How to Use this Site
This is an interactive ΔV map. Simply click on a node on a branch to
determine the target planet, and how you would like to explore it.
Toggle the checkboxes to tweak the calculations to your mission
parameters, and the required ΔV values as well as the relevant
transfer angles be displayed in real time.
Using a Delta-V Map
To use a typical ΔV map, you add all the values along the branch, from
your starting position to your target position. A white arrow in the
direction of your travel means you can aerobrake there and can therefore
exclude the value from your calculation. The values above a branch
indicate plane changes. This site performs all these calculations for you.
What is Delta-V (ΔV)
Delta-V, or ΔV, is a craft's capacity to change its velocity, and can
be interpreted as the range of a given craft. Similar to how a car may
say it has 50 km of fuel left, a spacecraft may have 5000 m/s of ΔV
left. Performing manoeuvres such as changing your orbit or landing on a
planet will use up some of your ΔV. Knowing how much ΔV is required to
perform a given task is essential for planning any mission.
The Mathematics
Rather than a look-up table, this site dynamically calculates the required ΔV for each mission profile.
After the route is selected, the calculator evaluates it using four primary calculation blocks.
In the expressions below:
- μ = GM is the standard gravitational parameter of the relevant central body
- r is the relevant orbital or parking-orbit radius
- a is the semi-major axis of the transfer ellipse.
Orbit to Escape
For a circular parking orbit of radius r0, the local orbital speed is
vcirc = √(μ / r0).
Pure escape from that radius requires
vesc = √(2μ / r0),
giving the ideal escape burn
Δvesc = vesc - vcirc.
Including hyperbolic excess velocity v∞, the escape burn becomes
Δvej = √(v∞2 + 2μ/r0) - √(μ/r0).
Interplanetary Transfer A-B
The interplanetary leg is modeled as an ideal coplanar Hohmann transfer from orbit A to orbit B.
The transfer semi-major axis is
at = (rA + rB) / 2.
The circular speeds:
vA = √(μ/rA)
vB = √(μ/rB).
The transfer-orbit speeds at the two ends:
vt,A = √(μ(2/rA - 1/at))
vt,B = √(μ(2/rB - 1/at)).
The ideal heliocentric burns are therefore:
ΔvA = |vt,A - vA|
ΔvB = |vB - vt,B|.
Capture to Low Orbit
On arrival, let the incoming hyperbolic excess velocity relative to the target be
v∞.
At periapsis radius rp, the hyperbolic periapsis speed is
vp,hyp = √(v∞2 + 2μ/rp).
The circular low-orbit speed at that same radius is
vcirc,p = √(μ/rp).
The ideal capture burn is then
Δvcap = vp,hyp - vcirc,p.
Transfer Windows
The Hohmann transfer time between two circular orbits is
ttrans = π√(at3 / μ).
The corresponding mean motions are:
nA = √(μ/rA3)
nB = √(μ/rB3).
The required departure phase angle for A to B is:
φA→B = π - nB ttrans,
while the reverse transfer is:
φB→A = π - nA ttrans.
Converting to degrees gives
φdeg = φ × 180 / π,
assuming the target is ahead of the origin in its orbit.
Assumptions
The calculator makes the following explicit assumptions:
- All transfer-window solutions are ideal two-body Hohmann transfers between the selected orbital radii.
- Departure and arrival burns are treated as impulsive burns rather than finite-duration burns.
- Mean motion is taken from sidereal period where available, otherwise reconstructed from
μ and semi-major axis.
- Interplanetary transfer geometry is evaluated from orbital radii rather than a full Lambert solution over arbitrary departure dates.
- Hyperbolic departure and capture are modeled with patched conics.
- Local parking orbits are treated as circular for low-orbit, escape, and capture calculations.
- Low-orbit radius is 10km above the planet's surface or atmosphere.
- Flyby or capture periapsis is 10km above the planet's surface or atmosphere.
- Escape and capture burns are evaluated at periapsis.
- Pure local escape assumes
v∞ = 0.
- For top-level interplanetary transfers, departure-side
v∞ = |vt,A - vA|.
- For top-level interplanetary arrivals, arrival-side
v∞ = |vB - vt,B|.
- Where orbital planes differ, the burn is combined with a plane-change rotation rather than treating it as a separate manoeuvre.
- Plane angle is derived from the relative inclination and longitude of ascending node only.
- Plane-change cost uses the impulsive approximation
Δv = 2v sin(θ/2) at the speed chosen for that branch.
- Surface-to-orbit and orbit-to-surface costs are taken from body data rather than being derived from thrust, drag, gravity turn, or entry simulation.
- Thrust limits, steering losses, long-burn Oberth inefficiency, and staging transients are ignored.
- Aerobraking conditions remove the entire ΔV cost for the relevant branch.
