem.
 
  • #3
Well the assignment explicitly asks: What amount of energy is needed to separate the stars to a distance infinitely far from each other.
 
  • #4
Well then, I'd say you have a point :)
 
  • #5


I can understand your confusion about the use of both potential and kinetic energy in calculating the total energy required to separate stars. Let me explain why both forms of energy are important in this scenario.

Firstly, potential energy is the energy that is stored in an object due to its position or configuration. In the case of separating stars, as the distance between them increases, the potential energy also increases. This is because the gravitational force between the stars is inversely proportional to the square of the distance between them. So, as the distance increases, the force decreases, and the stars have to do work against this force to move further apart, resulting in an increase in potential energy.

On the other hand, kinetic energy is the energy an object possesses due to its motion. In the case of separating stars, as they move further apart, their velocities also increase due to the conservation of momentum. This increase in velocity results in an increase in kinetic energy.

Now, to calculate the total energy required to separate the stars, we need to consider both potential and kinetic energy. This is because both forms of energy contribute to the total energy of the system. Ignoring one would result in an incomplete calculation of the total energy.

Furthermore, it is possible to imagine a scenario where the kinetic energy remains the same after the stars have been separated by an infinite distance. However, this would only be possible if there were no external forces acting on the stars, which is not the case in reality. In reality, there are always external forces such as gravitational forces from other celestial bodies that would affect the motion of the stars and change their kinetic energy.

In conclusion, both potential and kinetic energy are essential in calculating the total energy required to separate stars. They both play a crucial role in the dynamics of the system and cannot be ignored. I hope this explanation helps to clarify any confusion you may have had.
 

1. What is the difference between potential and kinetic energy?

Potential energy is the energy that an object has due to its position or configuration, while kinetic energy is the energy that an object has due to its motion. In the context of separating stars, potential energy would refer to the energy stored in the gravitational force between the two stars, while kinetic energy would refer to the energy of their relative motion.

2. How do you calculate the potential energy of two separating stars?

The potential energy of two separating stars can be calculated using the formula U = -Gm1m2/r, where G is the gravitational constant, m1 and m2 are the masses of the two stars, and r is the distance between them. This formula assumes that the stars are point masses and that the distance between them is much larger than their individual sizes.

3. How do you calculate the kinetic energy of two separating stars?

The kinetic energy of two separating stars can be calculated using the formula K = 1/2(m1v1^2 + m2v2^2), where m1 and m2 are the masses of the two stars and v1 and v2 are their respective velocities. This formula assumes that the stars have constant velocities and are not affected by any external forces.

4. What is the total energy of two separating stars?

The total energy of two separating stars is the sum of their potential and kinetic energies. This can be represented by the equation E = U + K. As the stars continue to separate, the potential energy decreases while the kinetic energy increases, resulting in a constant total energy.

5. How does the energy of separating stars affect their motion?

The energy of separating stars plays a crucial role in their motion. If the total energy is positive, the stars will continue to move apart with increasing velocity. If the total energy is negative, the stars will eventually slow down and start to come back towards each other. If the total energy is zero, the stars will reach a certain distance and then come to a stop. This concept is known as the law of conservation of energy, where energy cannot be created or destroyed, only transferred between different forms.

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