Data_analytics

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🌌 Assignment 2 -Analyzing Kepler's Data on Mars

This repository provides materials, datasets, and instructions for Analyzing Kepler's Data on Mars.

🌍 Overview

This module focuses on analyzing Mars's orbital data using trigonometric and regression techniques, including:

• Exploring Mars opposition data to identify orbital parameters.
• Computing orbital projections using triangulation data.
• Applying regression and nonlinear optimization.

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📊 Datasets

Mars Opposition Data

• File: mars_opposition_data.csv
• Description: Contains Mars's heliocentric longitude, geocentric latitude, and Keplerian approximations during its opposition with the Sun.
• Key Details:
  • Longitude Formula: s * 30 + Degree + Minute/60 + Second/3600 (degrees)
  • Includes columns for date and Mars's mean longitude (Kepler's equant approximation).

Triangulation Data

• File: triangulation_data.csv
• Description: Provides longitudinal Earth-Mars observational data for triangulation analysis.
• Key Details:
  • Heliocentric longitude of Earth and geocentric longitude of Mars.
  • Includes observation indices and corresponding dates.

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📝 Assignments

1. Mars Opposition Analysis

• Derive Mars's projected position and identify the best-fit parameters using a custom loss function.

2. Triangulation Data Analysis

• Use paired observations to triangulate Mars's ecliptic projections and determine its best-fit circular orbit around the Sun.

3. Orbital Plane Identification

• Apply iterative regression to determine Mars's orbital plane inclination using heliocentric latitudes.

4. Orbital Ellipse Calculation

• Compute Mars's 3D positions, fit a circle and ellipse on the orbital plane, and visualize the orbital elements.

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🔗 Resources

• Mars Opposition Data (mars_opposition_data.csv)
• Triangulation Data (triangulation_data.csv)

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