Analogy between satelite orbit and mass oscillating through earth

In summary, the period of a satellite orbiting the Earth at surface height is equal to the period of any mass thrown through a hole in the Earth, assuming the Earth's density is uniform. This is because the circular orbit can be broken down into two simple harmonic motions, with the same proportional relationship existing along a radial line in a uniform mass sphere. This analogy is used to explain the concept, but it is not entirely accurate as the Earth's density is not truly uniform.
  • #1
Ezio3.1415
159
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The period of a satellite revolving around the Earth earth at surface height is equal to the period of any mass thrown through a hole of the earth(which gains a simple harmonic motion)...

It seemed really interesting to me...

Why both of these periods are same?

T=2 π √(R/g)
 
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  • #2
Ezio3.1415 said:
Why both of these periods are same?
You can decompose the circular orbit into two simple harmonic motions in two dimensions. The gravitational force component in each dimension is proportional to the position along that dimension. The same proportional relationship exists along a radial line in a uniform mass sphere.
 
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  • #3
Ezio3.1415 said:
The period of a satellite revolving around the Earth earth at surface height is equal to the period of any mass thrown through a hole of the earth(which gains a simple harmonic motion)...

It seemed really interesting to me...

Why both of these periods are same?

T=2 π √(R/g)

That's only true if you assume the Earth's density is uniform. That's not quite correct.
 
  • #4
AT Yes,but we are doing another analogy to explain this analogy... I thought of it at first but assumed their could be another approach to explain this incident... It just seems so interesting to me...

Dauto Yes... That's why we have to assume that the Earth is a uniform mass sphere...
 
  • #5


Thank you for sharing your observation. The analogy between a satellite orbit and a mass oscillating through the Earth is an interesting one. Both situations involve a body moving in a circular path around a central object, and they also both have a period of motion.

The reason why the periods are the same can be explained by looking at the equation you provided, T=2π√(R/g). This equation represents the period of a simple harmonic motion, where T is the period, R is the amplitude (or distance from the equilibrium point), and g is the acceleration due to gravity.

In the case of a satellite orbiting the Earth, the satellite is constantly falling towards the Earth due to the force of gravity. However, its forward motion also keeps it from crashing into the Earth, creating a circular orbit. The period of this orbit is determined by the distance between the Earth and the satellite (R) and the strength of the Earth's gravitational pull (g).

Similarly, when a mass is thrown through a hole in the Earth, it experiences simple harmonic motion as it oscillates back and forth due to the force of gravity. The period of this motion is also determined by the distance from the center of the Earth (R) and the strength of gravity (g).

This means that both the satellite and the mass have the same period of motion because they are both subject to the same force of gravity and are moving at the same distance from the center of the Earth.

I hope this explanation helps to clarify the connection between these two scenarios. As scientists, we often use analogies to better understand complex concepts and phenomena, and this is a great example of how concepts from one area of science can be applied to another.
 

1. What is the analogy between satellite orbit and mass oscillating through Earth?

The analogy between satellite orbit and mass oscillating through Earth refers to the similarities in the motion and forces acting on a satellite in orbit and a mass oscillating on the surface of Earth. Just as a satellite is pulled towards Earth by gravity and experiences a centripetal force that keeps it in orbit, a mass oscillating on Earth's surface also experiences a restoring force that keeps it oscillating around a fixed point. Both motions are governed by the same laws of motion and gravitation.

2. How does the mass of the satellite or oscillating mass affect the analogy?

The mass of the satellite or oscillating mass does not affect the analogy between satellite orbit and mass oscillating through Earth. The motion and forces acting on both are still governed by the same laws of motion and gravitation. However, the amplitude and period of the oscillations may vary depending on the mass of the objects.

3. Can you explain the concept of centripetal force in the analogy?

In the analogy, centripetal force refers to the force that keeps the satellite in orbit or the mass oscillating on Earth's surface. This force is directed towards the center of the orbit or oscillation and is necessary to counteract the outward centrifugal force. In the case of a satellite, this force is provided by Earth's gravity, while for an oscillating mass, it is provided by the restoring force, such as tension in a spring or gravitational force of attraction towards a fixed point.

4. How does the distance from Earth's center affect the analogy?

The distance from Earth's center does not affect the analogy between satellite orbit and mass oscillating through Earth. The motion and forces acting on both are still governed by the same laws of motion and gravitation. However, the distance does affect the strength of the gravitational force and thus the period and velocity of the orbit or oscillation.

5. Is there any other real-life example that can be compared to the analogy?

Yes, there are several other real-life examples that can be compared to the analogy between satellite orbit and mass oscillating through Earth. Some examples include the orbit of planets around the sun, the motion of a pendulum, and the oscillation of a diving board. These all exhibit similar behaviors as satellite orbit and mass oscillating, where a balance between gravitational forces and restoring forces is necessary to maintain their motion.

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