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Exercise: 1. Single stage rocket:  Before a rocket begins to burn fuel, the rocket has a mass of  m r,i =2.81×10 7 kg, of which the mass of the fuel is  m f,i =2.46×10 7 kg. The fuel is burned at a constant rate with total burn time is 510 s and ejected at a speed v e = 3000 m/s relative to the rocket. If the rocket starts from rest in empty space, what is the final speed of the rocket after all the fuel has been burned? What we know: initial rocket mass m r,i =2.81×10 7 kg initial mass of the fuel m f,i =2.46×10 7 kg t = 510 s v e  = 3000 m/s So, we can calculate the dry mass of the rocket m r,d =m r,i -m f,i =0.35×10 7 kg. The mass ratio is then R = m r,i  /m r,d =8.03. So, the final speed of the rocket is then: V r,f =Δv r =v e lnR=6250m/s. 2. Two-stage rocket:  Now, we have similar example, the same rocket as in the previous example, but the fuel will be burnt in two stages ejecting the fuel in each of the stages at the same relative speed (v e  = 3000 m/s).  In first stage, the a

The Apollo 8 Apollo 8 mission launched on December 21, 1968, and it was the second crewed spaceflight mission flown in the Apollo space program. The first mission, Apollo 7, stayed in Earth orbit. Apollo 8 mission was the first ever mission to leave the Earth's gravitational sphere, and to reach the Moon. The crew orbited the Moon ten times and returned home. It went without the landing. However, the mission was the first mission to see and take a photo of the far side of the Moon.  The mission consisted of three astronauts: Frank Borman, James Lovell, and William Anders.  Apollo 8 was the third flight and the first crewed launch of the Saturn V rocket.  Earthrise: Taken from Apollo 8; source: Wiki When building a rocket, it is a good thing to do staging. Staging basically means throwing away big, expensive parts of your rocket while the rest continues on the way up. The main advantage is not to carry dead weight.  When one has multiple powered stages, the question arises as to how

Tsiolkovsky rocket equation The Tsiolkovsky rocket equation, or the classical rocket equation, or ideal rocket equation is an equation that mathematically describes the relationship between the mass of a rocket including the fuel and the propellant being expelled to allow for the rocket to move.  The lower the weight, the easier it is to escape the Earth’s gravitational pull. There is an interesting thought. The fuel is also part of the rocket weight that is being transported, which means that you need some fuel to carry fuel. SpaceX Falcon Heavy. Source> wiki It is credited to Konstantin Tsiolkovsky, who independently derived it and published it in 1903, although it had been independently derived and published already by William Moore in 1810, and later published in a separate book in 1813. Robert Goddard also developed the equation independently in 1912, and Hermann Oberth derived it independently about 1920. Initially at time  t  = 0, the mass of the rocket, including fuel, is m

Merlin Engines Photo of nine Merlin 1D engines firing on Falcon 9 launch 2018; credit: SpaceX Merlin is a family of rocket engines developed by SpaceX. They are currently a part of the Falcon 9 and Falcon Heavy launch vehicles, and were formerly used on the Falcon 1. Merlin engines use RP-1 and liquid oxygen as rocket propellants in a gas-generator power cycle. The Merlin engine was originally designed for sea recovery and reuse, but since 2016 the entire Falcon 9 booster is recovered for reuse by landing vertically on a landing pad using one of its nine Merlin engines. Merlin 1D sea level and vacuum; source: https://everydayastronaut.com/ Engine Types The Merlin engine family includes several variants, each tailored for specific applications: Merlin 1A: The initial version of the engine, used in the early Falcon 1 rockets. Merlin 1C: An upgraded version with increased thrust and improved efficiency, used in later Falcon 1 and early Falcon 9 rockets. Merlin 1D: The current workhorse en

SpaceX Falcon 9 Falcon 9 is a partially reusable, human-rated, two-stage-to-orbit, medium-lift launch vehicle designed and manufactured in the United States by SpaceX. That says wikipedia. Let's go deeper into it.  Falcon 9 is a reusable, two-stage rocket designed and manufactured by SpaceX to transport of people and payloads into Earth orbit and hopefully beyond. Falcon 9 rocket is the first orbital class of reusable rocket that flies to ISS and other private programs. It helps to reduce to price and cost of the flight of the rocket, as it is used again for the next plan helping the space game open to broader context. The first Falcon 9 launch was on 4 June 2010, and the first commercial resupply mission to the International Space Station (ISS) was launched on 8 October 2012. In 2020, it became the first commercial rocket to launch humans to orbit to ISS.  The height of the Falcon 9 is 70 m and diameter is 3.7 m. Mass is 549,054 kg.  The rocket has two stages. The first (booster)

A low Earth orbit (LEO) is an orbit around Earth with a period of 128 minutes or less (making at least 11.25 orbits per day) and an eccentricity less than 0.25. Most of artificial objects are in LEO. LEO is at an altitude less than about one third of the Earth's radius, or about 2000 km.  No human spaceflight took a place beyond LEO except of the Apollo program, see  Apollo program  overview. LEO is the easiest orbit to get to and stay in.  Low Earth Orbit (LEO) and Geosynchronous Orbit (GEO)  The mean orbital velocity needed to maintain a stable LEO is about 7.8 km/s, which is 28,000 km/h.  This speed depends on the exact altitude of the orbit. For example, if we calculate the orbital speed for a circular orbit of 200 km, the orbital velocity is 7.79 km/s. For example, for a higher 1,500 km orbit the velocity is reduced to 7.12 km/s.  The pull of gravity in LEO is only slightly less than on the Earth's surface. This is because the distance to LEO from the Earth's surface i