Gravity assists

*Learn more at:* https://terraforming.fandom.com/wiki/Gravity\_Assists

**Gravity assists** are orbital maneuvers used to alter a rocket's trajectory and speed using a celestial body's relative motion and gravity with little or no fuel. They are done to save fuel and reduce the budget at the expense of time. They have been used by many rockets throughout history.

Without gravity assists, the well-known Voyager *Grand Tour* would never have been possible. A Jupiter gravity assist helped *Cassini* reach Saturn. However, they have been largely used for smaller space missions. For example, ESA's *Rosetta* probe used two Earth and one Mars gravity assist to reach a comet, NASA's *MESSENGER* probe used many Earth, Venus, and Mercury gravity assists to enter Mercury orbit, and the Parker Solar Probe performed several Venus gravity assists to help approach the Sun.

## Gravity assists on different celestial bodies

Gravity assists are largely used during a Mercury return mission and usually use Venus and Mercury. Other than that, they can be performed with all other planets and the Moon.

### Mercury

During a Mercury mission, gravity assist can be used to lower the rocket's perihelion down to Mercury orbit.

In addition, when a rocket leaves Mercury, a gravity assist can increase its aphelion to the orbit of Venus, with which another gravity assist may be used to increase the aphelion back up to Earth orbit.

### Venus

Venus is primarily used for gravity assistance. The planet has enough gravity to perform one. With one or two gravity assists, a rocket coming from Earth can be sent to Mercury, Jupiter, or other distant planets, and a rocket coming from Mercury can be sent to Earth.

In addition, Venus is used for rockets that have only a little fuel left that cannot reach the Earth in one flight. A Mercury return mission or a Venus return mission may use all or nearly all the fuel of a rocket. If the player waits for a correct planetary alignment and uses a Venus gravity assist, it can raise the aphelion of the rocket to reach Earth orbit.

### Earth

The Earth can be used by a rocket travelling from Venus to Mars or from Mars to Venus or beyond, but this is uncommon.

Often, an Earth gravity assist can be used for a rocket in heliocentric orbit to get to Venus, Mercury, Mars, the asteroid belt, or Jupiter, thus saving fuel.

NASA sent the probe *OSIRIS-REx* to have an Earth gravity assist to reach the asteroid Bennu. The *Deep Impact rocket* performed several Earth gravity assists to gently adjust its orbit to encounter a comet.

**Warning:** The Moon could get in the way of an Earth gravity assist and drastically modify its effect.

#### Moon

The Moon has little gravity, but it can still be used for a gravity assist because of its proximity to Earth. One or multiple moon gravity assists can send a rocket into heliocentric orbit or escape Earth sphere of influence with the right alignment. NASA's *STEREO-A* and *STEREO-B* probes used a Moon gravity assist for this reason.

It is also possible to get an orbit of Earth when returning using the moon since it has enough gravity to slow down to the point to orbit of the returning rocket.

**Note:** Some trajectories would **always collide** with the moon if it slows down enough to the point of orbiting Earth.
### Mars

Mars was used for the *Dawn* and *Rosetta* missions for a gravity assist. Multiple Mars gravity assists can send a rocket into the asteroid belt or Jupiter. In addition, a Mars gravity assist can lower the perihelion closer to Earth.

Mars gravity assists are quite small because Mars has about 3/8 the gravity of Earth.

#### Mars's moons

The gravities of Mars's small moons are too low for a gravity assists. A gravity assist of one of its moons can very barely change the orbit of a rocket due to the lack of gravity on the moons, so they are basically useless, just like in real life.

### Jupiter

Jupiter has a high gravity, which makes it useful for gravitational assistance, such as when NASA used its gravity to give *Voyager 2* a speed boost to allow it to reach Saturn. However, in the **base** solar system, this gravitational boost is useless as no objects **beyond** Jupiter's orbit have been added, unless you want to escape the solar system.

Jupiter's gravity can be very useful as it can give the rocket a large gravitational assist, which can send the rocket to reach other planets and stars, but only if you are using a ***custom solar system*** that adds them in.

### Sun

In some simulators, like Kerbal Space Program, it is possible to use a Sun gravity assist, something that in reality is not possible (except for an interstellar mission for a rocket approaching from another star). In the Spaceflight Simulator, this is **not possible**, unless there are neighboring stars in a custom solar system pack.

## Technique

Gravity assists are possible because the spacecraft *steals* momentum from the celestial body in its motion around the celestial body it is orbiting. For this reason, gravity assists will always change the spacecraft speed relative to the celestial body around which the helping celestial body moves (gravity assists from the moon will change spacecraft speed relative to the Earth, and gravity assists from Venus will change spacecraft speed relative to the sun, but not relative to Venus).

### Main rules of gravity assists

Gravity assist can help increase or decrease the speed of a spacecraft, depending on the spacecraft's trajectory relative to the helping celestial body. To simplify the explanation, let's take the example of Mercury as a helping body, but what is true for Mercury and the sun also applies to other celestial bodies such as Venus and the sun, or the moon and the earth:

1. A gravity assist is always present **during the flyby** of a celestial body by a spacecraft; **the lower the spacecraft** gets to the celestial body, **the** **greater the gravity assist** will change the spacecraft speed (greater speed increase or speed decrease).
2. If the spacecraft trajectory **crosses** the line between Mercury and the sun, the gravity assist will **decrease** the spacecraft speed.
3. The spacecraft speed will increase if the spacecraft trajectory **does not cross** the line between Mercury and the sun.

Flybys are performed in the Spaceflight Simulator by using the "Navigate To" functionality (click on a celestial body and then on "Navigate To").

Once selected, the "Navigate To" makes a dotted trajectory appear, starting with a "Transfer Window" (or an "Escape" depending on the zoom level) and ending with an "Encounter". The "Transfer Window" is the point in the trajectory at which to begin the transfer, to speed up or slow down the spacecraft. "Encounter" is the point in the trajectory where the spacecraft will enter the navigation target. Once at the "Transfer Window" position, the delta v required to reach that target appears, and it is up to you to face the engines the right way and ignite them until the indicator says "0 m/s". Once this speed has been reached, immediately (or later in time) on the trajectory path, the trajectory within the celestial body sphere of influence will be displayed. It's time to tune your gravity assist!

As we said, depending on the flyby trajectory, the spacecraft can speed up or slow down, so extra care should be taken to tune this flyby path.

Here is an example of a Mercury flyby:
You can see in the picture above the position of Mercury and also the "Encounter" position, which is the position of Mercury when the spacecraft will enter its sphere of influence. If you zoom in on Mercury's current position (in the upper part of the screen), you may see this flyby trajectory (if no trajectory is displayed, but 0.0m/s is displayed for delta v, speed up time to get closer to the navigation target, and this trajectory will appear):

On this picture, the trajectory is below Mercury, but to know if it crosses or not the line between Mercury and the sun, to know if this gravity assist will speed up or slow down the spacecraft, we shall have a look at the previous picture, and the position of the "Encounter" point. This "encounter" point is on the bottom left part of the screen, so the sun is at the top right of it. This applies to the picture above. The sun is also on the top right of it, so this flyby won't make the spacecraft cross the line between mercury and the sun, and will therefore speed up the spacecraft.

Now let's change the spacecraft speed by performing a burn at a throttle of 0.1% with the engine facing either the moving directory, or the opposite (moving direction is shown with a white arrow when not in "Map" view). We will either see this trajectory going away from mercury or going closer to it. If we let the trajectory go closer, it will cross the planet, making a turn around the screen, to rise again above mercury on the other side, like in the picture below:
As we can see in the picture above, the spacecraft trajectory is above Mercury, and we know from the zoomed out view, with the position of the "Encounter" label, that the sun is in the top right corner. Therefore, this trajectory will cross the line between Mercury and the sun, and therefore create a slow down of the spacecraft by gravity assist.

Now we have described the main rules of gravity assist effects. Let's describe how to use it in practice in the Spaceflight Simulator.

### Practical use of gravity assists

As explained at the beginning of this page, gravity assist is useful for reaching Mercury by performing a flyby of Venus. But if you try gravity assist with the explanation above only, you may think that it is useless, because meeting the "Navigate To" displayed speed for Venus may consume more fuel than the one for mercury.

Because of this, using gravity assist requires some care in order to provide actual benefits in practice.

#### Choose your navigation starting point wisely.

If you try to "navigate to" from Earth orbit to Mercury, you may be surprised because, depending on the position of Earth and Mercury, the delta-v can be from above 2000m/s down to 1100m/s.
As we can see in the picture above, depending on the relative position of the spacecraft and the navigation target, the required delta-v can be very different, and therefore exceed or not the spacecraft capability.

In real-world missions, flight dynamics experts solve a highly complex mathematical problem to determine the best possible trajectory, such as the one shown at the top of this page, which depicts the path of the MESSENGER space probe from Earth to Mercury. In the Spaceflight Simulator, such computations are, of course, impossible, but another parameter, available in large quantities, makes gravity assist usable: time.

Gravity assists are only worthwhile when requiring delta v consumes less fuel than the one for a direct trajectory to the final destination. As we have seen above, depending on spacecraft and navigation target relative position, delta-V may be very different, but this difference is cyclic, as we can see in the example below:

The picture above shows the Delta-V cycling over each orbit around the sun from 75.5m/s back to 73.8m/s after reaching a maximum of 2173m/s. As we can see, the maximum is reached at the next orbit after the minimum, and the Delta-V decreases from this point down to a new minimum. Thus, it will be possible to consume as much time as necessary (six and a half years in the example above, based on the position of the earth in each picture) to get a delta-V which is small enough to make the gravity assist worth using.

Nevertheless, be careful to always check the Delta-V at its minimum during the orbit around the sun. The pictures above have always been taken at their minimum, but during the entire orbit around the sun, other much higher Delta-V are proposed, as we can see in the picture below:

Typically, an acceptable delta-V has an absolute value lower than 100 m/s, unless you have checked the entire cycle of Delta-V and the minimum is higher (this is the case for the last gravity assist before Mercury orbit insertion, with a Delta-V of 145 m/s).

#### Steps from one planet to another with gravity assists

When a rocket goes from one planet to another, the rocket wants to either get closer to the sun (from Earth to Venus, for example), or farther away (from Earth to Jupiter).

In both cases, the first thing to do is to speed up the spacecraft using its engines to raise its apogee outside the sphere of influence of the celestial body it is orbiting. Once there, the spacecraft does not orbit this celestial body but the sun, and gravity assists can be used (except if you want to use the gravity assist of a satellite, like the moon, to escape the earth's sphere of influence, in which case a simple flyby of the satellite on the correct side will bring it more speed).

If you want to go from one celestial body orbit to another, this always requires two main speed changes: the first one to enter the trajectory for the other celestial body, and the second to enter the other celestial body orbit. This corresponds to the use of the Hohmann transfer orbit. Each of these speed changes will act on either the aphelion or the perihelion of the spacecraft's orbit. For example, if you want to go from Earth to Mercury, after leaving the Earth, the rocket first needs to slow down to decrease the perihelion down to Mercury orbit, and once this perihelion is in Mercury orbit, it will need to decrease its speed again to lower its aphelion down to Mercury orbit. Note that a global rule in space flight dynamics is that, considering a celestial body and a spacecraft, the spacecraft will always return to the position it had at the time of its previous engine burn. That's why decreasing the height of a circular orbit requires the two engine burns of a Hohmann transfer orbit. If your rocket wants to reach a celestial body to travel further than the rocket from the sun, you'll need two speed increases instead of two speed decreases.

This maneuver requires you to first slow down your spacecraft each time it passes its aphelion, and when its perihelion is at the target distance from the sun, to slow it down again each time it passes its perihelion (this applies if you go from Earth to Mercury, but for the other direction, from Earth to Jupiter, you would first speed up at the perihelion, and then speed up at the aphelion).

To manage such speed changes at the right time when orbiting the sun:

1. Perform a burn to make the spacecraft orbit into tangency with the celestial body's orbit (the part of the spacecraft orbit inside the celestial body sphere of influence shall be less than 90 degrees of its orbit around the sun).
2. Then, the only part of the spacecraft orbit which can have an encounter with the celestial body used for gravity assist is this tangent part, so activate "Navigate To", and look for the part of the spacecraft orbit where the "Transfer Window" always appears (it should appear approximately at the same place of the orbit).
3. By speeding up time, check the displayed delta-V each time the spacecraft passes this "Transfer Window" part of the orbit (slow down time when getting close to this part of the orbit, because it may be quite narrow and could be easily missed). You should see that delta-V increases, and after some orbits around the sun, decreases. For example, by looking at these delta-V, you should be able to find out which is the relative position of the celestial body and the spacecraft which provides the minimum delta-V. For example, the delta-V could start at +140m/s, rise up to +2000m/s, then disappear for some orbits around the sun, and then appear again at -2000m/s to end at -140m/s before being again +140m/s. In such a case, perform the burn as soon as you see +140m/s again. Once the burn ends, you should get 0.0m/s.
4. When the spacecraft approaches the celestial body with a displayed delta-V close to 0.0m/s, have a look at the flyby trajectory to check if it passes the celestial body on the right side to get the required speed change (increase if you want to raise the aphelion of perihelion, or decrease otherwise). Try to perform the flyby as close as possible to the celestial body, but take care to not enter its atmosphere (if it has one), or take a margin for rough terrain if you perform a flyby of a celestial body without an atmosphere (don't hesitate to use Quick Save to be able to try again with a different trajectory if something unexpected appends, and always perform this flyby burn height correction at 0.1% engine throttle and with fast click on/click off in order to be accurate enough).
5. After the flyby, wait for the spacecraft to exit the celestial body sphere of influence to check which is the new orbit around the sun. If everything went as expected, only the aphelion or the perihelion should have changed significantly (more than 5%).
6. Repeat this procedure from step 3 to further change aphelion or perihelion until a targeted celestial body orbit is reached, or the orbit matches that of the celestial body (see Hohmann transfer orbit cited above to understand the aphelion/perihelion change steps to travel from one circular orbit to another).

When gaining experience, you should be able to almost immediately see where the best transfer should be, and only activate the "Navigate To" feature when getting close to this optimal position.

You'll see that gravity assist, when correctly used, is able to save a lot of fuel.

## See also

* Advanced Orbital Mechanics
* Aerobraking
* Aerocapture
* Deep Space Maneuvers
* Oberth Effect
* Trajectory Correction Maneuvers