# Gravity Assist Simulator - Planetary Flyby, Slingshot Speed Gain, Hohmann

> Simulate a gravity assist: set v∞ and periapsis to see the turn angle and Sun-frame speed gain, then get Hohmann Δv, flight time and launch windows.

- URL: https://qilingtools.com/en/physics/gravity-assist
- Category: Physics Tools (https://qilingtools.com/en/physics)
- Tags: [Physics](https://qilingtools.com/en/tags/physics), [Education](https://qilingtools.com/en/tags/education)
- Last updated: 2026-10-29
- Price: Free, no sign-up
- Privacy: Runs locally in the browser; files are never uploaded

Gravity assists are how interplanetary probes speed up or slow down without fuel. This tool shows one flyby in two frames at once. In the planet’s frame the probe follows a hyperbola and turns by some angle with unchanged speed. In the Sun’s frame you add the planet’s orbital velocity, and the turned vector can come out longer or shorter. Drag the aim point and the velocity vector to see the turn angle, periapsis speed and heliocentric speed change update live. A second tab works out Hohmann transfers between planets with the Δv, flight time and the next launch windows.

## How to use

1. Pick a preset such as Voyager 2 at Jupiter or Cassini at Venus, or choose a planet
2. Set the approach speed v∞, closest-approach altitude and approach angle, or drag on the canvases
3. Press Play to watch the path in the planet frame and Sun frame and read the speed gain
4. Switch to "Interplanetary Hohmann transfer" and choose departure and target planets and a date
5. Read the transfer time, departure and capture Δv, phase angle and upcoming launch windows

## Features

- Hyperbolic flyby: eccentricity, turn angle, impact parameter, periapsis speed
- Sun-frame velocity diagram you can drag to change the approach
- Synchronized animation in the planet frame and the Sun frame
- Speed-up or slow-down pass direction, with a one-click "best side"
- Hohmann transfers between planets: Δv, C3, time of flight, phase angle
- Launch windows and synodic periods from J2000 mean longitudes

## FAQ

### Where does the extra speed come from?

From the planet’s orbital motion. In the planet’s frame the probe leaves with the same speed it arrived with, only in a new direction. Transforming to the Sun’s frame adds the planet’s velocity V, and the length of that vector sum changes. The momentum and energy the probe gains are lost by the planet, but the planet is so massive that Voyager 2 changed Jupiter’s speed by only about one part in 10²⁵.

### Why does passing behind the planet speed you up?

Passing behind the planet, relative to its direction of motion, bends the probe’s relative velocity toward the planet’s direction of travel. The outgoing v∞ is then more aligned with the planet’s velocity, so their sum is longer and the probe speeds up. Passing in front does the opposite and slows it down. Parker Solar Probe uses repeated Venus flybys this way to lower its perihelion step by step.

### What is the most speed one flyby can add?

In the planet frame the velocity vector changes by 2v∞ sin(δ/2) = 2v∞/e, where δ is the turn angle and e = 1 + r_p v∞²/μ. A lower periapsis, a heavier planet and v∞ close to √(μ/r_p) all give a larger change. At Jupiter it can exceed 10 km/s; at Venus or Earth it is a few km/s. The periapsis cannot go below the surface or atmosphere, which caps the gain.

### Why are launch windows so far apart?

A Hohmann transfer needs the target planet to lead by a specific phase angle at departure so that it arrives at the meeting point at the same time as the probe. That geometry repeats once per synodic period: about 780 days (26 months) for Earth–Mars and 399 days for Earth–Jupiter. The tool estimates dates with circular, coplanar orbits; real windows also depend on eccentricity and inclination.

### Why fly all those loops instead of going straight there?

Going directly to the outer planets costs a lot of departure Δv: a Hohmann transfer to Jupiter from low Earth orbit needs about 6.3 km/s, and farther planets need more, while the rocket equation makes the propellant grow exponentially. With a few flybys of Venus, Earth and Jupiter, Cassini, Galileo and Voyager reached their targets on much smaller rockets, at the price of longer trips and tighter windows.

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