Liquid rocket booster
A liquid rocket booster (LRB) consists of liquid fuel and oxidiser as booster to give a Liquid-propellant rocket or a hybrid rocket an extra boost at take off. It is attached to the side of a rocket. In contrast to solid rocket booster it can be throttled.
A liquid rocket booster (LRB) uses liquid fuel and oxidiser to give a liquid-propellant or hybrid rocket an extra boost at take-off, and/or increase the total payload that can be carried. It is attached to the side of a rocket. Unlike solid rocket boosters, LRBs can be throttled down, and can be shut down safely in an emergency for additional escape options in human spaceflight.
For the Cold War era R-7 Semyorka missile, which later evolved into the Soyuz rocket, this concept was chosen because it allowed all of its many rocket engines to be ignited and checked for function while on the launch pad.
The Ariane 4 space launch vehicle could use two or four LRBs, the 42L, 44L, and 44LP configurations. As an example of the payload increase that boosters provide, the basic Ariane 40 model without boosters could launch around 2,175 kilograms into Geostationary transfer orbit, while the 44L configuration could launch 4,790 kg to the same orbit with four liquid boosters added.
Various LRBs were considered early in the Space shuttle development program and after the Challenger accident, but the Shuttle continued flying its Space Shuttle Solid Rocket Booster until retirement.
After the Space Shuttle retired, Pratt & Whitney Rocketdyne and Dynetics entered the "advanced booster competition" for NASA's next human rated vehicle, the Space Launch System (SLS), with a booster design known as "Pyrios", which would use two Rocketdyne F-1#F-1B booster engines derived from the Rocketdyne F-1 LOX/RP-1 engine that powered the first stage of the Saturn V vehicle in the Apollo program. In 2012, it was determined that if the dual-engined Pyrios booster was selected for the SLS Block II, the payload could be 150 metric tons (t) to Low Earth Orbit, 20 t more than the congressional minimum requirement of 130 t to LEO for SLS Block II. In 2013, it was reported that in comparison to the F-1 engine, the F-1B engine was to have improved efficiency, be more cost effective and have fewer engine parts. Each F-1B was to produce 1,800,000 lbf (8.0 MN) of thrust at sea level, an increase over the 1,550,000 lbf (6.9 MN) of thrust of the initial F-1 engine.
Many Chinese launch vehicles have been using liquid boosters. These include China's man-rated Long March 2F which uses four liquid rocket boosters each powered by a single YF-20B hypergolic rocket engine. The retired Long March 2E variant also used similar four liquid boosters. as did Long March 3B  and Long March 3C variants. China developed semi-cryogenic boosters for the Long March 7 and Long March 5, its newest series of launch vehicles as of 2017 .
Common Core Booster
The Common Core Booster (CCB) or Common Booster Core (CBC) was developed as new liquid fueled primary stages for the Atlas V rocket and the Delta IV rocket by the Evolved Expendable Launch Vehicle program. These could be used alone with possible strap-on solid rocket boosters or in a configuration of three CCBs tied together.
The planned Falcon Heavy EELV originally planned to utilize the same arrangement, with three Falcon 9 or 9R cores connected together with a propellant cross-feed system to allow feeding all 3 cores from the booster fuel tanks, and saving fuel in the main core until booster separation. As of 2016[update] this feature has been put on hold. Instead SpaceX intends to throttle down the center core shortly after lift off to conserve fuel, and throttle the center core back up upon booster separation.
-  astronautix.com
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