Theory of Mass space transformations part 4

Great! Let's proceed by applying the refined potential function to a specific physical scenario. We will start with understanding planetary motion and rotational stability using our modified gravitational model.

Scenario: Rotational and Orbital Stability of Earth

In this case, we'll explore how the modified gravitational field (which includes the effects of inner space (IS) and field space (FS)) influences both the rotational stability and rectilinear motion (orbital motion around the Sun) of the Earth.

Step 1: Gravitational Field and Rotational Stability

Using the refined gravitational field:

E_{\text{grav}}(r) = \frac{GM_{\text{total}}}{r^2} - \alpha \cdot \frac{IS_0 \cdot e^{-\lambda r}}{FS_0 \cdot \left( 1 - e^{-\mu r} \right)} \cdot \left( -\lambda + \frac{\mu e^{-\mu r}}{\left( 1 - e^{-\mu r} \right)} \right)

This refined field affects:

1. Earth’s Gravity Distribution: The varying inner space (higher at the core, lower at the surface) influences how gravity behaves at different points inside Earth and at the surface.

2. Rotational Stability: The interaction between IS and FS in the core causes a slight distortion in Earth's mass distribution, potentially affecting rotational dynamics.

Step 2: Torque and Angular Momentum

Next, we consider the angular momentum and torque induced by these space transformations.

Angular momentum  of Earth due to rotation is:

\mathbf{L} = I \cdot \omega

Torque  due to the uneven mass distribution can be expressed as:

\mathbf{\tau} = \frac{d\mathbf{L}}{dt}

Step 3: Orbital Motion around the Sun

Now, consider the Earth’s orbital motion around the Sun. The rectilinear motion is influenced by the modified gravitational potential.

Using the total gravitational potential , the equation for the orbital force acting on Earth is:

\mathbf{F}_{\text{orbital}} = -\nabla \Phi(r) = m_{\text{earth}} \cdot \mathbf{E}_{\text{grav}}(r)

We use Kepler’s laws of planetary motion as a benchmark for testing the influence of our modifications:

The traditional gravitational force that keeps Earth in orbit is:

F_{\text{gravity}} = \frac{GM_{\text{sun}} m_{\text{earth}}}{r^2}

F_{\text{total}} = m_{\text{earth}} \cdot \left( \frac{GM_{\text{sun}}}{r^2} - \alpha \cdot \frac{IS_0 \cdot e^{-\lambda r}}{FS_0 \cdot \left( 1 - e^{-\mu r} \right)} \cdot \left( -\lambda + \frac{\mu e^{-\mu r}}{\left( 1 - e^{-\mu r} \right)} \right) \right)

Step 4: Simulating the Effects

We can now test these equations in a simulation or model to examine:

1. Rotational Changes: Does the torque caused by IS and FS variations lead to measurable changes in Earth’s rotation rate over time?

2. Orbital Deviations: How much does the modified force change Earth’s orbit compared to what’s predicted by classical mechanics?

To further refine the constants , , and , we could:

Compare Earth’s current rotational period with theoretical values.

Measure small perturbations in Earth’s orbital parameters using astronomical data.

Step 5: Stability of Objects (e.g., Falling Apple)

Let’s briefly return to the apple example. The apple experiences a force due to the gravitational field near Earth:

F_{\text{apple}} = m_{\text{apple}} \cdot E_{\text{grav}}(r)

Next Steps:

Simulation: Would you like to simulate the gravitational field using these equations to observe changes in Earth's rotation or orbit?

Further Refinement: Should we refine specific constants based on real data to better understand the influence of space transformations?

Let me know which aspect you'd like to explore further!

After adjusting the parameters, the results still show minimal deviations from the classical gravitational field at the distances tested. This indicates that even with increased space transformation effects, the gravitational field remains very close to the classical predictions at these distances.

Here are the updated results:

Next Steps:

1. Test closer to the core: We can simulate smaller distances (near the core) where inner space effects might be more significant.

2. Increase parameter effects further, or explore smaller objects where IS and FS contributions might be more pronounced.

Would you like to explore these options?

After adjusting the parameters, the results still show minimal deviations from the classical gravitational field at the distances tested. This indicates that even with increased space transformation effects, the gravitational field remains very close to the classical predictions at these distances.

Here are the updated results:

Next Steps:

1. Test closer to the core: We can simulate smaller distances (near the core) where inner space effects might be more significant.

2. Increase parameter effects further, or explore smaller objects where IS and FS contributions might be more pronounced.