# Delta-V Calculator

The delta-V calculator is a tool used to calculate the change in velocity (delta-V) required for a spacecraft or object to achieve a specific mission objective, such as entering orbit, changing orbits, or reaching a destination in space. It is a fundamental calculation in astrodynamics and mission planning.

The formula for calculating delta-V depends on the specific maneuver or objective being considered. Here are some common formulas used in delta-V calculations:

1. Hohmann Transfer: For a Hohmann transfer, which is used to transfer between two coplanar circular orbits, the delta-V is given by:

delta-V = sqrt(2 * μ / r1) – sqrt(μ / r1)

Where: delta-V is the required change in velocity (delta-V) μ is the gravitational parameter of the central body (e.g., Earth) r1 is the initial radius or altitude of the spacecraft’s orbit

1. Circular Orbit Insertion: To achieve a circular orbit from an elliptical orbit, the delta-V is given by:

delta-V = sqrt(μ * ((2 / r) – (1 / a)))

Where: delta-V is the required change in velocity (delta-V) μ is the gravitational parameter of the central body r is the final radius of the circular orbit a is the semi-major axis of the elliptical orbit

1. Plane Change: For a plane change maneuver, where the spacecraft needs to change its orbital plane, the delta-V is given by:

delta-V = 2 * v * sin(Δθ / 2)

Where: delta-V is the required change in velocity (delta-V) v is the velocity of the spacecraft in the initial orbit Δθ is the desired change in the orbital plane angle

These are just a few examples of the formulas used in delta-V calculations, and the specific formula depends on the maneuver or objective being considered. It’s important to consider factors such as gravitational forces, orbital parameters, and mission requirements when performing delta-V calculations.

The delta-V calculator is essential in mission planning and spacecraft design, aiding engineers and scientists in determining the propulsion requirements and fuel budgets for space missions.