Semimajor Axis Of Elliptic Orbit Given Apogee And Perigee Radii Calculator

Formula Used:

\[ a_e = \frac{r_{e,apogee} + r_{e,perigee}}{2} \]

Semi Major Axis of Elliptic Orbit:

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1. What is the Semimajor Axis of Elliptic Orbit?

The Semimajor Axis of Elliptic Orbit is half of the major axis, which is the longest diameter of the ellipse describing the orbit. It represents the average distance between the orbiting body and the center of the object it orbits.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ a_e = \frac{r_{e,apogee} + r_{e,perigee}}{2} \]

Where:

\( a_e \) — Semi Major Axis of Elliptic Orbit (m)
\( r_{e,apogee} \) — Apogee Radius in Elliptic Orbit (m)
\( r_{e,perigee} \) — Perigee Radius in Elliptic Orbit (m)

Explanation: The semimajor axis is simply the average of the apogee (maximum distance) and perigee (minimum distance) radii, providing a measure of the orbit's size.

3. Importance of Semimajor Axis Calculation

Details: The semimajor axis is a fundamental parameter in orbital mechanics that determines the orbital period according to Kepler's third law. It is crucial for satellite positioning, orbital trajectory planning, and understanding the energy characteristics of orbits.

4. Using the Calculator

Tips: Enter both apogee and perigee radii in meters. Both values must be positive numbers representing valid orbital distances from the center of the primary body.

5. Frequently Asked Questions (FAQ)

Q1: What is the difference between semimajor axis and average orbital radius?
A: The semimajor axis is exactly half of the major axis length, while the average orbital radius is the mean distance over one complete orbit, which is approximately equal to the semimajor axis for near-circular orbits.

Q2: How does semimajor axis relate to orbital period?
A: According to Kepler's third law, the square of the orbital period is proportional to the cube of the semimajor axis (T² ∝ a³).

Q3: Can this formula be used for all types of orbits?
A: This specific formula applies to elliptical orbits. For circular orbits, apogee and perigee radii are equal, making the calculation straightforward.

Q4: What units should be used for the input values?
A: The calculator expects values in meters, but the formula works with any consistent unit system as long as both radii use the same units.

Q5: How accurate is this calculation for real-world orbital mechanics?
A: This calculation provides the basic geometric semimajor axis. For precise orbital calculations, additional factors such as gravitational perturbations and non-spherical gravity fields may need to be considered.