Specific Energy Of Elliptic Orbit Given Semi Major Axis Calculator

Formula Used:

\[ \varepsilon_e = -\frac{[GM.Earth]}{2 \times a_e} \]

Specific Energy of Elliptical Orbit:

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1. What is Specific Energy of Elliptical Orbit?

Specific Energy of Elliptical Orbit is the total orbital energy per unit mass of an orbiting body. It is the sum of the kinetic energy and the gravitational potential energy, representing the energy state of an object in elliptical orbit around Earth.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ \varepsilon_e = -\frac{[GM.Earth]}{2 \times a_e} \]

Where:

\( \varepsilon_e \) — Specific Energy of Elliptical Orbit (J/kg)
\( [GM.Earth] \) — Earth's Geocentric Gravitational Constant (3.986004418 × 10¹⁴ m³/s²)
\( a_e \) — Semi Major Axis of Elliptic Orbit (meters)

Explanation: The formula calculates the specific orbital energy based on the semi-major axis of the elliptical orbit, using Earth's standard gravitational parameter.

3. Importance of Specific Energy Calculation

Details: Calculating specific orbital energy is crucial for orbital mechanics, spacecraft trajectory planning, and understanding the energy requirements for orbital maneuvers and transfers.

4. Using the Calculator

Tips: Enter the semi-major axis of the elliptic orbit in meters. The value must be positive and greater than zero for valid calculation.

5. Frequently Asked Questions (FAQ)

Q1: What does negative specific energy indicate?
A: Negative specific energy indicates a bound orbit (elliptical or circular), where the object is gravitationally bound to Earth.

Q2: How is semi-major axis related to orbital period?
A: According to Kepler's third law, the orbital period is proportional to the 3/2 power of the semi-major axis.

Q3: Can this formula be used for other celestial bodies?
A: Yes, but you would need to replace [GM.Earth] with the gravitational parameter of the specific celestial body.

Q4: What are typical values for specific orbital energy?
A: For low Earth orbit, specific energy is typically around -30 MJ/kg, while for geostationary orbit it's about -5 MJ/kg.

Q5: How does specific energy relate to escape velocity?
A: Zero specific energy corresponds to a parabolic orbit (escape trajectory), while positive specific energy indicates a hyperbolic orbit.