Energy conservation for a point at the Earth's surface

In summary: The summary is: In summary, the conversation discusses the difference in potential energy at noon and midnight for a mass at the Earth's equator during an entire day, and how it is balanced by another kind of energy variation due to the Earth's rotation and the connection between masses in a system. The conversation also mentions the effect of variable gravitational forces and tides caused by these differences.
  • #1
Kamikaze_951
7
0
Hi everyone,

This is my first post here and I am really sorry for that question, but I have found the answer nowhere.

Consider a mass at the Earth's equator that is static in the Earth's referential during an entire day. Put the Earth at one of its equinoxes to simplify the problem. Then, at noon, the potential energy due to the sun of a mass m at that point is :

E_p noon = -GMm/(distance Sun-Earth - radius of Earth)

At midnight,

E_p midnight = -GMm/(distance Sun-Earth + radius of Earth)

Clearly, there is a difference in potential energy. By energy conservation, it should be balanced (by another kind of periodic energy variation). However, if the mass stand on solid ground, its rotation speed is the Earth rotation speed and it should be constant during the day (not going up and down) and therefore, the difference in kinetic energy is null.

My questions : What balances this difference in potential energy? Is there a mistake in my reasoning?
 
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  • #2
You have only got half the rotation of course ... when you do a whole rotation the net energy change is zero.

Not happy? Well that really just means that, wherever the energy went, we got it back.

As a mass "falls" from the dark side of the Earth towards the light side (towards the sun) is gains energy which goes into "lifting" the equivalent mass on the light side into the dark side. Since the masses are balanced, and they are connected by the rest of the Earth, there is no gain or loss.

You get the same for any rotation in gravity ... or any conservative force field.
 
  • #3
Your post just made me realize that I considered the wrong system (Sun+mass rather than Sun+Earth) and forgot to take into account the energy transfer between two masses of the same system.

Your answer was very helpful and I thank you a lot for it.
 
  • #4
No worries - it's actually a very common mistake.
 
  • #5
If you look at force differences of this size, keep in mind that the Earth orbits the sun, which leads (in the reference frame of earth) to a centrifugal force outwards - "down" at day and "up" at night.

Note that the effect of variable gravitational forces is bigger if you use the moon. Tides exist due to these differences, and there are power plants which use those tides.
 
  • #6
The OP's question assumes an unbalanced earth, which is wrong.
 

What is energy conservation for a point at the Earth's surface?

Energy conservation for a point at the Earth's surface refers to the principle that the total energy of a point at the Earth's surface remains constant over time. This means that energy cannot be created or destroyed, but can only be transferred or converted from one form to another.

Why is energy conservation important for a point at the Earth's surface?

Energy conservation is important for a point at the Earth's surface because it helps to maintain a stable environment and allows for the sustainable use of resources. It also helps to reduce the negative impacts of energy production and consumption on the environment.

What factors affect energy conservation at the Earth's surface?

Several factors can affect energy conservation at the Earth's surface, including climate, topography, land use, and human activities. These factors can impact the amount of solar radiation that reaches the Earth's surface and the efficiency of energy production and consumption.

How can individuals contribute to energy conservation at the Earth's surface?

Individuals can contribute to energy conservation at the Earth's surface by adopting energy-efficient practices such as using renewable energy sources, reducing energy consumption, and properly maintaining energy-consuming devices. They can also support policies and initiatives that promote energy conservation.

What are some current initiatives for energy conservation at the Earth's surface?

There are many initiatives and programs in place to promote energy conservation at the Earth's surface, including renewable energy targets, energy efficiency standards, and carbon pricing. Additionally, there are ongoing research efforts to develop new technologies and strategies for energy conservation at the Earth's surface.

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