The Hohmann Transfer Calculator is a crucial tool for space mission planners, engineers, and enthusiasts. It accurately computes the necessary Delta-V (change in velocity) and transfer time to move a spacecraft between two circular orbits around a central body, ensuring propellant efficiency and mission success.
Formula:
The Hohmann Transfer Calculator determines the propellant-efficient orbital maneuver to transfer a spacecraft between two circular orbits around a central body. It uses the following fundamental principles:
- Initial Orbital Velocity (v1): Calculated for the starting circular orbit.
- Final Orbital Velocity (v2): Calculated for the target circular orbit.
- Semi-Major Axis of Transfer Orbit (atransfer): The average radius of the elliptical transfer path.
- Velocity at Periapsis (vp_transfer): The speed required at the closest point of the transfer ellipse to the central body.
- Velocity at Apoapsis (va_transfer): The speed required at the farthest point of the transfer ellipse from the central body.
- Delta-V1 (Initial Burn): The change in velocity needed to inject the spacecraft from the initial circular orbit into the transfer ellipse.
- Delta-V2 (Final Burn): The change in velocity needed to circularize the orbit at the target radius from the transfer ellipse.
- Total Delta-V: The sum of Delta-V1 and Delta-V2, representing the total change in velocity (and thus fuel expenditure).
- Hohmann Transfer Time (Δt): Half the orbital period of the transfer ellipse.
Key variables include:
- μ (Standard Gravitational Parameter): A constant for the central body (e.g., Earth, Sun), equal to GM (gravitational constant x mass of body).
- r1: Radius of the initial circular orbit from the center of the central body.
- r2: Radius of the target circular orbit from the center of the central body.