# Delta-v

measure of amount of effort to change trajectory

Delta-v, meaning delta velocity and symbolized as Δv, is a measure of a spacecraft's ability to change it's trajectory (the path it will take in the future). Delta velocity in simple terms means 'the change in speed' It is measured by a unit of speed, usually meters per second (m/s).# Abbreviations key:Escape Orbit (C3), Geosynchronous orbit (GEO), Geostationary transfer orbit (GTO), Earth–Moon L5 Lagrangian point (L5), Low Earth orbit (LEO) Graph showing the approximate required Delta-V for Mars, the Moon, and Earth, both ways. The red arrows show the directions in which it is possible to slow a craft down using the atmosphere of what it is going toward.

Factors that go into calculating delta-v are:

1. The mass of the spacecraft.
2. The amount of gravity in which the spacecraft currently finds itself.
3. The thrust and efficienty of the engine.
4. The amount of fuel the spacecraft has.

As an example of how delta-v is used, we can imagine a goal: flying a spacecraft into low Earth orbit. (In simple words, getting a rocket to spin around the Earth). We would first calculate how much delta-v will be required for that journey. Then, with the factors in the above list, we can calculate how much delta-v our spacecraft would need to go on that journey. Like if a person were to drive his car from point A to point B, he'd need to know how much fuel he needs in his car first. But in rocket science, using delta-v is much more relevant, as we have to completely design our spacecraft, including all factors mentioned above.

To reach Low Earth orbit, (LEO) our spacecraft would need roughly 10,000 m/s of delta-v.

Delta-v can be seen a budget, because if our spacecraft were to use up the 10,000 m/s of delta-v, it wouldn't be able to complete its journey to low Earth orbit.

Delta-v is calculated using this integral equation:

$\Delta {v}=\int _{t_{0}}^{t_{1}}{\frac {|T(t)|}{m(t)}}\,dt$ where

• T(t) is the thrust at time t.
• m(t) is the mass at time t.