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The way I understood it (please correct me if I'm wrong), the easiest (least energy) way to reach the Moon it to put the spacecraft into a highly elliptic geocentric orbit whose apogee reaches the Moon. So I'm assuming that was also the (intended) trajectory of Luna 1. Luna 1 missed the Moon due to an error, but then entered a heliocentric orbit. Why would that happen? Shouldn't it continue orbiting the Earth?

Alternatively, Luna 1 was launched with an escape velocity instead (at least this source says so). Why would they launch it like that? Doesn't that require more energy?

And in general, did all Moon missions use an elliptic geocentric orbit or something else? For example, Apollo missions.

Edit: It says here that S-IVB also entered a heliocentric orbit after separating from CSM/LM. So TLI does indeed propel to escape velocity?

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According to the Wikipedia article on Luna 1, “The Soviet engineers did not trust automated systems for controlling the engine burns, so they communicated to the rocket via radio. The signal to stop firing the engine Block E stage was sent too late, and it imparted an extra 175 m/s to Luna 1. Consequently Luna 1 missed its target by 5,995 kilometers.”

According to Wikipedia, Luna 1 reached escape velocity, which is consistent with its ultimate Heliocentric orbit. https://www.thisdayinaviation.com/tag/luna-1. This NASA article implies escape velocity was achieved by the burn alone, unassisted by accidental Lunar Gravitational Assist. https://nssdc.gsfc.nasa.gov/nmc/spacecraft/display.action?id=1959-012A

Moon mission trajectories are an n-body problem. These trajectories are usually approached with a patched conic approximation (a series of 2-body problems). https://link.springer.com/article/10.1007/s40295-020-00229-w . This gives reasonable results for most missions. Missions involving Lagrange points are poorly analyzed by patched conic approximations.

The assumed Luna 1 mission was to impact on the lunar surface. This can be achieved by conic trajectories other than an ellipse. Since Luna 1 left Earth above escape velocity, its trajectory was not “an elliptic orbit whose apogee reaches the moon”.

To answer your other question, “Yes”, most Moon missions use an elliptic geocentric orbit as a first approximation for the transit from Earth to moon.

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  • $\begingroup$ Thanks! How about Apollo missions? That source I linked states that third stage S-IVB entered heliocentric orbit after separating. Why would they launch it like that? Doesn't that need more energy? $\endgroup$
    – kolufild
    Nov 6 '21 at 10:44
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    $\begingroup$ Luna-1 reached Moon orbit after 34 hours, compared to the 70 hours of the Apollo missions. That seems to imply that it clearly was on an escape trajectory even without the 175 m/s extra. It also arrived "too early", i.e. passed in front of the Moon, which makes a positive gravity assist impossible. $\endgroup$
    – asdfex
    Nov 6 '21 at 10:51
  • $\begingroup$ How about Apollo? $\endgroup$
    – kolufild
    Nov 6 '21 at 11:17
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    $\begingroup$ @kolufild, at TLI, the Apollo 11 stack was going 10.8 km/s (from the Mission Report), so slightly below escape velocity. After staging, residual propellants were vented, giving enough delta-v to send the S-IVB around the trailing edge of the moon, where a lunar gravity assist did the rest. (This appears to have failed in the case of Apollo 12; an object believed to be its S-IVB returned for a visit in 2002.) $\endgroup$
    – John Auld
    Nov 7 '21 at 0:03
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Wikipedia is a very unreliable source, especially when it comes to Soviet cosmonautics. Therefore, I will comment on the phrase "signal to stop firing the engine Block E stage was sent too late"

Source https://www.kik-sssr.ru/RUP-s.htm

При пусках первых лунных космических аппаратов, для более точного наведения ракеты-носителя на начальном участке и качественного выведения третьей ступени в точку запуска ее двигателей, осуществлялось радиоуправление на участке работы 2-й ступени изделия 8К72. Его осуществляли пункты радиоуправления.

During the launches of the first lunar spacecraft, for more accurate guidance of the launch vehicle in the initial section and high-quality launch of the third stage to the launch point of its engines, radio control was carried out in the operation section of the 2nd stage of the 8K72 orbital launch vehicle. It was carried out by radio control points.

Система радиоуправления входила в связь с ракеты-носителя перед разделением ступеней на 110-й секунде, когда прекращалось изменение тангажа, и ракеты-носителя ложилась на участок разгона 2-й ступени с постоянным тангажом под углом 42°, на который выставлялись пеленгаторы пунктов радиоуправления. Вторая ступень оканчивала работу после выдачи предварительной (выключение основных двигателей блока Ц) и главной команд (выключение рулевых двигателей блока Ц) в районе 300-310 секунд.

The radio control system entered into communication with the launch vehicle before the separation of the stages at the 110th second, when the pitch change stopped, and the launch vehicle lay on the acceleration section of the 2nd stage with a constant pitch at an angle of 42 °, to which the direction finders of the radio control points were set. The second stage finished its work after issuing preliminary (turning off the main engines of the C block) and main commands (turning off the steering engines of the C block) in the region of 300-310 seconds.

Но 2 января 1959 года радиосистема управления не выдала главную команду на выключение двигателя ракеты, запущенной с задачей попадания в Луну аппаратом "Луна-1". При расследовании оказалось, что антенна радиопеленгатора главного пункта ошибочно была выставлена для связи с бортом носителя не по главному лепестку диаграммы направленности, а по одному из боковых.

But on January 2, 1959, the radio control system did not issue the main command to turn off the engine of the rocket launched with the task of hitting the Moon by the Luna-1 spacecraft. During the investigation, it turned out that the direction finder antenna of the main point was erroneously positioned for communication with the carrier's side not along the main lobe of the directional pattern, but along one of the side lobes.

В.В. Порошков в своей книге "Ракетно-космический подвиг Байконура" (2007 г.) пишет, что "Промах мимо Луны связан не с неточностью системы управления, а с обыкновенным разгильдяйством, связанным с празднованием Нового года. Представитель разработчика системы радиоуправления, выставляя 1 января плоскость антенн пункт радиоуправления, ошибся по углу места на 2 градуса, выставив 44 градуса вместо 42. Его никто не проконтролировал (сказался праздник). Во время полета данные от пеленгатора в счетно-решающее устройство поступали, но параметр по углу места всё время шел с ошибкой, воспринимаясь как отклонение ракеты вниз от расчетной траектории. Поэтому счетно-решающее устройство не выключало двигатель второй ступени, ожидая, пока данные по углу места не придут в пределы допуска. При обработке материалов регистрации пункт радиоуправления в 16-м отделе службы научно-исследовательских работ полигона ошибку обнаружил ст. лейтенант Николай Леонидович Семенов. Она была подтверждена проверкой на пункте радиоуправления, где настройка после работы была сохранена."

V.V. Poroshkov in his book "The Rocket and Space Feat of Baikonur" (2007) writes that "A slip past the Moon is not associated with inaccuracy of the control system, but with the usual slovenliness associated with the celebration of the New Year. The representative of the developer of the radio control system on January 1, exposing the plane antennas of the radio control point, made a mistake in the elevation angle by 2 degrees, setting 44 degrees instead of 42. No one checked it (the New Year holiday affected). During the flight, data from the direction finder were sent to the calculator, but the elevation parameter was always going with an error , perceived as a deviation of the rocket downward from the calculated trajectory. Therefore, the calculator did not turn off the second stage engine, waiting for the elevation data to come within the tolerance range. The mistake was discovered by senior lieutenant Nikolai Leonidovich Semyonov at radio control point where the setting after work has been saved. "

В 2011 году в США вышла книга Евгения Александровича Ануфриенко, ветерана НИИП-5 и ЦНИИ-50. На стр 469 этой электронной книги "Моя первая жизнь" утверждается, что объект "... прошел мимо Луны из-за ошибки лейтенанта Ващука, здоровенного красавца с пышной шевелюрой, неправильно выставившего антенну системы радиоуправления". По словам Ануфриенко, вскоре этот лейтенант получил прозвище "Творец "Мечты" - по имени (в прессе) "первой советской космической ракеты".

In 2011, a book by Evgeny Alexandrovich Anufrienko, a veteran of NIIP-5 and TsNII-50, was published in the USA. On page 469 of this e-book "My First Life" it is stated that the object "... passed by the Moon due to the mistake of Lieutenant Vashchuk, a huge handsome man with lush hair, who incorrectly exposed the antenna of the radio control system." According to Anufrienko, this lieutenant soon received the nickname "The Creator of the Dream(Mechta)" - after the name (in the press) of "the first Soviet space rocket."

Н.А. Липкин в своей монографии (2003 год) говорит о техногенной причине неправильной работы пункта радиоуправления (стр. 54-55)

N.A. Lipkin in his monograph (2003) talks about the man-made reason for the improper operation of the radio control point (pp. 54-55)

Из «Докладной записки в ЦК КПСС о запуске первого КА к Луне»: «В результате ненормальностей в работе системы радиоуправления, выключение двигателя второй ступени произошло пр скорости, превышающей расчетную. Вследствие этого максимальная скорость третьей ступени космической ракеты превысила расчетную приблизительно на 41 м/сек.»

From the "Memorandum to the Central Committee of the CPSU on the launch of the first spacecraft to the Moon": "As a result of abnormalities in the operation of the radio control system, the engine of the second stage was turned off at a speed exceeding the design one. As a result, the maximum speed of the third stage of the space rocket exceeded the calculated one by approximately 41 m / sec. "

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    $\begingroup$ How does this answer the question? It just elaborates on the (accurate) statement in Wikipedia, that the engine was turned off too late. The automatic Google translation is quite hard to read in most parts. $\endgroup$
    – asdfex
    Nov 6 '21 at 18:12

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