Gravity drag
Encyclopedia
In astrodynamics
Astrodynamics
Orbital mechanics or astrodynamics is the application of ballistics and celestial mechanics to the practical problems concerning the motion of rockets and other spacecraft. The motion of these objects is usually calculated from Newton's laws of motion and Newton's law of universal gravitation. It...

and rocketry
Rocket
A rocket is a missile, spacecraft, aircraft or other vehicle which obtains thrust from a rocket engine. In all rockets, the exhaust is formed entirely from propellants carried within the rocket before use. Rocket engines work by action and reaction...

, gravity drag (or gravity losses) is a measure of the loss in the net performance of a rocket while it is thrusting in a gravitational field
Gravitational field
The gravitational field is a model used in physics to explain the existence of gravity. In its original concept, gravity was a force between point masses...

. In layman's terms, it is the cost of having to hold the rocket up in a gravity field.

It is the difference between on one hand the delta-v
Delta-v
In astrodynamics a Δv or delta-v is a scalar which takes units of speed. It is a measure of the amount of "effort" that is needed to change from one trajectory to another by making an orbital maneuver....

expended and on the other hand the theoretical delta-v for the actual change in speed and altitude, plus the delta-v for other losses such as air drag, that are experienced by a thrust
Thrust
Thrust is a reaction force described quantitatively by Newton's second and third laws. When a system expels or accelerates mass in one direction the accelerated mass will cause a force of equal magnitude but opposite direction on that system....

ing spacecraft
Spacecraft
A spacecraft or spaceship is a craft or machine designed for spaceflight. Spacecraft are used for a variety of purposes, including communications, earth observation, meteorology, navigation, planetary exploration and transportation of humans and cargo....

.

Gravity losses depend on the time over which thrust is applied as well the direction the thrust is applied in. Gravity losses as a proportion of delta-v are minimised if maximum thrust is applied for a short time, or if thrust is applied in a direction perpendicular to the local gravitational field. During the launch and ascent phase, however, thrust must be applied over a long period with a major component of thrust in the opposite direction to gravity, so gravity losses become significant. For example, to reach a speed of 7.8 km/s in low Earth orbit
Low Earth orbit
A low Earth orbit is generally defined as an orbit within the locus extending from the Earth’s surface up to an altitude of 2,000 km...

requires a delta-v of between 9 and 10 km/s. The additional 1.5 to 2 km/s delta-v is due to gravity losses and atmospheric drag.

## Example

Consider the simplified case of a vehicle with constant mass accelerating vertically upwards with a constant thrust per unit mass a in a gravitational field of strength g. The actual acceleration of the craft is a-g and it is using delta-v
Delta-v
In astrodynamics a Δv or delta-v is a scalar which takes units of speed. It is a measure of the amount of "effort" that is needed to change from one trajectory to another by making an orbital maneuver....

at a rate of a per unit time.

Over a time t the change in speed of the spacecraft is (a-g)t, whereas the delta-v expended is at. The gravity drag is the difference between these figures, which is gt. As a proportion of delta-v, the gravity drag is g/a.

A very large thrust over a very short time will achieve a desired speed increase with little gravity drag. On the other hand, if a is only slightly greater than g, the gravity drag is a large proportion of delta-v. Gravity drag can be described as the extra delta-v needed because of not being able to spend all the needed delta-v instantaneously.

This effect can be explained in two equivalent ways:
• The specific energy gained per unit delta-v is equal to the speed, so spend the delta-v when the rocket is going fast; in the case of being decelerated by gravity this means as soon as possible.
• It is wasteful to lift fuel unnecessarily: use it right away, and then the rocket does not have to lift it.

These effects apply whenever climbing to an orbit with higher specific orbital energy, such as during launch to Low Earth orbit
Low Earth orbit
A low Earth orbit is generally defined as an orbit within the locus extending from the Earth’s surface up to an altitude of 2,000 km...

(LEO) or from LEO to an escape orbit. This is a worst case
Worst Case
Worst Case is the 3rd book in the Michael Bennett series from James Patterson and Michael Ledwidge.-Plot summary:NYPD Detective Mike Bennett and his new partner FBI Special Agent Emily Parker are on the trail of Francis Mooney, a Manhattan trusts and estates lawyer with terminal lung cancer...

calculation - in practice, gravity drag during launch and ascent is less than the maximum value of gt because the launch trajectory does not remain vertical and the vehicle's mass is not constant, due to consumption of propellant and staging
Multistage rocket
A multistage rocket is a rocket that usestwo or more 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 attached alongside another stage. The result is effectively two or more rockets stacked on top of or...

.

## Vector considerations

Thrust is a vector quantity, and the direction of the thrust has a large impact on the size of gravity losses. For instance, gravity drag on a rocket of mass m would reduce a 3mg
G-force
The g-force associated with an object is its acceleration relative to free-fall. This acceleration experienced by an object is due to the vector sum of non-gravitational forces acting on an object free to move. The accelerations that are not produced by gravity are termed proper accelerations, and...

thrust directed upward to an acceleration of 2g. However, the same 3mg thrust could be directed at such an angle that it had a 1mg upward component, completely canceled by gravity, and a horizontal component of 2.8mg, achieving a 2.8g horizontal acceleration.

As orbital speeds are approached, vertical thrust can be reduced as centrifugal force (in the rotating frame of reference around the center of the Earth) counteracts a large proportion of the gravitation force on the rocket, and more of the thrust can be used to accelerate.

It's important to note that minimising gravity losses is not the only objective of a launching spacecraft. Rather, the objective is achieve the position/velocity combination for the desired orbit. For instance, the way to maximize acceleration is to thrust straight downward; however, thrusting downward is clearly not a viable course of action for a rocket intending to reach orbit.

On a planet with an atmosphere, the objective is further complicated by the need to achieve the necessary altitude
Altitude
Altitude or height is defined based on the context in which it is used . As a general definition, altitude is a distance measurement, usually in the vertical or "up" direction, between a reference datum and a point or object. The reference datum also often varies according to the context...

to escape the atmosphere, and to minimize the losses due to atmospheric drag during the launch itself. These facts sometimes inspire ideas to launch orbital rockets from high flying airplanes
Air launch to orbit
Air launch to orbit is the method of launching rocket launch vehicles at altitude from a horizontal-takeoff turbojet aircraft, either subsonic or supersonic...

, to minimize atmospheric drag, and in a nearly horizontal direction, to minimize gravity losses.

## External links

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