Analysis of Typical Earth-Mars Launch Trajectory on Mission Profiles and Launch Window Extension

Geng Guang-you , Wang Jue, Song Qiang, Zhang Zhi-guo, Wang Jian-ming

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Analysis of Typical Earth-Mars Launch Trajectory on Mission Profiles and Launch Window Extension

Geng Guang-you1,2, Wang Jue1,3, Song Qiang2, Zhang Zhi-guo2, Wang Jian-ming2

(1. School of Astronautics, Beihang University, Beijing, 100191; 2. Beijing Institute of Astronautical Systems Engineering, Beijing, 100076; 3.China Academy of Launch Vehicle Technology, Beijing, 100076)

Taking into account characteristics and range safety of different launch vehicles implemented in recent years, there are obvious differences in launch trajectories of recent typical Mars exploration missions. Through the principle of flight mechanics on direct Earth-Mars transfer trajectory, characteristics of recent Mars exploration departure trajectories are analyzed and summarized, mainly on mission profiles and how to extend the launch window.

Earth-Mars launch trajectory; Transfer trajectory; Launch window; Hyperbolic escape trajectory

0 Introduction

The average distance between Mars and the Sun is 1.524Au[1]. The sidereal period of revolution of Mars is 687 days. The period of conjunction with the Earth is 780 days. The included angle between Mars’ orbit and the ecliptic is about 1.85o. The eccentricity of Mars’ orbit is about 0.093 (the orbital eccentricity of the Earth is about 0.017). Different Earth-Mars relative positions caused by different launch years, lead to the complicated design of Earth-Mars transfer orbit, which mainly includes the heliocentric elliptical arc and the hyperbolic transfer trajectories at both ends (Earth or Mars). The transfer orbits characterized by non-coplanar, small eccentricity and multi-perturbation have been studied for a long time as a nonlinear or typical multi-extremum problem. However, the success rate of Mars exploration is only near 50% so far, including flyby, orbiting and landing (about 22successes).

In addition, the latitudes of most launch complex are different apparently; their scopes of launch azimuth and range safety also constrain the trajectory launched. So in recent years, the departure hyperbolic trajectories toward Mars are very different, here we’ll analyze and summarize why the characteristics of recent Mars exploration launch trajectories are so different.

1 Earth-Mars Transfer Flight Mechanics Model

Ignoring the influence of other perturbation forces and the flight phase inside the gravitational sphere of influence (SOI), the Earth-Mars transfer orbit is a typical Lambert's problem. The mathematic expression of the two-point transfer orbit is as follows[1～4]:

Where μ is the gravitational constant of the centric celestial body; a is the semi-major axis of the transfer orbit; r1, r2 and c are distances between the departure point, the arrival point and the centric celestial body, respectively; the angle between r1 and r2 is θ, Fig.1 is illustration.

From the north pole of Ecliptic, see Fig.2.

Fig.2 Earth-Mars Transfer Orbit Illustration

In general, the exact mechanics model of the Earth-Mars transfer orbit involves the gravity (the whole process) of the Sun, the Moon and eight planets,the dominant2terms of the Earth and Mars and the higher order non-spherical terms, the latter are not so important and can be omitted, as well as the impact of light pressure terms; without loss of generality, here the mechanics model is given to consider the Earth and Mars2coefficients:

Based on the above analysis, it can be seen that for the Earth-Mars transfer orbit of the certain year, the DLA of the hyperbolic trajectory at the gravity boundary of SOI affects the launch vehicle's azimuth (viz. orbital inclination); the velocity change ΔVPE+ΔVPM affects the departure and arrival energy, and right ascension angle (RLA) affects the launch time. Although launch trajectories of Mars exploration are different due to different years, the characteristics of the departure and arrival energy and the DLA are similar. Therefore, in this case, for the Earth-Mars transfer orbit with a transfer time about 5～10 months launched in 2018, DLA and velocity change ΔVPE+ΔVPM analysis results are presented as Fig.3 and Fig.4. To be convenient, here we assume ΔVPEmeans the velocity increased from the departing 200 km altitude parking circle orbit to the escape hyperbolic trajectory of the Earth, andΔVPM means the velocity decreased from the reentry hyperbolic trajectory to the 500 km altitude circle orbit of Mars.

Fig.4 DLA &RLA Varies with Launch Date andTransfer Time in 2018

Then we find the optimal window of the total velocity change is from 2458240 JD (corresponding to May 1, 2018) to 2458270 JD, i.e. the optimal launch period lasts about 30 days, and with the transfer time of about 200 days, that means it’s a type I transfer.

Fig.4 indicates that the DLA and RLA are determined by the departure and arrival date, thus the launch vehicle’s trajectory inclination (viz. azimuth demand) and launch time are determined as well, if we suppose the departure date and transfer days of the trajectory.

Through the above, we could get the departure hyperbolic trajectory toward Mars, the below shows the typical launch trajectories for Mars exploration.

2 Typical Launch Trajectory for Mars Exploration

At present, most Martian probes’ orbits are polar or with large obliquity. Typical trajectory profiles launched and patterns on how to extend launch window are analyzed below.

2.1 ExoMars / Schiaparelli Mission Launched by ESA/Russia[5]

This is a Mars exploration projected by ESA and Russian Space Agency, with ExoMars as the Trace Gas Orbiter (TGO) and Schiaparelli as the Mars Lander. The total mass is 4332 kg. Finally, ExoMars Orbiter successfully circled around Mars, but Schiaparelli failed during landing, hitting the surface of Mars directly.

The mission is launched instantaneously by the storable propellant rocket, Proton.The launch period is from 7thto 27thJanuary or from 14thto 25thMarch 2016. Breeze M is a good choice to perform deep space exploration because it works very efficiently due to its specific impulse up to 325 s, compact structure design and annular throwaway propellant tank. Located at the latitude of 45.6o, Baikonur launch site cannot resort the Earth's rotation speed much, but with the high DLA ability attained, thereby making optimal launch window possible.

This mission is Proton’s first successful deep space launch in recent 20 years. Taking 10 hours and 44 minutes from the liftoff to the separation of the probe, the rocket's first three stage flight profiles are similar to common GTO launches. After that, Breeze M ignited four times, transferring from the three parking orbits to the hyperbolic escape trajectory toward Mars, the three parking orbits were 51.55°×175 km circle, 51.58°×292 km×5272 km, 51.55°×693 km×21079 km. After releasing the probe, Breeze M entered into the abandoned orbit to avoid the interference.

The actual launching date is 14thMarch 2016 and the launch azimuth is 61.3o. The corresponding trajectory inclination is 51.5o and the probe arrived at Mars about 7 months later. On 16thOctober, Schiaparelli is separated from the orbiter at 5833.3 m/s speed and entered the atmosphere of Mars. Due to failure of the parachute braking device, the lander crashed. On 19thOctober 15:24 UTC, TGO orbiter entered the elliptical orbit, and later, finally circled around Mars with the orbit altitude of 400 km on March 2018.

2.2 Mars Exploration Missions Launched by Atlas V of U.S.[6]

In recent years, Atlas V series launched several Mars probes. Atlas V541 launched MAVEN in 2013, Curiosity in 2011, and reconnaissance orbiter in 2005. Curiosity even made a successful landing with parachutes. The other two were launched by Atlas V401 configuration (both probes entered large elliptical orbits of Mars). Atlas V401 is a two stage rocket using liquid oxygen–kerosene at first stage, and the second stage, Centaur with LO2/LH2. Atlas V541 added four solid boosters.

As a flagship launch vehicle of United States, it has abundant launch capability. The launch period is generally about 20 days, with the daily launch window varies from 30 minutes to 2 hours. According to the available information, to ensure the launch window, the coast time varies dynamically according to the change of the liftoff time. As the super-cryogenic propellant upper stage could ignite more than 3 times within 6 hours, it can be speculated that a fixed azimuth is selected according to the trajectory inclination required by deep space exploration, depending on the liftoff time, a dog-leg maneuver with the loss of launch capability to some extent would be taken. The data show that 94o or 104o azimuths are used for different missions respectively, with corresponding orbital inclination of 28.7o or 35.5o (the latter with a primary yaw program firstly). Escape declination (DLA), right ascension angle (RLA), and launch energy C3 are taken as target parameters for Earth escape hyperbolic trajectory design.

NASA's MAVEN mission launched in 2013 is mainly used to study the evolution of the Martian atmosphere and water presence. The launch period lasted 20 days, from 18thNovember to 7thDecember, 2013, see Tab.1. While the daily window lasted up to 2 hours; on special situations, the launch period can be postponed until 23rdDecember (up to a maximum of 36 days ). Main launch period restricted the DLA within 28° (so there is no extra loss of launch capability caused by increasing the azimuth). The Earth's hyperbolic escape trajectory was achieved by the fixed azimuth and dynamical adjustment of the coasting time. Centaur upper stage would optimize the escape trajectory phase, if the liftoff time changed.

Tab.1 Earth Escape C3, RLA, DLA, Arrival Date of Mars

Launch Date18th Nov.Launch Period Open27th Nov.LP Medium7th Dec.LP Day 20 C3/(km2·s-2)12.0710.309.40 DLA/(o)13.3818.8426.93 RLA/(o)198.26200.58200.88 Arrival Date2014-09-242014-09-242014-09-24

On 18thNovember 2013 18:28 UTC, at the beginning of the 2 hours launch window, Atlas V 401 adopted a 94o azimuth (corresponding to 28.6° orbital inclination), lifted a 2454 kg Mars rover MAVEN into the escape trajectory from Cape Canaveral Air Force Base. During the actual launch sequence, coasting time between Centaur upper stage’s two ignitions was 1656 s (with the rolling thermal control program during the coasting phase), with 570 s and 329 s for two burns respectively. The perigee of transfer trajectory was 192 km. The entire flight took 308 days, with 4 orbital corrections. MAVEN arrived at Mars on 02:24 UTC, 22thSeptember 2014 (the close of the arrival window was next 28thSeptember, corresponding to the launch window closed on 7thDecember). The 1321 N engine (main engine 6×200N) consumed more than half of the fuel in more than 36 minutes, generating a velocity of 1233 m/s and entering a large elliptical orbit with periapsis of 380 km, orbital inclination of 75o and period of 35 hours. Later it maneuvered into a 150 km×6275 km, 4.5 hours period elliptical orbit. One-way speed-of-light time from Mars to Earth is 4～20 minutes which depends on the Earth's relative position.

2.3 Mars Exploration Missions Launched by Delta II of U.S.[7]

Delta II series launched a lot of Mars probes, including Mars Global Surveyor and Mars Pathfinder respectively in 1996, Mars Climate Orbiter in 1998, Mars Polar Lander in 1999, Mars Odyssey in 2001, MER-A Spirit and MER-B Opportunity respectively in 2003, Dawn and Phoenix Mars Lander respectively in 2007.

Among missions launched in recent years, Delta 7925H launched Dawn in 2007 and MER-B Opportunity in 2003, while 7925 launched the remaining missions. Delta II 7925H used nine solid rocket boosters and first stage of LO2/Kerosene, second stage of N2O4/Hydrazine50, and the solid upper stage. 7925H employed longer solid boosters and larger fairings than 7925. Due to its limited launch capability, Delta II series have a typical launch window of about 19 minutes to 44 minutes per day for a launch period of 20 days. According to the available information, Delta II series adopt two fixed azimuth corresponding to the two lift off time to achieve the launch; for example, Phoenix launched in 2007, MER-A Spirit and MER-B Opportunity launched in 2003, all clearly adopted the method.

The data show that 93o and 99o azimuths are used for different missions, respectively, see Tab.2. The corresponding orbital angles are 28.6o and 29.8o, respectively. The following is a description of the Phoenix Mars mission launched in 2007 by Delta II.

Phoenix probe weighs 680 kg. The main task is to explore water ice and early life on the surface of Mars. Its launch period is 3rdAugust 2007.

On 3rdAugust launch window, the first launch opportunity was 5:35:18 EDT (US Eastern Time); the second launch opportunity is 6:11:24 EDT (Eastern US time), due to the relative position of celestial bodies, et al; the next window is generally about 10 minutes earlier than the previous day. For orbital parameters of 3rdAugust, at separation of the probe, the altitude is 2255 km and the velocity is 11 021.5 m/s according to the 93o azimuth.

Tab.2 Planned Launch Sequence of the Phoenix Timing

EventFlight Time/(min: sec) 93°Azimuth99° Azimuth Liftoff00:00.000:00.0 Stage I-II Separation04:31.304:31.3 First Cutoff – Stage II (SECO-1)09:20.509:21.0 First Restart – Stage II73:47.271:51.3 Second Cutoff – Stage II (SECO-2)76:02.374:06.3 Target Interface Point (TIP)87:42.885:46.9

2.4 MOM Probe Launched by Indian PSLV-XL[8]

Indian PSLV is a four and a half stage-rocket (boosters, core 1ststage and 3rdstage using solid propulsion systems, core 2ndstage and 4thstage using liquid propulsion systems). PSLV injected the probe into the sub-GTO orbit firstly, then multiple perigee burns were performed to compensate the liftoff time offsets, which was almost the same idea used in United States’ first lunar orbit mission or Chang'e I, China's first lunar exploration in 2007. It was originally planned to launch on 28thOctober, 2013, but was delayed for about 1 week. The whole flight profile is as follows.

On 5thNovember, 2013, at 14:38 (09:08 UT), Indian PSLV-XL launch vehicle lifted off. It sent the Mars probe to an elliptical orbit with orbital inclination of 19.27o (about 104o launch azimuth), perigee of 250 km, and apogee of 23 500 km. Then after igniting 6 times, the probe is sent into a hyperbolic transfer orbit. The fourth maneuver only raised the apogee to 78 276 km (originally planned 100 000 km) due to the power solenoid conflict, and two days later an additional maneuver raised the apogee to 118 642 km. About 300 days later, the probe arrived at Mars on 24thSeptember, 2014. Its 440 N main engine (and 8×22N reaction control system) ignited for 1454 seconds and consumed 249.5 kg propellant, decelerated 1098.7 m/s into an elliptical orbit with periapsis of 423 km and apoapsis of 80 000 km to Mars.

2.5 Rosetta Probe Launched by Ariane V[9]

The purpose of Rosetta probe is to detect the comet 67P/Churyumov-Gerasimenko. The first obstacle to be overcome is the limited launch window. In order to meet up with Comet Wirtanen, Rosetta must be launched within a period of about 20 days, starting on 26thFebruary 2004 (postponed from the January 2003). On six of those days within the period, there must be a launch window of just 20～30 minutes. The remaining days account for a roll back of the launch vehicle for replenishing of the cryogenic fuel. If the opportunity is missed, this mission will have to be postponed while another target is selected.

After flying by the Earth 3 times and Mars once, the probe entered into the orbit heading to the asteroid and comet, which is Ariane's first deep space exploration launched in recent years.

The Ariane V launched at 07:17 UTC on 2ndMarch 2004 from Kourou, which is near the equator, most likely used a “fixed azimuth + dog-leg maneuver + coasting time adjustment” method to achieve the launch window. The flight lasted 1 hour and 45 minutes from liftoff to the separation of probe which weighs 3187 kg. When solid boosters stopped working, the onboard computer began to optimize the target of the parking orbit and the escape hyperbolic trajectory.

The hyperbolic escape trajectory parameters are as follows:∞= 3.545 km/s, DLA= 2o. As the launch is delayed, the actual parking orbit and target orbital parameters are adjusted; in this situation, the first stage entered into a 200 km×4000 km parking orbit, and about 2 hours later, the upper stage entered into the hyperbolic trajectory toward Mars.

3 Characteristics of Typical Launch Trajectory Toward Mars in Recent Years

Relevant information for launch vehicles of U.S., ESA, etc shows that, the key points of the Earth escape trajectory towards Mars targets are: RLA, DLA, and escape C3 parameters. Based on the above analysis of typical Mars exploration trajectory launched in recent years, and coupled with the mechanics of flight, the following conclusions are drawn:

a) Since Russia’s launch complex is located at high latitude, and Proton (including Breeze M) with storable propellants, among its approximate 20 or 11 days launch period, Proton launch instantaneously. Multi-perigee burns are performed by Breeze M to achieve Mars exploration hyperbolic escape orbit in 10 more hours.

b) For early Delta II series, among its approximate 20 days launch period, each launch window is generally about 19 minutes to 44 minutes, and the data clearly show that Delta II set two fixed azimuth corresponding to two liftoff moments, respectively, composing a launch window to ensure the liftoff (and possibly using a similar launch mode of Atlas V when there is sufficient launch capability), and injects the probe directly to the hyperbolic transfer orbit toward Mars.

c) Atlas V, as a flagship of U.S. launch vehicle now, for the sufficient launch capability and guidance control ability, 20 days launch period is generally selected, and daily launch window varies from 30 minutes to 2 hours Maven even reached a daily window of 2 hours. According to the orbital inclination required by Mars exploration, Atlas V can accommodate dynamical change of the liftoff time within the launch window via a fixed azimuth, adjustment of dog-leg maneuver and coasting time. The data show that 94o or 104o azimuth are used for different missions with corresponding orbital inclination of 28.7o or 35.5o, respectively (the latter includes a primary yaw program). Atlas V sent the probe directly into the hyperbolic transfer orbit toward Mars.

d) Due to PSLV’s limited launch capability, the probe is sent into a sub-GTO orbit firstly, then carries out multi-perigee burns lasting for several days, finally entering Mars exploration hyperbolic escape trajectory. This can be catalogued into a modified version of the Russian launch mode.

e) Six days during the 20 days launch period are selected by ESA, and a deep-space escape hyperbolic trajectory with a launch window of 20～30 minutes per day is designed. It is likely that the method of ‘fixed azimuth + dog-leg maneuver + coast time adjustment’ is adopted to ensure the launch window.

Overall, except for different relative positions between the Earth and Mars, typical mission profiles and launch window extensions of Earth-Mars launch trajectories depend closely on each rocket’s launch capability and guidance ability of navigation systems onboard.

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世界典型火星探測發(fā)射軌道及窗口拓展分析

耿光有1,2，王 玨1,3，宋 強(qiáng)2，張志國2，王建明2

（1. 北京航空航天大學(xué)宇航學(xué)院，北京，100191；2. 北京宇航系統(tǒng)工程研究所，北京，100076；3.中國運(yùn)載火箭技術(shù)研究院，北京，100076）

由于運(yùn)載火箭自身特點及飛行航、落區(qū)約束的差異，致使世界典型運(yùn)載火箭直接火星探測任務(wù)的發(fā)射軌道存在明顯不同。從直接火星轉(zhuǎn)移的飛行力學(xué)原理的角度進(jìn)行了分析，重點關(guān)注了典型火星探測任務(wù)的軌道剖面設(shè)計及窗口拓展方法，完成了對當(dāng)前火星探測任務(wù)典型出發(fā)軌道特點的分析總結(jié)。

地球-火星發(fā)射軌道；轉(zhuǎn)移軌道；發(fā)射窗口；雙曲逃逸軌道

V41

A

2018-01-03

10.7654/j.issn.1004-7182.20180104

1004-7182(2018)01-0018-07

耿光有（1972-），男，博士，研究員，主要研究方向為運(yùn)載火箭飛行力學(xué)及總體設(shè)計研究

Geng Guangyou (1972-), male, Ph.D, research professor, mainly focus on flight mechanics and systems design of launch vehicle