Gravity Turn
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A gravity turn or zero-lift turn is a maneuver used in launching a spacecraft into, or descending from, an
orbit In celestial mechanics, an orbit (also known as orbital revolution) is the curved trajectory of an object such as the trajectory of a planet around a star, or of a natural satellite around a planet, or of an artificial satellite around an ...
around a celestial body such as a
planet A planet is a large, Hydrostatic equilibrium, rounded Astronomical object, astronomical body that is generally required to be in orbit around a star, stellar remnant, or brown dwarf, and is not one itself. The Solar System has eight planets b ...
or a
moon The Moon is Earth's only natural satellite. It Orbit of the Moon, orbits around Earth at Lunar distance, an average distance of (; about 30 times Earth diameter, Earth's diameter). The Moon rotation, rotates, with a rotation period (lunar ...
. It is a
trajectory optimization Trajectory optimization is the process of designing a trajectory that minimizes (or maximizes) some measure of performance while satisfying a set of constraints. Generally speaking, trajectory optimization is a technique for computing an open-loop ...
that uses
gravity In physics, gravity (), also known as gravitation or a gravitational interaction, is a fundamental interaction, a mutual attraction between all massive particles. On Earth, gravity takes a slightly different meaning: the observed force b ...
solely through the vehicle's own
thrust Thrust is a reaction force described quantitatively by Newton's third law. When a system expels or accelerates mass in one direction, the accelerated mass will cause a force of equal magnitude but opposite direction to be applied to that ...
. First, the thrust is not used to change the spacecraft's direction, so more of it is used to accelerate the vehicle into orbit. Second, and more importantly, during the initial ascent phase the vehicle can maintain low or even zero
angle of attack In fluid dynamics, angle of attack (AOA, α, or \alpha) is the angle between a Airfoil#Airfoil terminology, reference line on a body (often the chord (aircraft), chord line of an airfoil) and the vector (geometry), vector representing the relat ...
. This minimizes transverse aerodynamic stress on the launch vehicle, allowing for a lighter launch vehicle. The term gravity turn can also refer to the use of a planet's gravity to change a spacecraft's direction in situations other than entering or leaving the orbit. When used in this context, it is similar to a
gravitational slingshot A gravity assist, gravity assist maneuver, swing-by, or generally a gravitational slingshot in orbital mechanics, is a type of spaceflight flyby which makes use of the relative movement (e.g. orbit around the Sun) and gravity of a planet o ...
; the difference is that a gravitational slingshot often increases or decreases spacecraft velocity and changes direction, while the gravity turn only changes direction.


Launch procedure


Vertical climb

A gravity turn is commonly used with rocket powered vehicles that launch vertically, like the
Space Shuttle The Space Shuttle is a retired, partially reusable launch system, reusable low Earth orbital spacecraft system operated from 1981 to 2011 by the U.S. National Aeronautics and Space Administration (NASA) as part of the Space Shuttle program. ...
. The rocket begins by flying straight up, gaining both vertical speed and altitude. During this portion of the launch, gravity acts directly against the thrust of the rocket, lowering its vertical acceleration. Losses associated with this slowing are known as
gravity drag In astrodynamics and rocketry, gravity loss is a measure of the loss in the net performance of a rocket while it is thrusting in a gravitational field. In other words, it is the cost of having to hold the rocket up in a gravity field. Gravity los ...
, and can be minimized by executing the next phase of the launch, the pitchover maneuver or roll program, as soon as possible. The pitchover should also be carried out while the vertical velocity is small to avoid large aerodynamic loads on the vehicle during the maneuver. The pitchover maneuver consists of the rocket gimbaling its engine slightly to direct some of its thrust to one side. This force creates a net torque on the ship, turning it so that it no longer points vertically. The pitchover angle varies with the launch vehicle and is included in the rocket's
inertial guidance system An inertial navigation system (INS; also inertial guidance system, inertial instrument) is a navigation device that uses motion sensors (accelerometers), rotation sensors ( gyroscopes) and a computer to continuously calculate by dead reckoning ...
. For some vehicles it is only a few degrees, while other vehicles use relatively large angles (a few tens of degrees). After the pitchover is complete, the engines are reset to point straight down the axis of the rocket again. This small steering maneuver is the only time during an ideal gravity turn ascent that thrust must be used for purposes of steering. The pitchover maneuver serves two purposes. First, it turns the rocket slightly so that its flight path is no longer vertical, and second, it places the rocket on the correct heading for its ascent to orbit. After the pitchover, the rocket's angle of attack is adjusted to zero for the remainder of its climb to orbit. This zeroing of the angle of attack reduces lateral aerodynamic loads and produces negligible lift force during the ascent.


Downrange acceleration

After the pitchover, the rocket's flight path is no longer completely vertical, so gravity acts to turn the flight path back towards the ground. If the rocket were not producing thrust, the flight path would be a simple
ellipse In mathematics, an ellipse is a plane curve surrounding two focus (geometry), focal points, such that for all points on the curve, the sum of the two distances to the focal points is a constant. It generalizes a circle, which is the special ty ...
like a thrown ball (it is a common mistake to think it is a parabola: this is only true if it is assumed that the Earth is flat, and gravity always points in the same direction, which is a good approximation for short distances), leveling off and then falling back to the ground. The rocket is producing thrust though, and rather than leveling off and then descending again, by the time the rocket levels off, it has gained sufficient altitude and velocity to place it in a stable orbit. If the rocket is a
multi-stage A multistage rocket or step rocket is a launch vehicle that uses two or more rocket ''stages'', each of which contains its own engines and propellant. A ''tandem'' or ''serial'' stage is mounted on top of another stage; a ''parallel'' stage is ...
system where stages fire sequentially, the rocket's ascent burn may not be continuous. Some time must be allowed for stage separation and engine ignition between each successive stage, but some rocket designs call for extra free-flight time between stages. This is particularly useful in very high thrust rockets, where if the engines were fired continuously, the rocket would run out of fuel before leveling off and reaching a stable orbit above the atmosphere. The technique is also useful when launching from a planet with a thick atmosphere, such as the Earth. Because gravity turns the flight path during free flight, the rocket can use a smaller initial pitchover angle, giving it higher vertical velocity, and taking it out of the atmosphere more quickly. This reduces both aerodynamic drag as well as aerodynamic stress during launch. Then later during the flight the rocket coasts between stage firings, allowing it to level off above the atmosphere, so when the engine fires again, at zero angle of attack, the thrust accelerates the ship horizontally, inserting it into orbit.


Descent and landing procedure

Because heat shields and parachutes cannot be used to land on an airless body such as the
Moon The Moon is Earth's only natural satellite. It Orbit of the Moon, orbits around Earth at Lunar distance, an average distance of (; about 30 times Earth diameter, Earth's diameter). The Moon rotation, rotates, with a rotation period (lunar ...
, a powered descent with a gravity turn is a good alternative. The
Apollo Lunar Module The Apollo Lunar Module (LM ), originally designated the Lunar Excursion Module (LEM), was the lunar lander spacecraft that was flown between lunar orbit and the Moon's surface during the United States' Apollo program. It was the first crewed sp ...
used a slightly modified gravity turn to land from lunar orbit. This was essentially a launch in reverse except that a landing spacecraft is lightest at the surface while a spacecraft being launched is heaviest at the surface. A computer program called Lander that simulated gravity turn landings applied this concept by simulating a gravity turn launch with a negative mass flow rate, i.e. the propellant tanks filled during the rocket burn. The idea of using a gravity turn maneuver to land a vehicle was originally developed for the Lunar Surveyor landings, although Surveyor made a direct approach to the surface without first going into lunar orbit.


Deorbit and entry

The vehicle begins by orienting for a retrograde burn to reduce its orbital velocity, lowering its point of
periapsis An apsis (; ) is the farthest or nearest point in the orbit of a planetary body about its primary body. The line of apsides (also called apse line, or major axis of the orbit) is the line connecting the two extreme values. Apsides perta ...
to near the surface of the body to be landed on. If the craft is landing on a planet with an atmosphere such as
Mars Mars is the fourth planet from the Sun. It is also known as the "Red Planet", because of its orange-red appearance. Mars is a desert-like rocky planet with a tenuous carbon dioxide () atmosphere. At the average surface level the atmosph ...
the deorbit burn will only lower periapsis into the upper layers of the atmosphere, rather than just above the surface as on an airless body. After the deorbit burn is complete the vehicle can either coast until it is nearer to its landing site or continue firing its engine while maintaining zero angle of attack. For a planet with an atmosphere the coast portion of the trip includes entry through the atmosphere as well. After the coast and possible entry, the vehicle jettisons any no longer necessary
heat shield In engineering, a heat shield is a component designed to protect an object or a human operator from being burnt or overheated by dissipating, reflecting, and/or absorbing heat. The term is most often used in reference to exhaust heat management a ...
s and/or parachutes in preparation for the final landing burn. If the atmosphere is thick enough it can be used to slow the vehicle a considerable amount, thus saving on fuel. In this case a gravity turn is not the optimal entry trajectory but it does allow for approximation of the true
delta-v Delta-''v'' (also known as "change in velocity"), symbolized as and pronounced , as used in spacecraft flight dynamics, is a measure of the impulse per unit of spacecraft mass that is needed to perform a maneuver such as launching from or l ...
required. In the case where there is no atmosphere however, the landing vehicle must provide the full delta-v necessary to land safely on the surface.


Landing

If it is not already properly oriented, the vehicle lines up its engines to fire directly opposite its current surface velocity vector, which at this point is either parallel to the ground or only slightly vertical, as shown to the left. The vehicle then fires its landing engine to slow down for landing. As the vehicle loses horizontal velocity the gravity of the body to be landed on will begin pulling the trajectory closer and closer to a vertical descent. In an ideal maneuver on a perfectly spherical body the vehicle could reach zero horizontal velocity, zero vertical velocity, and zero altitude all at the same moment, landing safely on the surface (if the body is not rotating; else the horizontal velocity shall be made equal to that of the body at the considered latitude). However, due to rocks and uneven surface terrain the vehicle usually picks up a few degrees of angle of attack near the end of the maneuver to zero its horizontal velocity just above the surface. This process is the mirror image of the pitch over maneuver used in the launch procedure and allows the vehicle to hover straight down, landing gently on the surface.


Guidance and control

The steering of a rocket's course during its flight is divided into two separate components; control, the ability to point the rocket in a desired direction, and
guidance Guidance may refer to: Arts and media * Guidance (album), ''Guidance'' (album), by American instrumental rock band Russian Circles * Guidance (film), ''Guidance'' (film), a Canadian comedy film released in 2014 * Guidance (web series), ''Guidance ...
, the determination of what direction a rocket should be pointed to reach a given target. The desired target can either be a location on the ground, as in the case of a
ballistic missile A ballistic missile is a type of missile that uses projectile motion to deliver warheads on a target. These weapons are powered only during relatively brief periods—most of the flight is unpowered. Short-range ballistic missiles (SRBM) typic ...
, or a particular orbit, as in the case of a launch vehicle.


Launch

The gravity turn trajectory is most commonly used during early ascent. The guidance program is a precalculated lookup table of pitch vs time. Control is done with engine gimballing and/or aerodynamic control surfaces. The pitch program maintains a zero angle of attack (the definition of a gravity turn) until the vacuum of space is reached, thus minimizing lateral aerodynamic loads on the vehicle. (Excessive aerodynamic loads can quickly destroy the vehicle.) Although the preprogrammed pitch schedule is adequate for some applications, an adaptive
inertial guidance system An inertial navigation system (INS; also inertial guidance system, inertial instrument) is a navigation device that uses motion sensors (accelerometers), rotation sensors ( gyroscopes) and a computer to continuously calculate by dead reckoning ...
that determines location, orientation and velocity with
accelerometers An accelerometer is a device that measures the proper acceleration of an object. Proper acceleration is the acceleration (the rate of change of velocity) of the object relative to an observer who is in free fall (that is, relative to an inertia ...
and
gyroscope A gyroscope (from Ancient Greek γῦρος ''gŷros'', "round" and σκοπέω ''skopéō'', "to look") is a device used for measuring or maintaining Orientation (geometry), orientation and angular velocity. It is a spinning wheel or disc in ...
s, is almost always employed on modern rockets. The
British British may refer to: Peoples, culture, and language * British people, nationals or natives of the United Kingdom, British Overseas Territories and Crown Dependencies. * British national identity, the characteristics of British people and culture ...
satellite launcher
Black Arrow Black Arrow, officially capitalised BLACK ARROW,Gibson and Buttler 2007, . was a British satellite expendable launch system. Black Arrow originated from studies by the Royal Aircraft Establishment for carrier rockets based on the earlier Blac ...
was an example of a rocket that flew a preprogrammed pitch schedule, making no attempt to correct for errors in its trajectory, while the Apollo-Saturn rockets used "closed loop" inertial guidance after the gravity turn through the atmosphere. The initial pitch program is an
open-loop A control loop is the fundamental building block of control systems in general and industrial control systems in particular. It consists of the process sensor, the controller function, and the final control element (FCE) which controls the process ...
system subject to errors from winds, thrust variations, etc. To maintain zero angle of attack during atmospheric flight, these errors are not corrected until reaching space. Then a more sophisticated closed-loop guidance program can take over to correct trajectory deviations and attain the desired orbit. In the Apollo missions, the transition to closed-loop guidance took place early in second stage flight after maintaining a fixed inertial attitude while jettisoning the first stage and interstage ring. Because the upper stages of a rocket operate in a near vacuum, fins are ineffective. Steering relies entirely on engine gimballing and a
reaction control system A reaction control system (RCS) is a spacecraft system that uses Thrusters (spacecraft), thrusters to provide Spacecraft attitude control, attitude control and translation (physics), translation. Alternatively, reaction wheels can be used for at ...
.


Landing

To serve as an example of how the gravity turn can be used for a powered landing, an Apollo type lander on an airless body will be assumed. The lander begins in a circular orbit docked to the command module. After separation from the command module the lander performs a retrograde burn to lower its periapsis to just above the surface. It then coasts to periapsis where the engine is restarted to perform the gravity turn descent. It has been shown that in this situation guidance can be achieved by maintaining a constant angle between the thrust vector and the line of sight to the orbiting command module. This simple guidance algorithm builds on a previous study which investigated the use of various visual guidance cues including the uprange horizon, the downrange horizon, the desired landing site, and the orbiting command module. The study concluded that using the command module provides the best visual reference, as it maintains a near constant visual separation from an ideal gravity turn until the landing is almost complete. Because the vehicle is landing in a vacuum, aerodynamic control surfaces are useless. Therefore, a system such as a gimballing main engine, a reaction control system, or possibly a
control moment gyroscope A control moment gyroscope (CMG) is an attitude control device generally used in spacecraft attitude control systems. A CMG consists of a spinning rotor and one or more motorized gimbals that tilt the rotor’s angular momentum. As the rotor til ...
must be used for attitude control.


Limitations

Although gravity turn trajectories use minimal steering thrust they are not always the most efficient possible launch or landing procedure. Several things can affect the gravity turn procedure making it less efficient or even impossible due to the design limitations of the launch vehicle. A brief summary of factors affecting the turn is given below. *
Atmosphere An atmosphere () is a layer of gases that envelop an astronomical object, held in place by the gravity of the object. A planet retains an atmosphere when the gravity is great and the temperature of the atmosphere is low. A stellar atmosph ...
— In order to minimize
gravity drag In astrodynamics and rocketry, gravity loss is a measure of the loss in the net performance of a rocket while it is thrusting in a gravitational field. In other words, it is the cost of having to hold the rocket up in a gravity field. Gravity los ...
the vehicle should begin gaining horizontal speed as soon as possible. On an airless body such as the Moon this presents no problem, however on a planet with a dense atmosphere this is not possible. A trade-off exists between flying higher before starting downrange acceleration, thus increasing gravity drag losses; or starting downrange acceleration earlier, reducing gravity drag but increasing the aerodynamic drag experienced during launch. * Maximum dynamic pressure — Another effect related to the planet's atmosphere is the maximum dynamic pressure exerted on the launch vehicle during the launch.
Dynamic pressure In fluid dynamics, dynamic pressure (denoted by or and sometimes called velocity pressure) is the quantity defined by:Clancy, L.J., ''Aerodynamics'', Section 3.5 :q = \frac\rho\, u^2 where (in SI units): * is the dynamic pressure in pascals ...
is related to both the atmospheric density and the vehicle's speed through the atmosphere. Just after liftoff the vehicle is gaining speed and increasing dynamic pressure faster than the reduction in atmospheric density can decrease the dynamic pressure. This causes the dynamic pressure exerted on the vehicle to increase until the two rates are equal. This is known as the point of maximum dynamic pressure (abbreviated " max Q"), and the launch vehicle must be built to withstand this amount of stress during launch. As before a trade off exists between gravity drag from flying higher first to avoid the thicker atmosphere when accelerating; or accelerating more at lower altitude, resulting in a heavier launch vehicle because of a higher maximum dynamic pressure experienced on launch. *Maximum engine
thrust Thrust is a reaction force described quantitatively by Newton's third law. When a system expels or accelerates mass in one direction, the accelerated mass will cause a force of equal magnitude but opposite direction to be applied to that ...
— The maximum thrust the rocket engine can produce affects several aspects of the gravity turn procedure. Firstly, before the pitch over maneuver the vehicle must be capable of not only overcoming the force of gravity but accelerating upwards. The more acceleration the vehicle has beyond the acceleration of gravity the quicker vertical speed can be obtained allowing for lower gravity drag in the initial launch phase. When the pitch over is executed the vehicle begins its downrange acceleration phase; engine thrust affects this phase as well. Higher thrust allows for a faster acceleration to orbital velocity as well. By reducing this time the rocket can level off sooner; further reducing gravity drag losses. Although higher thrust can make the launch more efficient, accelerating too much low in the atmosphere increases the maximum dynamic pressure. This can be alleviated by throttling the engines back during the beginning of downrange acceleration until the vehicle has climbed higher. However, with solid fuel rockets this may not be possible. *Maximum tolerable
payload Payload is the object or the entity that is being carried by an aircraft or launch vehicle. Sometimes payload also refers to the carrying capacity of an aircraft or launch vehicle, usually measured in terms of weight. Depending on the nature of t ...
acceleration — Another limitation related to engine thrust is the maximum acceleration that can be safely sustained by the crew and/or the payload. Near main engine cut off (MECO), when the launch vehicle has consumed most of its fuel, the vehicle will be much lighter than it was at launch. If the engines are still producing the same amount of thrust, the acceleration will grow as a result of the decreasing vehicle mass. If this acceleration is not kept in check by throttling back the engines, injury to the crew or damage to the payload could occur. This forces the vehicle to spend more time gaining horizontal velocity, increasing gravity drag.


Use in orbital redirection

For spacecraft missions where large changes in the direction of flight are necessary, direct propulsion by the spacecraft may not be feasible due to the large delta-v requirement. In these cases it may be possible to perform a flyby of a nearby planet or moon, using its gravitational attraction to alter the ship's direction of flight. Although this maneuver is very similar to the
gravitational slingshot A gravity assist, gravity assist maneuver, swing-by, or generally a gravitational slingshot in orbital mechanics, is a type of spaceflight flyby which makes use of the relative movement (e.g. orbit around the Sun) and gravity of a planet o ...
it differs in that a slingshot often implies a change in both speed and direction whereas the gravity turn only changes the direction of flight. A variant of this maneuver, the
free return trajectory In orbital mechanics, a free-return trajectory is a trajectory of a spacecraft traveling away from a primary body (for example, the Earth) where gravity due to a secondary body (for example, the Moon) causes the spacecraft to return to the primar ...
allows the spacecraft to depart from a planet, circle another planet once, and return to the starting planet using propulsion only during the initial departure burn. Although in theory it is possible to execute a perfect free return trajectory, in practice small correction burns are often necessary during the flight. Even though it does not require a burn for the return trip, other return trajectory types, such as an aerodynamic turn, can result in a lower total delta-v for the mission.


Use in spaceflight

Many spaceflight missions have utilized the gravity turn, either directly or in a modified form, to carry out their missions. What follows is a short list of various mission that have used this procedure. *
Surveyor program The Surveyor program was a NASA program that, from June 1966 through January 1968, sent seven robotic spacecraft to the surface of the Moon. Its primary goal was to demonstrate the feasibility of Soft landing (rocketry), soft landings on the Moo ...
— A precursor to the Apollo Program, the Surveyor Program's primary mission objective was to develop the ability to perform soft landings on the surface of the Moon, through the use of an automated descent and landing program built into the lander. Although the landing procedure can be classified as a gravity turn descent, it differs from the technique most commonly employed in that it was shot from the Earth directly to the lunar surface, rather than first orbiting the Moon as the Apollo landers did. Because of this the descent path was nearly vertical, although some "turning" was done by gravity during the landing. *
Apollo program The Apollo program, also known as Project Apollo, was the United States human spaceflight program led by NASA, which Moon landing, landed the first humans on the Moon in 1969. Apollo followed Project Mercury that put the first Americans in sp ...
— Launches of the
Saturn V The Saturn V is a retired American super heavy-lift launch vehicle developed by NASA under the Apollo program for human exploration of the Moon. The rocket was human-rated, had multistage rocket, three stages, and was powered by liquid-propel ...
rocket during the Apollo program were carried out using a gravity turn in order to minimize lateral stress on the rocket. At the other end of their journey, the lunar landers utilized a gravity turn landing and ascent from the Moon.


Mathematical description

The simplest case of the gravity turn trajectory is that which describes a point mass vehicle, in a uniform gravitational field, neglecting air resistance. The thrust force \vec is a vector whose magnitude is a function of time and whose direction can be varied at will. Under these assumptions the differential equation of motion is given by: :m \frac = \vec - mg \hat\;. Here \hat is a unit vector in the vertical direction and m is the instantaneous vehicle mass. By constraining the thrust vector to point parallel to the velocity and separating the equation of motion into components parallel to \vec and those perpendicular to \vec we arrive at the following system: \begin \dot &= g(n - \cos) \;,\\ v \dot &= g \sin\;. \\ \end Here the current thrust to weight ratio has been denoted by n = F/mg and the current angle between the velocity vector and the vertical by \beta = \arccos, where \vec_1 = \vec/v. This results in a coupled system of equations which can be integrated to obtain the trajectory. However, for all but the simplest case of constant n over the entire flight, the equations cannot be solved analytically and must be integrated numerically.


References

{{orbits Rocketry Spaceflight concepts