Update README.md
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@@ -18,11 +18,13 @@ The simulator consists of several key components:
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The simulator uses Newton's law of universal gravitation to calculate the forces between celestial bodies. The gravitational force between two bodies is given by:
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$$ F = G \frac{m_1 m_2}{r^2} $$
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$$
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F = G \frac{m_1 m_2}{r^2}
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$$
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Where:
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- $F$ is the gravitational force between the two bodies
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- $G$ is the gravitational constant ($$6.67430 \times 10^{-11} \, \text{N} \cdot \text{m}^2 / \text{kg}^2$$)
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- $G$ is the gravitational constant ($6.67430 \times 10^{-11} \, \text{N} \cdot \text{m}^2 / \text{kg}^2$)
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- $m_1$ and $m_2$ are the masses of the two bodies
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- $r$ is the distance between the centers of the two bodies
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@@ -31,9 +33,18 @@ Where:
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The motion of each celestial body is updated using numerical integration. We use a simple Euler method for updating positions and velocities:
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1. Calculate the net force on each body
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2. Calculate acceleration: $$ \vec{a} = \frac{\vec{F}}{m} $$
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3. Update velocity: $$ \vec{v}_{new} = \vec{v}_{old} + \vec{a} \Delta t $$
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4. Update position: $$ \vec{x}_{new} = \vec{x}_{old} + \vec{v}_{new} \Delta t $$
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2. Calculate acceleration:
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```math
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$$ \vec{a} = \frac{\vec{F}}{m} $$
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```
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3. Update velocity:
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```math
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$$ \vec{v}_{new} = \vec{v}_{old} + \vec{a} \Delta t $$
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```
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4. Update position:
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```math
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$$ \vec{x}_{new} = \vec{x}_{old} + \vec{v}_{new} \Delta t $$
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```
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Where $\Delta t$ is the time step of the simulation.
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