Delta-v

Delta-v, also known as change in velocity, is an important idea in space travel. It tells us how much speed a spacecraft needs to change to do things like leave a planet, land on a moon, or move around in space. Even though it sounds like just changing speed, delta-v is really about how much "push" a spacecraft can create with its fuel.

For example, imagine a rocket that burns all its fuel. The delta-v of that rocket is the total speed change it can make during that burn. This number helps engineers figure out how much fuel, called propellant, they need for any space mission.

Delta-v comes from the engines that push the spacecraft, like rocket engines. The more thrust an engine has and the longer it burns, the more delta-v it can create. When planning trips between planets, scientists use special charts to see how much delta-v is needed for different launch dates.

Definition

Delta-v, written as Δv, is a way to measure how much speed a spacecraft needs to change to do things like launch, land, or move around in space. It tells us how much push a spacecraft needs compared to its weight to make these moves.

The formula for delta-v uses the thrust and mass of the spacecraft at different times. Thrust is the force that pushes the spacecraft forward, and mass is how much the spacecraft weighs.

Specific cases

When no outside forces push or pull on a spacecraft, we can figure out the change in speed it needs using a special math rule. If the push from the spacecraft’s engines points in the same direction the whole time, the change in speed is just how much the speed goes up or down.

For rockets, we usually pretend there are no forces like wind or gravity when we work out how much speed they need to change. We use a special formula for this. But when rockets take off from a planet, we also need to think about extra speed they lose because of air and gravity.

Orbital maneuvers

Main articles: orbital maneuver and rocket equation

Spacecraft can change their paths by using special engines called thrusters. When these engines fire, they push the spacecraft. This push changes the spacecraft's speed or direction. Changing speed is important for moving from one orbit to another or for landing on a planet or moon.

The amount of speed change a spacecraft can make depends on its fuel and how strong the thrusters are. Scientists and engineers use math to figure out how much speed change is possible. Even as the spacecraft uses fuel and gets lighter, this math helps plan the best way to move in space. Sometimes, they imagine the speed change happens all at once. This makes calculations easier and works well for many types of engines.

T = v exh ρ {\displaystyle T=v_{\text{exh}}\ \rho }

v ˙ = T m = v exh ρ m {\displaystyle {\dot {v}}={\frac {T}{m}}=v_{\text{exh}}\ {\frac {\rho }{m}}}

m ˙ = − ρ {\displaystyle {\dot {m}}=-\rho \,}

Δ v = − ∫ t 0 t 1 v exh m ˙ m d t {\displaystyle \Delta {v}=-\int _{t_{0}}^{t_{1}}{v_{\text{exh}}\ {\frac {\dot {m}}{m}}}\,dt}

Δ v = − ∫ m 0 m 1 v exh d m m {\displaystyle \Delta {v}=-\int _{m_{0}}^{m_{1}}{v_{\text{exh}}\ {\frac {dm}{m}}}}

Δ v = v exh ln ⁡ ( m 0 m 1 ) {\displaystyle \Delta {v}=v_{\text{exh}}\ \ln \left({\frac {m_{0}}{m_{1}}}\right)}

Production

Delta-v is the speed change a spacecraft needs to move, like taking off from a planet or changing its path in space. It is usually created by the push from a rocket engine, but other engines can also help.

The amount of delta-v needed helps engineers plan their spacecraft. More delta-v means the spacecraft needs more fuel. So, designers try to use less delta-v and build spacecraft that can create more of it. They can do this by using staging, making the engine more efficient with a higher specific impulse, or using more of the spacecraft’s weight for fuel with a better propellant mass fraction.

Multiple maneuvers

When a spacecraft makes more than one move, we can find the total effect by adding up the changes in speed for each move. This makes planning the trip easier, because we only need to add up the speed changes instead of doing more difficult math.

Delta-v budgets

When planning how spacecraft will move, people use something called delta-v budget to guess how much fuel they will need. The amount of fuel needed grows fast with more delta-v, and it also depends on how fast the fuel burns.

We can't just look at the energy of the spacecraft to know how much delta-v we need. For example, when launching a spacecraft, it often starts in an orbit close to where it leaves Earth, using Earth's spin to help. But if we need to change the orbit for the mission, we need more delta-v, even though the energy in the new orbit might be the same.

When rockets fire for a short time, we can think of the change in speed as just delta-v. We can add up all the small changes to find the total delta-v needed, even though the spacecraft's speed changes between these burns because of gravity.

Delta-v is also needed to keep satellites moving in their orbits. Since satellites can't get more fuel once they're in space, the amount of fuel they start with can decide how long they can stay useful.

Oberth effect

Main article: Oberth effect

It turns out that when we add delta-v in the same direction the spacecraft is moving, we get more energy from the move. This is called the Oberth effect.

For example, pushing a satellite when it is moving fast (close to Earth) works better than when it is moving slow (far from Earth).

Another example is when a spacecraft flies close to a planet. Burning fuel when it is closest gives a bigger speed increase, especially when the planet is big with strong gravity, like Jupiter.

Porkchop plot

Main article: Porkchop plot

Because planets move around the Sun, the amount of delta-v needed changes with time. A diagram showing how much delta-v is needed over time is called a porkchop plot. This helps decide when to launch a mission so that the spacecraft can do what we need it to do.

Around the Solar System

This part shows how much delta-v is needed for different moves around the Sun using normal rockets. Red arrows show where a spacecraft could use the atmosphere of a planet to help, and black numbers show the delta-v in kilometers per second needed.

Escape orbit

GEO

Geosynchronous orbit

GTO

Geostationary transfer orbit

L4/5

Earth–Moon L₄ L₅ Lagrangian point

LEO

Low Earth orbit

LEO reentry

For example, the Soyuz spacecraft leaves the ISS in two steps. First, it needs a delta-v of 2.18 m/s to safely move away from the space station. Then it needs another 128 m/s to come back through the atmosphere.