Moon Earth binar system by math

In summary, the Moon Earth binary system is a unique phenomenon in our solar system where the Moon orbits Earth as its natural satellite. This system is governed by the laws of gravity and has a significant impact on Earth's tides and rotation. The Moon and Earth have been closely linked for billions of years, and studying this relationship helps us better understand the formation and evolution of our planet. The mathematical calculations and observations of this binary system have provided valuable insights into the dynamics of celestial bodies.
  • #1
Vrbic
407
18
Hello,
I'm interesting in Earth Moon evolution history. I understand it is very complex problem, and I can find many articles about that. But I would like to start from beginning and add real condition on my model step by step (I hope good way to do something).
I would like to start with ordinary gravitation bound system (without tides effects), I hope I'm right it is problem from theoretical mechanics. Could somebody advise me some steps or some scripts or text where is described something like that? Only rotation around each other and their spins are taken into account for a start.

Thank you for your posts.
 
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  • #2
Vrbic said:
Hello,
I'm interesting in Earth Moon evolution history. I understand it is very complex problem, and I can find many articles about that. But I would like to start from beginning and add real condition on my model step by step (I hope good way to do something).
I would like to start with ordinary gravitation bound system (without tides effects), I hope I'm right it is problem from theoretical mechanics. Could somebody advise me some steps or some scripts or text where is described something like that? Only rotation around each other and their spins are taken into account for a start.

Thank you for your posts.

I googled Origin Of The Moon, and got lots of good hits. The Wikipedia entry looks okay, and here is a hit from Space.com:

http://www.space.com/19275-moon-formation.html

:smile:
 
  • #3
What kind of model are you making? What values or factors do you want to put into the model and what do you want to get out of the model? Is this something similar to making a computer model/animation of the Moon orbiting the Earth, or something else?
 
  • #4
Drakkith said:
What kind of model are you making? What values or factors do you want to put into the model and what do you want to get out of the model? Is this something similar to making a computer model/animation of the Moon orbiting the Earth, or something else?
I would like to prepare some general mathematical equations describing "ideal binary system" of Earth - Moon with set of parameters. And try what would happen with period, velocity, distance if I change for example way of spin, mass etc. I would like to transform these equation to Wolf. Mathematica and create some animation. And then setting more realistic conditions for example some friction force, tidal force etc.
 
  • #5
berkeman said:
I googled Origin Of The Moon, and got lots of good hits. The Wikipedia entry looks okay, and here is a hit from Space.com:

http://www.space.com/19275-moon-formation.html

:smile:
Thank you for your post, I've googled it also, but I'm looking for some mathematical theory of motion, not origin. I theoretically know what is happened and happening.
 
  • #6
What you're trying to do is not simple. I've created a simple model/animation of the Earth orbiting the Sun, but I was only able to do so after taking a college physics class and understanding what the equations mean, how they work, why they work, etc. As with much of science, just knowing what the equations are is not a substitute for truly understanding them. Personally I recommend taking a physics class if possible, and if not that then I recommend a college level physics book. I can recommend one if you'd like.

However, if you just wish to see what happens when you change various parameters, you might try a program/game called Universe Sandbox.
 

FAQ: Moon Earth binar system by math

1. What is the significance of the Moon-Earth binary system?

The Moon-Earth binary system refers to the relationship between the Earth and its only natural satellite, the Moon. This system is significant as it plays a crucial role in shaping the Earth's climate, tides, and even the development of life on our planet.

2. How is the Moon-Earth binary system calculated mathematically?

The Moon-Earth binary system can be calculated using Newton's law of universal gravitation, which states that the force of gravity between two objects is directly proportional to the product of their masses and inversely proportional to the square of the distance between them. This equation is used to determine the mutual gravitational attraction between the Earth and the Moon.

3. What is the distance between the Earth and the Moon?

The average distance between the Earth and the Moon is approximately 384,400 kilometers (238,855 miles). However, this distance is not constant due to the elliptical orbit of the Moon around the Earth.

4. How does the Moon affect the Earth's tides?

The Moon's gravitational pull on the Earth causes ocean tides. As the Moon orbits around the Earth, its gravitational force causes the oceans on the side of the Earth closest to the Moon to bulge, creating a high tide. At the same time, the oceans on the opposite side of the Earth experience a low tide due to the Moon's gravitational pull being weaker.

5. Can the Moon-Earth binary system change over time?

Yes, the Moon-Earth binary system is constantly evolving. The Moon is gradually moving away from the Earth at a rate of approximately 3.78 centimeters (1.5 inches) per year, which affects the Earth's rotation and the length of a day. In addition, other factors such as collisions with asteroids or changes in the Earth's orbit can also alter the dynamics of this system over time.

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