moon landing calculations

88 0 obj endobj 25 0 obj to work on calculating the trajectory for America’s first space trip with Alan Shepherd’s 1961 mission, an early step toward a moon landing. endobj Landmark Tracking Data 1-10 9. >> 191 0 obj << 45 0 obj endobj endobj It doesn't! << /S /GoTo /D (subsection.7.2) >> 8 0 obj endstream %�� 20 0 obj Neil DeGrasse Tyson Shuts Down Moon Landing Hoax Theory With Simple Calculation. /Parent 156 0 R Internally, however, the computer’s software used SI units for all powered-flight navigation and guidance calculations, and values such as altitude and altitude rate were only converted to imperial units when they needed to be shown on the computer’s display. << /S /GoTo /D (subsection.7.3) >> The Apollo Guidance Computer (AGC) was one of the first computers to use integrated circuits. Pictures relate to moon landing footage. 4 0 obj Mar 27, 2017 Domagoj Valjak. x��]s�8��+�+\��}\�M��4�x��3%6u�b��N��WX��$�Ʊ3��M�v��WB�;Թ8��H� �3�꘿B)��t��"{Ƚ��%NV�Q�|��F�Y9 (Minimum Time Problem Formulation) 9 0 obj 100 0 obj Imperial generally has more than one unit for a given quantity, so before any calculation can be done, a choice of units has to be made (working with miles, yards, feet and inches at the same time is not even a consideration here). (Project Scope) To put that into more concrete terms, the latest phones typically have 4GB of RAM. endobj The speed of a crash landing on its surface is typically between 70 and 100% of the escape velocity of the target moon, and thus this is the total velocity which must be shed from the target moon's gravitational attraction for a soft landing to occur. Therefore, using SI units, the above equation can be simplified as: A force of 1 newton on a mass of 1 kilogram produces an acceleration of 1 metre per second squared. A slug is defined as the mass that is accelerated by 1 ft/s2 when a force of 1 pound (lbf) is exerted on it. In contrast to SI, the use of imperial units is cumbersome and confusing. (Problem Formulation) (`Deflection' Problem Formulation) 148 0 obj << (5km Parking Orbit) << /S /GoTo /D (section.8) >> This picture was taken by Neil Armstrong prior to the moon landing. Pictures that can be put into sequence order for the moon landing. She would retire from NASA in 1986. For mass there is the slug, and for force there is the poundal. .k�6�ԕB3��V3o��Β �~�.X�OL�m�ct:�� \}��CY3�y�Ԓ��,y��7�f��}�>?��`�E^��u�y��K��a7��'2�f�qG��$��EAfˇE�� #�|U��q�}��)Q�f�jy�4��;��[t�ۆ�b�ּ*$y��Ǝ. Using the Newtonian Formula, the listed gravitational constant and the accepted masses, and distances of Sun, Earth & Moon, I found that during New Moon, the Sun's attraction for the Moon Is almost 3 times that of the Earth. The Apollo 11 Saturn V rocket on its journey to the Moon in 1969. (The Ascent Problem) The Apollo Guidance Computer is a good example of this. The Apollo 11 computer had a processor – an electronic circui… endobj endobj The computer display readouts were in units of feet, feet per second, and nautical miles – units that the Apollo astronauts, who had mostly trained as jet pilots, would have been accustomed to using. Translunar Coast Activities a. Cislunar Navigation 3-7, 3-17 b. << /S /GoTo /D (subsection.7.5) >> CSM Maneuver Update Pads 2-2 3. 3. moon landing pictures. endobj endobj The journey begins with launch of the Saturn V from Earth (shown on the left). 73 0 obj Plotting the path from a launch pad on Earth to a landing site on the moon — and back again — was made possible in the 1960s by using what we know of the mechanics of the two bodies. Luna 9, the first spacecraft to perform a soft landing on the Moon, used a 3 day 7 hour transfer2. (The Abort Problem) endobj One pound-force is defined as the force due to gravity acting on a mass of one pound at sea level on Earth. To this end, the Lunar Excursion Module (LEM) was designed to carry astronauts to and from the lunar surface. Apollo 11 used a 72 hour (3.0 day) transfer5. endobj 101 0 obj 77 0 obj Flight Plan Notes 1-13 SECTION II - UPDATE FORMS 1. >> endobj (`Hop' Results) << /S /GoTo /D [118 0 R /Fit] >> Here h0 is the initial height, v0 is the initial velocity, mass is the mass of the lander without fuel, fuel is the initial fuel, g is acceleration due to gravity, k is the relative velocity of the exhaust gases, and is the rate of change of the mass by burning. All four conspiracies would be uncovered in less than four years, according to Grimes’ calculations. Using simple calculations, he confirmed that the Apollo 11 mission really reached the Moon. The Moon Landing definitely started off as a predominantly foreign affair and a result of Superpower tension. endobj 85 0 obj endobj fantastic! They say the computers on board the Apollo spacecraft were not even as powerful as your smartphone. 92 0 obj Technology is developing faster than ever before, and with the emergence of the newest generation of smartphones and the state-of-the-art microprocessors, everyone can have a supercomputer in their pocket. endobj �ٝ�Y!�?q-ٳ�lt�Џ�а��4�+47��0�*k�߭{�Dx��&�a;�u If we, today, said - "Let us build another Saturn V rocket and Apollo CSM/LEM and go to the moon!" Conventionally feet, pounds and seconds would be used. Plotting the path from a launch pad on Earth to a landing site on the moon — and back again — was made possible in the 1960s by using what we know of the mechanics of the two bodies. endobj Using SI units, calculations involving Newton’s second law are straight forward. 28 0 obj A Rare Look at NASA Calculations Before Computers. xڝVMs7��W��Ռ�%�ܯ��8cO܉nI��]-.7��}��%ם�� { $�vL��~\H� endobj 49 0 obj 60 0 obj endobj Lunar Landing Site Data 1-10 8. NASA’s mathematicians used Newton’s laws of motion in their space flight calculations. Moon Phase Calendar – Calculate moon phases for any year. %PDF-1.5 Your moon sign is just as important as your sun sign because it is considered to be a reflection of your personality and how you are likely to… The computer which landed Apollo 11 on the Moon was about as powerful as a contemporary pocket calculator. 109 0 obj 32 0 obj The 50th anniversary of the moon landing offers a chance to reflect on Apollo space mission, as well as the funding that made it happen. stream /Contents 146 0 R (The Descent Problem) Pictures are quite blurry. 72 0 obj << /S /GoTo /D (subsection.6.1) >> 41 0 obj Therefore, once every month the Moon, obeying the stronger force, should cease orbiting the Earth and head toward the Sun. << /S /GoTo /D (subsection.7.9) >> 2. endobj 89 0 obj MoonCalc shows the motion of the Moon and Moon phase for a particular day at a particular location.. You can see the moon positions for moon rising, selected time and Moonset.The thin yellow-colored curve shows the trajectory of the moon. endobj Event Time Announcer – Show local times worldwide for your event. /Filter /FlateDecode Although the American victory was insignificant in the Cold War, it was a huge propaganda victory and was a victory for capitalism and democracy. For a single, rational measurement system. endobj << /S /GoTo /D (section.6) >> A GERMAN moon mission is set to finally demolish – or prove – claims that the American Apollo moon landings were a HOAX. << /S /GoTo /D (subsection.5.4) >> /D [118 0 R /XYZ 54 700.075 null] For physics calculations, their use has to be explicitly stated as pound-force (lbf) and pound-mass (lbm). The Apollo Moon Landings: How They Worked (Infographic) Diagrams and NASA artwork show how Apollo astronauts flew to the moon. /Type /Page << /S /GoTo /D (subsection.7.6) >> The trip to the Moon and the landing are depicted on the trajectory at the bottom of the graphic. e.g. This can be expressed in the following equation: In the International System of Units (SI), the newton (symbol N) is the unit of force. According to … The Apollo missions and subsequent moon landings have been at the center of controversy and conspiracy for years. /ProcSet [ /PDF /Text ] 113 0 obj These are not easy calculations. TLI-T&D 3-3, 3-4 3. (Gauss Pseudospectral Method) 44 0 obj >> endobj << /S /GoTo /D (subsection.5.5) >> u|&ShG��T��w�07M�ԜHt?�{�u��jd��ޞ�:0F�P��x��~��m$��T�ڏ/w̯01!��΅��Y�W��'��h8� ��i�ܨ#��>�� U3"�x&��B={��x��T�P�C��A��s�x-.ێ&�4/�"�mn^�Q1Js[{M�fab?��f��. In what amounts to an admission that imperial units are unfit for purpose, there is an alternative approach that involves defining novel units for either mass or force, such that the proportionality constant k is equal to one. endobj endobj Tweet. 65 0 obj (`Two-Staged' Results) Lunar Prospector6 flew a 105 hour (4.375 day) transfer. ('Hop' Problem Formulation) endobj (Apollo Flight Plan) 69 0 obj >> endobj (Results) Day and Night World Map – See which parts of the Earth are currently illuminated by the Sun. G�5 Efforts related to the Apollo project cost the government about $25.8 billion between 1960 and 1973, according to data collected by space nonprofit The Planetary Society . (Apollo Flight Plan) With regard to processing speed, the TI-73 was 140 times faster than the Apollo computer and the TI-84 was almost 350 times faster. /Length 1067 112 0 obj (Apollo Overview) << /S /GoTo /D (subsection.7.4) >> (Solution Overview) SI units were used for arguably the most critical part of the missions – the calculations that were carried out by the Lunar Module’s onboard Apollo Guidance Computer (AGC) during the computer-controlled phases of the spacecraft’s descent to the surface of the Moon, and for the journey of the Ascent stage of the craft during its return to lunar orbit, where it would rendezvous with the Command and Service Module (CSM). endobj endobj endobj << /S /GoTo /D (appendix.B) >> To demonstrate why using SI units for such calculations is simpler and clearer than using imperial units, it is a useful exercise to take Newton’s second law as an example to compare the differences. endobj 105 0 obj Program for Soft Landing on the Moon. 33 0 obj << /S /GoTo /D (section.5) >> These are not easy calculations. 117 0 obj endobj Using the first of these methods, to calculate the force required to impart a certain acceleration to a spacecraft, it would be necessary to know the spacecraft’s mass in slugs, a unit that has never been in general use**. endobj 93 0 obj /Filter /FlateDecode Without disagreeing with what’s already been said, there was some disagreement early on, mostly because the German scientists that made up much of the core of the expertise of the early US space program felt more comfortable using metric units. ��)��@ṫ�uڬMܬ�ng�5�0k��:+o߻�/r �`9��w{�Zs٘axBM}�ˁ��H]�K�h�'ɀ{�/��E�21�l�5�{ӏ�8�i%0�{gp��Gة�)�{O�=��Ͱ�j�etiNf8� A poundal is defined as the force necessary to accelerate a mass of 1 pound (lbm) at 1 ft/s2. endobj LM Maneuver Update Pads 2-27 SECTION III - DETAILED TIMELINE l. Launch Phase 3-1 2. (Visualization) But she was most famous for her work on the 1962 orbital mission by John Glenn. The closer the moon in the middle, the higher the moon … 36 0 obj endobj 84 0 obj endobj 29 0 obj 16 0 obj endobj endobj Katherine’s incredible achievement made it possible for other women and people of colour to follow in her footsteps, breaking down barriers of race and gender. endobj As is the case in the UK with road signage, the use of metric units in the USA is often hidden from public view. For Newton’s second law, if units of pounds and feet are used in the equation F = k m a, the proportionality constant k does not equal one. (`Two-Staged' Problem Formulation) 145 0 obj << Back in the heyday of NASA and the space race, electronic calculators had yet to be invented. Neil Armstrong became the first person to step onto the lunar surface on July 21, 1969, at 02:56 UTC; Buzz Aldrin joined him 19 minutes later. Johnson would go on to work on the Apollo program, too, including performing trajectory calculations that assisted the 1969 moon landing. The iPhone also has up to 512GB of ROM memory. Similarly, fruit and vegetables have never been authorised for sale by the slug (any requirement for the word slugs to appear on the contents label of a packet of lettuce would probably have made that a non-starter). (Results) What are moon signs in astrology? An organisation called PTScientists (Part Time Scientists) will … This meant that everything had to be done by hand, including all of the calculations necessary to send a man to the moon. Creola Katherine Johnson (née Coleman; August 26, 1918 – February 24, 2020) was an American mathematician whose calculations of orbital mechanics as a NASA employee were critical to the success of the first and subsequent U.S. crewed spaceflights. This … endobj endobj a year ago. 53 0 obj endobj It’s an iconic image for the citizens of … During her 35-year career at NASA and its predecessor, she earned a reputation for mastering complex manual calculations and helped pioneer … Creative Commons "Sharealike" Reviews. 'Hidden Figures': How Black Women Did The Math That Put Men On The Moon Back in the days of the space race, "computers" were people — often women — who performed vital calculations.