Semi Major Axis of Phasing Ellipse Calculator

Formula Used:

\[ a = \left( \frac{n \cdot \sqrt{\mu}}{2\pi} \right)^{\frac{2}{3}} \]

Semi Major Axis of Ellipse:

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1. What is the Semi Major Axis of Phasing Ellipse?

The Semi Major Axis of a Phasing Ellipse is a fundamental parameter in orbital mechanics that determines the size and period of an elliptical orbit. It represents half of the longest diameter of the elliptical orbit and is crucial for calculating orbital period and energy.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ a = \left( \frac{n \cdot \sqrt{\mu}}{2\pi} \right)^{\frac{2}{3}} \]

Where:

\( a \) — Semi Major Axis of Ellipse (meters)
\( n \) — Number of Period
\( \mu \) — Gravitational Parameter (m³/s²)
\( \pi \) — Mathematical constant (approximately 3.14159)

Explanation: This formula calculates the semi-major axis based on the number of orbital periods and the gravitational parameter of the central body.

3. Importance of Semi Major Axis Calculation

Details: The semi-major axis is essential for determining orbital characteristics such as orbital period, energy, and stability. It's crucial for satellite deployment, space mission planning, and orbital mechanics calculations.

4. Using the Calculator

Tips: Enter the number of periods and gravitational parameter. Both values must be positive numbers. The gravitational parameter is typically known for celestial bodies (Earth: ~3.986×10¹⁴ m³/s²).

5. Frequently Asked Questions (FAQ)

Q1: What is the gravitational parameter?
A: The gravitational parameter (μ) is the product of the gravitational constant G and the mass M of a celestial body (μ = G×M).

Q2: How is this different from circular orbit calculations?
A: This formula specifically calculates the semi-major axis for elliptical orbits based on the number of periods, while circular orbits have simpler relationships between radius and period.

Q3: What are typical values for gravitational parameters?
A: Earth: 3.986×10¹⁴ m³/s², Sun: 1.327×10²⁰ m³/s², Moon: 4.905×10¹² m³/s².

Q4: Can this be used for interplanetary trajectories?
A: Yes, the formula applies to any elliptical orbit around any celestial body, given the appropriate gravitational parameter.

Q5: How accurate is this calculation?
A: The calculation is mathematically exact for two-body problems without perturbations. Real-world applications may require additional corrections for perturbations.