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<!DOCTYPE html>
<html lang="en">
<head>
<meta charset="UTF-8">
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<title>Keplerian Orbital Elements - Niko Natsoulas</title>
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<div class="orbital-page-container">
<header class="header-container">
<div class="header-left">
<span class="header-name">Niko Natsoulas</span>
<a href="index.html" class="home-button">Home</a>
</div>
<div class="header-title">
<h1 class="page-title">Keplerian Orbital Elements</h1>
<p class="page-subtitle">Interactive visualization of orbital elements</p>
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<style>
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<section class="orbital-elements">
<div class="visualization-container">
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<div class="view-controls">
<h3>View Controls</h3>
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<input type="checkbox" id="autopan-toggle" checked>
<label for="autopan-toggle">Autopan</label>
</div>
<div class="slider-group">
<label for="horizontal-angle">Horizontal Angle</label>
<input type="range" id="horizontal-angle" min="-180" max="180" value="0">
<span class="slider-value" id="horizontal-angle-value">0°</span>
</div>
<div class="slider-group">
<label for="vertical-angle">Vertical Angle</label>
<input type="range" id="vertical-angle" min="-180" max="180" value="0">
<span class="slider-value" id="vertical-angle-value">0°</span>
</div>
</div>
<div class="orbital-controls">
<h3>Orbital Elements</h3>
<div class="slider-group">
<label for="semi-major-axis">Semi-major axis (a) [AU]</label>
<input type="range" id="semi-major-axis" min="1" max="10" step="0.1" value="5">
<span class="slider-value" id="semi-major-axis-value">5.0</span>
</div>
<div class="slider-group">
<label for="eccentricity">Eccentricity (e)</label>
<input type="range" id="eccentricity" min="0" max="0.99" step="0.01" value="0">
<span class="slider-value" id="eccentricity-value">0.00</span>
</div>
<div class="slider-group">
<label for="inclination">Inclination (i) [°]</label>
<input type="range" id="inclination" min="0" max="180" step="1" value="0">
<span class="slider-value" id="inclination-value">0°</span>
</div>
<div class="slider-group">
<label for="raan">Right Ascension of Ascending Node (Ω) [°]</label>
<input type="range" id="raan" min="0" max="360" step="1" value="0">
<span class="slider-value" id="raan-value">0°</span>
</div>
<div class="slider-group">
<label for="arg-periapsis">Argument of Periapsis (ω) [°]</label>
<input type="range" id="arg-periapsis" min="0" max="360" step="1" value="0">
<span class="slider-value" id="arg-periapsis-value">0°</span>
</div>
<div class="slider-group">
<label for="true-anomaly">True Anomaly (ν) [°]</label>
<input type="range" id="true-anomaly" min="0" max="360" step="1" value="0">
<span class="slider-value" id="true-anomaly-value">0°</span>
</div>
</div>
</div>
</div>
</section>
<div class="scroll-prompt">
<p>Scroll down for explanations of the Keplerian Orbital Elements Framework <i class="fas fa-arrow-down"></i></p>
</div>
<section class="element-explanations">
<h2>Orbital Elements and Key Concepts</h2>
<div class="explanation-grid">
<div class="explanation-item">
<h3>Semi-major axis (a)</h3>
<p>Half the longest diameter of the elliptical orbit. It determines the orbit's size and is directly related to the orbital period.</p>
<p class="equation">$$T = 2\pi\sqrt{\frac{a^3}{\mu}}$$</p>
<p>Where T is the orbital period and μ is the gravitational parameter.</p>
</div>
<div class="explanation-item">
<h3>Eccentricity (e)</h3>
<p>Describes the orbit's shape, ranging from 0 (circular) to 1 (parabolic). Values between 0 and 1 represent elliptical orbits.</p>
<p class="equation">$$e = \sqrt{1 - \frac{b^2}{a^2}}$$</p>
<p>Where b is the semi-minor axis.</p>
</div>
<div class="explanation-item">
<h3>Inclination (i)</h3>
<p>The angle between the orbital plane and the reference plane. Ranges from 0° to 180°.</p>
<p class="equation">$$\cos i = \frac{\mathbf{h} \cdot \hat{\mathbf{z}}}{|\mathbf{h}||\hat{\mathbf{z}}|}$$</p>
<p>Where h is the angular momentum vector and ẑ is the unit vector of the reference plane's normal.</p>
</div>
<div class="explanation-item">
<h3>Right Ascension of Ascending Node (Ω)</h3>
<p>Angle from the reference direction to the ascending node, measured in the reference plane. Ranges from 0° to 360°.</p>
<p class="equation">$$\tan \Omega = \frac{\mathbf{n} \cdot \hat{\mathbf{y}}}{\mathbf{n} \cdot \hat{\mathbf{x}}}$$</p>
<p>Where n is the node line vector, and x̂ and ŷ are unit vectors in the reference plane.</p>
</div>
<div class="explanation-item">
<h3>Argument of Periapsis (ω)</h3>
<p>Angle from the ascending node to the periapsis, measured in the orbital plane. Ranges from 0° to 360°.</p>
<p class="equation">$$\cos \omega = \frac{\mathbf{n} \cdot \mathbf{e}}{|\mathbf{n}||\mathbf{e}|}$$</p>
<p>Where e is the eccentricity vector.</p>
</div>
<div class="explanation-item">
<h3>True Anomaly (ν)</h3>
<p>Angle from the periapsis to the orbiting body's current position, measured in the direction of motion. Ranges from 0° to 360°.</p>
<p class="equation">$$\cos \nu = \frac{\mathbf{e} \cdot \mathbf{r}}{|\mathbf{e}||\mathbf{r}|}$$</p>
<p>Where r is the position vector of the orbiting body.</p>
</div>
<div class="explanation-item">
<h3>Reference Plane</h3>
<p>The light blue plane in the visualization, representing the fundamental plane of the coordinate system (e.g., Earth's equatorial plane).</p>
</div>
<div class="explanation-item">
<h3>Orbital Plane</h3>
<p>The light orange plane containing the orbit. Its orientation is defined by the inclination and RAAN.</p>
</div>
<div class="explanation-item">
<h3>Line of Nodes</h3>
<p>The intersection of the orbital plane and the reference plane. It connects the ascending and descending nodes.</p>
<p class="equation">$$\mathbf{n} = \hat{\mathbf{z}} \times \mathbf{h}$$</p>
<p>Where n is the node line vector, ẑ is the reference plane normal, and h is the angular momentum vector.</p>
</div>
<div class="explanation-item">
<h3>Periapsis</h3>
<p>The point of closest approach to the central body in an elliptical orbit. Marked by a dashed white line in the visualization.</p>
<p class="equation">$$r_p = a(1-e)$$</p>
<p>Where r<sub>p</sub> is the periapsis distance.</p>
</div>
</div>
</section>
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<p>© 2024 Niko Natsoulas. All rights reserved.</p>
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