Conservation of Energy: Why Does One Planet Moving Violate It?

In summary, the book "Simple Nature" (Ben Crowell, April 2010 edition) argues that two objects that feel each other's gravity will eventually drop together and collide. The author provides a physical explanation for why this would happen, citing the conservation of energy.
  • #1
walk_w/o_aim
27
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In explaining why it does not make sense for two objects feeling each other's gravity to simply stay in place, the book "Simple Nature" (Ben Crowell, April 2010 edition) states that:

The Fooites and Barians realize that the gravitational interaction between their planets will cause them to drop together and collide. ... And yet ... maybe they should consider the possibility that the two planets will simply hover in place for some amount of time, because that would satisfy conservation of energy. Now the physical implausibility of the hovering solution becomes even more apparent. Not only does one planet have to “decide” at precisely what microsecond to go ahead and fall, but the other planet has to make the same decision at the same instant, or else conservation of energy will be violated.

My question is, why does one planet moving and not the other violate the conservation of energy? I could say that some of the initial gravitational energy between the planets is converted into kinetic energy for only one of the planets. I believe that it can be explained in terms of Newton's action-reaction law, but at this point in the book, forces have not even been discussed yet.

What am I missing here? Any light on the matter would be much appreciated. Thank you.
 
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  • #2
If the only thing to consider is conservation of energy, then what you say is correct. The author is probably just implicitly using some additional assumption, such as conservation of momentum.
 
  • #3
the_house said:
If the only thing to consider is conservation of energy, ...

I'm sorry. I should have mentioned that the concepts that have been introduced in the book at that point are conservation of mass, Galilean relativity, and conservation of energy. The kinetic and gravitational energy equations are also given as experimental results.
 
  • #4
I think I got it. Based on the_house's comment, I read ahead to the conservation of momentum chapter, and finally understood the idea of using a different frame of reference that the author attempted to explain in regards to the conservation of energy. I believe an explanation of something along these lines should be acceptable:

Energy is supposed to be conserved from the point of view of any inertial frame of reference. If the two planets are viewed from a frame of reference such that their initial velocities are v, then, when only one of the planets move (in the original frame of reference), the first planet moves at the same speed v, but the speed of the other planet decreases. This means that the change in kinetic energy is negative. However, the distance between the planets decreases, meaning that the change in gravitational energy is also negative. This leads to some sort of loss in energy, which violates the conservation of energy.

Thanks!
 
  • #5


I can explain why one planet moving and not the other does not violate the conservation of energy. Conservation of energy is a fundamental law of physics that states that energy cannot be created or destroyed, only transferred or transformed from one form to another. In the case of two objects feeling each other's gravity, there is a transfer of potential energy (due to their position in the gravitational field) to kinetic energy (as they move towards each other). This transfer of energy is equal and opposite for both objects, satisfying conservation of energy.

In the scenario described in the book, if one planet were to suddenly start moving while the other remained stationary, it may seem like energy is being created or destroyed. However, this is not the case. The planet that starts moving gains kinetic energy, but at the same time, the stationary planet gains an equal amount of potential energy. This transfer of energy maintains the overall conservation of energy.

Furthermore, the idea of the two planets hovering in place goes against the laws of motion and the concept of equilibrium. In order for an object to remain in a state of equilibrium, the forces acting on it must be balanced. In the case of the two planets, the force of gravity between them would not be balanced, as one planet would be pulling on the other with a greater force. This would cause the planets to move towards each other, not remain in a state of equilibrium.

In conclusion, the conservation of energy is not violated when one planet moves and the other does not. The transfer of energy between the planets is equal and opposite, maintaining the overall balance of energy in the system. This concept is fundamental to our understanding of the physical world and has been extensively tested and proven through experiments and observations.
 

FAQ: Conservation of Energy: Why Does One Planet Moving Violate It?

What is the law of conservation of energy?

The law of conservation of energy states that energy cannot be created or destroyed, but can only be transferred or transformed from one form to another.

How does one planet moving violate the law of conservation of energy?

One planet moving does not violate the law of conservation of energy. In fact, the law applies to all objects and systems, including planets. The energy of a planet in motion is constantly changing, but the total amount of energy remains constant.

Why is the conservation of energy important?

The conservation of energy is important because it helps us understand and predict the behavior of physical systems. It also allows us to make use of energy in various forms, such as heat, light, and electricity, for practical purposes.

Is the conservation of energy a universal law?

Yes, the conservation of energy is considered a universal law in physics. It has been confirmed through countless experiments and observations and is a fundamental principle in understanding the behavior of the universe.

Can energy be lost or disappear?

No, according to the law of conservation of energy, energy cannot be lost or disappear. It can only be converted into other forms of energy. For example, when a light bulb is turned on, electrical energy is transformed into light and heat energy.

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