Trajectory Analysis of the Soviet 1962 Mars Missions

The Soviet planetary probe, Mars 1, was the first spacecraft to survive launch to be sent on its way to the Red Planet. Although Mars 1 fell silent during its record-long journey and failed to return any data from Mars, it was the first of what would one day become a successful family of Soviet planetary spacecraft. Presented here is an analysis of the trajectories available during the 1962 Mars launch window, the details of the trajectory followed by Mars 1 as well as the intended trajectories of its less fortunate sister craft, 2MV-3 No. 3 and 2MV-4 No. 1.

Background

The Soviet’s 2MV series of probes launched towards Venus and Mars in the fall of 1962 consisted of a standardized spacecraft bus called the orbital compartment carrying a package called the planetary compartment that was geared towards a specific mission and target. In the case of the 2MV probes to Mars there were two design variants: The first was designated 2MV-4 which was fitted with a planetary compartment that carried a film-based imaging system as well as infrared and ultraviolet instruments designed to study Mars during a flyby. The sole 2MV-4 to survive launch to Mars, Mars 1, was of this design and had a mass of 893.5 kg. The second variant was the 2MV-3 which carried a spherical shaped lander about a meter in diameter designed to separate from the orbital compartment before encounter and land on the Martian surface with data returned directly to Earth during descent and after landing. The orbital compartment would be destroyed during entry into the Martian atmosphere. The mass of the 2MV-4 has yet to be disclosed but is generally believed to be comparable to Mars 1.

For the 1962 Mars window, a pair of 2MV-4 flyby probes and a single 2MV-3 lander were prepared for launch to Mars on the then new 8K78 rocket (later known by the name “Molniya” after the communication satellite series that also used this rocket). The first to be launched, 2MV-4 No. 3, lifted off on October 24, 1962 but was destroyed when the turbopump of the escape stage’s engine exploded 16 seconds into its burn that would have sent it to Mars. The second probe, 2MV-4 No. 4, was launched on November 1, 1962 after a three-day delay because of the Cuban missile crises. It was successfully sent on its way to Mars and was designated Mars 1. Unfortunately, issues with its attitude control system severely affected the operation of the spacecraft. The last contact with Mars 1 was on March 21, 1963 (142 days into its 230-day flight to Mars) which flew silently past Mars on June 19. The last 2MV probe to Mars and the only one to carry a lander, 2MV-3 No.1, was launched on November 4, 1962 but was stranded in its Earth parking orbit due to yet another malfunction of the Blok L escape stage of the 8K78.

1962 Mars Trajectories

For the 1962 launch opportunity to Mars, there were two types of trajectories available: relatively fast Type I trajectories where the spacecraft would travel through less than 180° in its orbit around the Sun before its encounter with Mars and longer Type II trajectories where the spacecraft would travel more than 180° in its orbit around the Sun before its encounter with Mars. As can be seen in the plot of minimum C₃ launch energy as a function of launch date in Figure 1 (taken directly from Clark et al.), the Type II trajectories (the lower curve in Figure 1) were energetically more favorable than the Type I trajectories (the upper curve in Figure 1). While more payload could have been launched towards Mars in the Type II trajectories, the time of flight to Mars in these trajectories was significantly longer than the faster Type I trajectories and the communication range was much larger as well. Given the limited lifetimes of spacecraft (Soviet or American) during these early years of the Space Age, the Type I trajectories were preferred despite the payload penalty.

Figure 1: Plot of minimum C3 launch energy as a function of launch date for Type I (upper curve) and Type II (lower curve) trajectories taken from Clark et al. The three red “+” show the conditions for the following: 1) 2MV-4 No. 3, 2) Mars 1 (2MV-4 No. 4) and 3) 2MV-3 No.1. Click on image to enlarge. (JPL/NASA)

The C₃ launch energy requirements for Type I trajectories as a function of launch date and time of flight are illustrated in the contour plot shown in Figure 2 (taken directly from Clark et al.). The minimum launch energy towards Mars occurred on October 30 with a C₃ of 15.1 km²/s². For minimum energy Type I trajectories, the general trend is towards longer times of flight for later launch dates with a sharp jump of a month or more in the times of flight occurring after the first week of November 1962. The distance to Mars at the time of encounter tended to increase also with launch date with the distance at encounter for minimum launch energy trajectories displaying a sharp increase from around 260 million km to over 300 million km after the first week of November as well. Taken together, these factors made the last week of October and first week of November 1962 the most desirable launch window towards Mars since the payload could be maximized while at the same time minimizing the time of flight to Mars and the communication distance.

Figure 2: This plot, taken from Clark et al., shows contours of C3 launch energy plotted as a function of launch date (X-axis) and time of flight (Y-axis). The three red “+” show the conditions for the following: 1) 2MV-4 No. 3, 2) Mars 1 (2MV-4 No. 4) and 3) 2MV-3 No.1. Click on image to enlarge. (JPL/NASA)

Since the 2MV-3 carried a lander, the approach speed towards Mars was also a factor in the mission design.  When the Soviet Mars landers were being designed, the properties of the Martian atmosphere were uncertain but the consensus of the scientific community at this time was that the it was primarily composed of nitrogen with a surface pressure of about 80 hPa (today we now know that Mars has an atmosphere dominated by carbon dioxide with a typical surface pressure of about 6 hPa).  While details of the design of the 2MV-3 lander have yet to be released beyond its 305 kg mass and its instrument complement, it is generally believed to be a spheroid about a meter in diameter just like the early Soviet Venus landers.

In an effort to determine the characteristics of the early Soviet Mars landers, I performed a series of computer simulations of entry trajectories in 1990 specifically to study the case of the Zond 2 mission launched in November of 1964 (which was still suspected of carrying a lander at this time).  For this work, shown in the contour plot in Figure 3, I determined the altitude at which a meter in diameter entry probe would slow to the local speed of sound (when, presumably, a parachute could be safely deployed) as a function of impact parameter (i.e. the perpendicular distance between the unperturbed path of the spacecraft and the center of the target body) and probe mass. For these calculations, it was assumed that the Martian atmosphere was composed of 90% nitrogen and 10% carbon dioxide with a surface pressure of 80 hPa.  As it turns out, this was at the low end of estimates that Soviet engineers were considering which were more in the 100 to 300 hPa range so my simulation would have been a worst-case scenario for the Soviet engineers.  In my simulations it was further assumed that the surface temperature was 270ºK, the temperature in the stratosphere was a constant 145ºK and that the temperature gradient from the surface to the stratosphere was -3.77ºK/km. While the 6.3 km/s entry velocity expected for Zond 2 is slightly lower than that expected for the 2MV-3 lander, the results are still close enough to be instructive.

Figure 3: A contour plot of the parachute deployment altitude (km AGL based on when a meter in diameter, spherical entry probe slows to the local speed of sound) as a function of impact parameter (X-axis) and the entry probe mass (Y-axis) based on a simulation assuming a Martian atmosphere composed primarily of nitrogen with a surface pressure of 80 hPa. The yellow line indicates the 305 kg mass of the 2MV-3 Mars lander with the masses of Venera 4, 5, 6 and 8 landers also indicated. Click on image to enlarge.  (A.J. LePage)

My conclusion at the time was that a spherical lander with a mass of less than 350 kg could probably safely land on Mars with the assumed atmosphere which compares favorably with the actual mass of 305 kg (indicated by the yellow horizontal line in Figure 3).  The results show that not only was a safe landing possible with asymptotic approach velocities on the order of 4 km/s, but that there would be a window about 2000 km wide that would allow a 2MV-3 lander to slow enough to deploy its parachute at least 5 km above the Martian surface.  Given the crude nature of interplanetary navigation at the time (in addition to the uncertain nature of the Martian atmosphere), this sort of margin was important to ensure a landing.  When selecting an approach trajectory towards Mars, it was also important to minimize the asymptotic approach speed to maintain as wide a margin as possible.

For the 1962 launch window, contours of C₃ launch energy as a function of launch date and asymptotic approach speed with respect to Mars is shown in Figure 4 (taken directly from Clark et al.). In general, minimum launch energy and Class II trajectories (where the spacecraft encounters Mars after the spacecraft passes through the aphelion of its orbit around the Sun) offer the lowest encounter velocities with the general trend of lower approach speeds with later launch dates. Faster Class I trajectories (where the spacecraft encounters Mars before the spacecraft passes through the aphelion of its orbit around the Sun) resulted in encounter velocities that can greatly exceed the desired 4 km/s asymptotic approach speed. As a result, minimum energy trajectories were more desirable for the 1962 launch window

Figure 4: This plot, taken from Clark et al., shows contours of launch energy plotted as a function of launch date (X-axis) and asymptotic velocity with respect to Mars (Y-axis). The three red “+” show the conditions for the following: 1) 2MV-4 No. 3, 2) Mars 1 (2MV-4 No. 4) and 3) 2MV-3 No.1. Click on image to enlarge. (JPL/NASA)

2MV Trajectory Analyses

Since the launch and encounter dates of the 2MV Mars missions are known, it is a straightforward process to use the data in Clark et al. to analyze their trajectories. The results of the analysis are summarized below in Table 1 as well as indicated in Figures 1, 2 and 4 above.

Table 1: Summary of 2MV Trajectories to Mars

As can be seen, all three spacecraft were launched (or were intended to be launched) on trajectories with a C₃ in the 15.2 to 15.9 km²/s² range. The tight grouping of the launch energies strongly suggests that they all had about the same mass, namely the announced 893.5 kg launch mass of Mars 1.

An examination of Figure 2, however, shows that the trajectory of 2MV-4 No. 3 was a bit of an anomaly compared to the other two 2MV trajectories. It was launched on a Class II trajectory with a time of flight of 236 days. It could have been launched on a Class I trajectory with the same C₃ launch energy on October 24, 1962 and reached Mars about May 31, 1963 after a flight of 219 days – 17 days earlier than its intended encounter date. Given the uncertain longevity of spacecraft in this era, it would be logical to assume that the shorter time of flight would have been more desirable. But instead 2MV-3 No. 3 was launched on a longer trajectory.

I speculate that the trajectory choice might have been driven by logistics. During the 1960s, multiple planetary encounters by Soviet planetary spacecraft were typically grouped together and spaced about two days apart. There must have been some advantage to do so involving the logistics of tracking and ground control. Maybe a more important consideration for the 1962 Mars window was the logistics involved with launching the 2MV spacecraft. While the shorter 219-day Class I trajectory would have gotten 2MV-4 No. 3 to Mars more quickly, the asymptotic approach velocity would have been 4.8 km/s which is faster than the 4.0 km/s of the Class II trajectory actually intended to be used. While that would be of little concern for a simple flyby spacecraft, a 2MV-3 lander following a Class I trajectory would have an entry velocity of about 7.0 km/s instead of 6.5 km/s for the Class II trajectory of the same launch energy. As shown earlier, given the uncertainties in navigation and of the properties of the Martian atmosphere at this time, a slower entry speed was more desirable to maximize the already uncertain margins for error.

The intentionally low approach speed for 2MV-4 No. 3 only makes sense if the trajectories for the 1962 Mars window had been designed so that any of the 2MV spacecraft variants – flyby or lander – could have been switched on short notice (because of a last minute problem with a particular 2MV spacecraft uncovered during testing, for example) without the need for having two sets of parameters to determine launch windows and program the launch vehicle. The fact that all three spacecraft had about the same asymptotic approach speed of 3.9 to 4.0 km/s seems to suggest that the spacecraft were meant to be interchangeable to simplify the logistics of launching them. This also suggests that the three spacecraft had about the same 893.5 kg mass as Mars 1 to aid in this interchangeability. So in the end it would appear that logistics played a role in the choice of trajectories in addition to the usual criteria of launch energy and encounter speed.

Of course it needs to be noted that the 2MV-3 lander was doomed to failure from the start.  The Martian atmospheric pressure was less than 6% as dense as the engineers had assumed and was composed primarily of carbon dioxide which would have resulted in a reduced scale height (i.e. what atmosphere Mars did have would tend to hug the surface more than assumed decreasing the effective braking distance available).  As a result, the drag produced by a spherical lander would have been insufficient for a safe landing and the 2MV-3 lander would have crashed without transmitting any data.  It would be a couple more years before astronomers realized how far off their initial estimates for the density of the Martian atmosphere were.

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Related Reading

“If At First You Don’t Succeed… Part I”, The Space Review, Article #2477,  March 24, 2014 [Article]

“If At First You Don’t Succeed… Part II”, The Space Review, Article #2480,  March 31, 2014 [Article]

“Trajectory Analysis of the Soviet 1964 Venus Missions”, Drew Ex Machina, April 2, 2014 [Post]

General References

V.C. Clark, Jr., W.E. Bollman, R.Y. Roth and W.J. Scholey, “Design Parameters for Ballistic Interplanetary Trajectories Part I. One-way Transfers to Mars and Venus”, Technical Report No. 32-77, JPL, January 16, 1963
p. 71, Fig 4-7, “Mars 1962: Minimum injection energy vs launch date”
p. 252, Fig 11-1 “Mars 1962: Time of flight vs launch date”
p. 256, Fig 11-14 “Mars 1962: Asymptotic speed with respect to Mars vs launch date”

Wesley T. Huntress and Mikhail Ya. Marov, Soviet Robots in the Solar System: Mission Technologies and Discoveries, Springer-Praxis, 2011

Andrew J. LePage, “The Mystery of Zond 2”, Journal of the British Interplanetary Society, Volume 46, Number 10, pp. 401-404, October 1993 [Abstract]

V.G. Perminov, The Difficult Road to Mars: A Brief History of Mars Exploration in the Soviet Union, Monographs in Aerospace History No. 15, NASA History Division, July 1999

Timothy Varfolomeyev, “Soviet Rocketry that Conquered Space Part 5: The First Planetary Probe Attempts, 1960–1964”, Spaceflight, Vol. 40, No. 3, pp. 85–88, March 1998

HORIZONS Web-interface, JPL [Link]