Panoramic Issues of the Martian Exploration Luis Vázquez Departamento de Matemática Aplicada...

43
Panoramic Issues of the Martian Exploration Luis Vázquez Departamento de Matemática Aplicada Facultad de Informática Universidad Complutense de Madrid / 28040-Madrid [email protected] www.fdi.ucm.es/profesor/lvazquez www.meiga-metnet.org Convento da Arrabida Scientific Problems of Space Exploration-Mars and Beyond June 29- July 3, 2015

Transcript of Panoramic Issues of the Martian Exploration Luis Vázquez Departamento de Matemática Aplicada...

Page 1: Panoramic Issues of the Martian Exploration Luis Vázquez Departamento de Matemática Aplicada Facultad de Informática Universidad Complutense de Madrid.

Panoramic Issues of the Martian Exploration

Luis Vázquez Departamento de Matemática Aplicada

Facultad de InformáticaUniversidad Complutense de Madrid / 28040-Madrid

[email protected]/profesor/lvazquez

www.meiga-metnet.org

Convento da ArrabidaScientific Problems of Space Exploration-Mars and Beyond

June 29- July 3, 2015

Page 2: Panoramic Issues of the Martian Exploration Luis Vázquez Departamento de Matemática Aplicada Facultad de Informática Universidad Complutense de Madrid.

TOP TEN DISCOVERIES of the

MARS EXPLORATION PROGRAM(MEPAG: Mars Exploration Program Analysis Group)

1. ANCIENT, PERSISTENT LIQUID WATER.2. COMPLEX SURFACE GEOLOGY.3. MODERN WATER.4. RECENT CLIMATE CHANGE.5. PLANETARY MAGNETISM.6. MARTIAN CLIMATE AND WEATHER.7. MODERN PROCESSES.8. METHANE ON MARS.9. GRAVITY AND FIGURE.10. MARS RADIATION ENVIRONMENT.

Page 3: Panoramic Issues of the Martian Exploration Luis Vázquez Departamento de Matemática Aplicada Facultad de Informática Universidad Complutense de Madrid.

SPACE PROGRAMME

Elements of the Present Situation

 1. The Available Data Inventories:

–ESA PSA and NASA PDS.

–Some of national space agencies mission data.

–Technical and supporting data of individual instruments.

–Laboratory data, e.g. chemical and physical properties of gases, materials.

–Ground-based observational data.

 2. Accessibility:

– Data are spread in many kinds of databases.

– Data are owned by various different organizations having their own data rules.

– The data in various inventories are not always easy to access.

 3. The Data:

– The amount of data is growing very fast.

– Practically all the planetary investigations require strong modelling efforts in support of the observational

data; e. g. Climatic system on Earth.

– All current data (except for Earth) is provided by single observational platforms (orbiters, lander, and

probes).

Page 4: Panoramic Issues of the Martian Exploration Luis Vázquez Departamento de Matemática Aplicada Facultad de Informática Universidad Complutense de Madrid.

Possible Objectives to be Reached (H2020)

 

1. Proper Information of data sources with clear user instructions should be catalogued and

made available.

2. The data in various inventories should be made more easily to access.

3.

•To develop suitable strategies and algorithms for the Data Mining: for example to detect

phenomena short in time and/or localized in space; the time/space scales involved in the

Martian phenomena …etc.

•We need to focus on the Simultaneous Modelling Efforts with in situ data.

•To develop Data Mining and Modelling Tools integrated in

Computational Platforms based on Cloud Computing.

4. Familiarize science community with existing data.

5. Make data really accessible, including laboratory data which is often highly important.

 

Page 5: Panoramic Issues of the Martian Exploration Luis Vázquez Departamento de Matemática Aplicada Facultad de Informática Universidad Complutense de Madrid.

Possible H2020 Space Activities

 

1.To support the improving of planetary modelling activity.

2.To organize periodical Schools devoted to students at different levels.

3. To organize outreach activities related to the data bases.

4. To organize competitive analysis of given data bases among

teams of young researchers and students in different institutions.

Page 6: Panoramic Issues of the Martian Exploration Luis Vázquez Departamento de Matemática Aplicada Facultad de Informática Universidad Complutense de Madrid.

Big Data and Cloud Computing 

When we have to face with the following two tasks:

•The use of large and massive simulations.

•To deal with large amounts of data (big data).

 

For the first task we should have as reference the use of “Cloud Computing” which offers

many advantages when we need access to high performance computing facilities. For the

second task we can use what is learned from dealing with big data in other contexts. Some

general issue that we have to face are high performance big data clustering, visualization and

interactive analysis by using massive data streams as well as big data analytic workflows.

 

MARS Data

A reference for possible actions is the following:

1.A compilation of the currently existing data about each Mars Mission.

2.To organize the data with a similar structure of the analogous data for Earth.

3.To associate to the data a metadata file defined by the specifications of the sensors, the

conditions of measurement and the indicators on the validity of the data.

Page 7: Panoramic Issues of the Martian Exploration Luis Vázquez Departamento de Matemática Aplicada Facultad de Informática Universidad Complutense de Madrid.

MARS Data: ATMOSPHERE

 

 

1.It is important to reflect the parameters related to the validity of data as it

happens in the data from de national meteorological services.

2.The data about the solar radiation.

3.Comparisons between measurements and the results obtained by using

radiative transfer models.

4.To study the compatibility between the measures on Mars surface with those

derived from the measurements of the orbiters.

5.To assimilate radiative parameters from satellite measurements.

6.To develop tools to find possible correlations among different observed

variables.

7.To use available data for calculating derived products: different space

scales.

Page 8: Panoramic Issues of the Martian Exploration Luis Vázquez Departamento de Matemática Aplicada Facultad de Informática Universidad Complutense de Madrid.
Page 9: Panoramic Issues of the Martian Exploration Luis Vázquez Departamento de Matemática Aplicada Facultad de Informática Universidad Complutense de Madrid.

Image from MER-Spirit

Page 10: Panoramic Issues of the Martian Exploration Luis Vázquez Departamento de Matemática Aplicada Facultad de Informática Universidad Complutense de Madrid.

SUNSET IN MARS

Gusev Crater (Mars): Twilight at 18.20 of the sol 464 of Spirit (April, 23 2005)

Dust Distribution in the Martian Atmosphere

Page 11: Panoramic Issues of the Martian Exploration Luis Vázquez Departamento de Matemática Aplicada Facultad de Informática Universidad Complutense de Madrid.

MARS Data: RADIATION + MAGNETIC FIELD

  

1. It is important to reflect the parameters related to the validity of data as it happens

in the data from de national meteorological services.

2. The data about the solar radiation.

3.Comparisons between measurements and the results obtained by using radiative

transfer models.

4.To study the compatibility between the measures on Mars surface with those

derived from the measurements of the orbiters.

5.To assimilate radiative parameters from satellite measurements.

6.To develop tools to find possible correlations among different observed variables.

7.The data about the Martian Dust. Magnetic and Electric effects.

8.Data from the ionosphere-magnetic field coupling

9.Data and models of the evolution of the Martian Magnetic Field.

10.Data from Martian Analogues in the Earth.

11.The data from MARSIS and other orbiters

•To analyse the ionosphere-magnetic coupling.

•Correlation with the solar activity and the crustal magnetic field.

•Magnetic field at different heights and correlation with the magnetic anomalies.

 

Page 12: Panoramic Issues of the Martian Exploration Luis Vázquez Departamento de Matemática Aplicada Facultad de Informática Universidad Complutense de Madrid.

Mars Magnetic Field Mars Magnetic Field

Page 13: Panoramic Issues of the Martian Exploration Luis Vázquez Departamento de Matemática Aplicada Facultad de Informática Universidad Complutense de Madrid.

 

MARS INTERIOR: MARTIAN MOONS

 

There are some basic considerations related to Enhancing Digital Maps: 

1.A compilation of the high resolution images obtained by Mars orbiters open the possibilities

to study the parameters as surface slopes, surface roughness, and tectonic break lines of the

Martian Moons.

2.Combination and correlation of the above data from ESA, NASA and ROSCOSMOS

missions would increase the scientific return. The images from different missions, channels

and orbits need to be tied to a common reference frame.

3.In order to make the block adjustments of the images obtained in different orbits to derive

orthoimage mosaics and Digital Terrain Models for Mars and the Martian moons, precise

information, not only about Mars and its satellites orbital motions, but also about the

parameters relating Earth–Mars reference systems are required.

4.To improve the different spatial parameters relating Earth–Mars reference systems by

correlating the Phobos and Deimos shadow passages on images acquired with the Mars

Express orbiter and observations of Martian moons eclipses by the landers Spirit, Curiosity

and the Mars Science Laboratory.

Page 14: Panoramic Issues of the Martian Exploration Luis Vázquez Departamento de Matemática Aplicada Facultad de Informática Universidad Complutense de Madrid.

Eclipses de Fobos

Image Credit: NASA/JPL-Caltech/MSSS

Page 15: Panoramic Issues of the Martian Exploration Luis Vázquez Departamento de Matemática Aplicada Facultad de Informática Universidad Complutense de Madrid.

a-1) Metodología y sofware desarrollados. Objetivos:

1. Diseño de la estrategia observacional para detectar eclipses de Fobos.

2. Validación de los modelos orbitales y parámetros conectando Sistemas de Referencia involucrados

3. Método de determinación de coordenadas a partir de los datos de observación de eclipses

Aspectos científicos:

Page 16: Panoramic Issues of the Martian Exploration Luis Vázquez Departamento de Matemática Aplicada Facultad de Informática Universidad Complutense de Madrid.

a-2) Aplicación en misiones a Marte pasadas y futuras:

4. Oportunidades de observación de Eclipses de Phobos con Mars Science Laboratory

5. Detectar eclipses de Fobos para la misión Metnet Precursor.

6. Análisis de datos de Viking del FMI

Aspectos científicos:

Page 17: Panoramic Issues of the Martian Exploration Luis Vázquez Departamento de Matemática Aplicada Facultad de Informática Universidad Complutense de Madrid.

We compute the times in which the shadow pseudo-ellipse intersects the MSL landing ellipse.

PHOBOS ECLIPSE BEGINNING (UTC) FOR THE MSL ELLIPSE LANDING SITE USING THE TEMPORAL CHRONOGRAM APPROACH.

Observational dates and times for the eclipses to occur over MSL landing ellipse applying the temporal chronogram approach in 2012, 2013 and 2014, when some point of the 25x20 landing ellipse border is within the shadow ellipse.

Page 18: Panoramic Issues of the Martian Exploration Luis Vázquez Departamento de Matemática Aplicada Facultad de Informática Universidad Complutense de Madrid.

Eclipses del 13 y 17 Sept. 2012 han sido detectados por Curiosity- MSL

ECLIPSES OBSERVADOS

Sept. 13, 2012 solar eclipse simulated views from:

= 4.59º S = 137.44º E

Raw Images of the Sept. 13, 2012 solar eclipse (credit:NASA/JPL/Caltech/Malin Space Science Systems ).

Sept. 17, 2012 solar eclipse simulated views from:

= 4.59º S = 137.44º E

Page 19: Panoramic Issues of the Martian Exploration Luis Vázquez Departamento de Matemática Aplicada Facultad de Informática Universidad Complutense de Madrid.

Sept. 13, 2012 eclipse solar

Créditos :Equipo de Estudios Geodésicos de Marte (Astronomía y Geodesia, UCM), composición de imágenes simuladas para el eclipse del día 13 de septiembre de 2012 siguiendo el modelo descrito en Barderas, Romero et al. (*).

Créditos :NASA/JPL-Caltech/MSSS, eclipse solar fotografiado el 13 de septiembre por la MSL.

Las predicciones para los instantes de contacto inicial y final concuerdan con la precisión de las observaciones al nivel de 1 s.

(*) G. Barderas, P. Romero L. Vazquez, J.L. Vazquez-Poletti, and I.M. Llorente. 2012. Opportunities to observe solar eclipses by Phobos with the Mars Science Laboratory. Monthly Notices of the Royal Astronomical Society Vol 426,3195-3200. November 2012

Page 20: Panoramic Issues of the Martian Exploration Luis Vázquez Departamento de Matemática Aplicada Facultad de Informática Universidad Complutense de Madrid.

Planet. Space Sci. (2011), doi:10.1016/j.pss.2011.06.020

ESTRATEGIA PARA OBSERVAR TRANSITOS DE FOBOS en la misión MMPM

DAYTIME during 1h with offsets of 7:657 h

Romero, P., Barderas, G., Vazquez-Poletti, J., Llorente, I., 2011. Spatial chronogram to detect Phobos eclipses on Mars with the MetNet Precursor Lander. Planetary and Space Science 59, 1542–15502011, Planetary and Space Science, 59, 1542.

Page 21: Panoramic Issues of the Martian Exploration Luis Vázquez Departamento de Matemática Aplicada Facultad de Informática Universidad Complutense de Madrid.

Análisis de datos de Viking del FMI

Harri A., Schmidt W., Romero P., Vazquez L., Barderas G., Kemppinen O., Aguirre C., Vazquez-Poletti J., Llorente I., Haukka H., Paton M., 2012. Phobos eclipse detection on Mars: theory and practice. In Reports 2012:2, Finnish Meteorological Institute.

Page 22: Panoramic Issues of the Martian Exploration Luis Vázquez Departamento de Matemática Aplicada Facultad de Informática Universidad Complutense de Madrid.

Aplicaciones

1.Validación de los modelos orbitales y parámetros que conectan los Sistemas de Referencia involucrados

2.Barderas, G., Romero, P., 2012. Observations of Phobos shadow: Analysis of parameters connecting Earth-Mars reference frames. Planetary and Space Science, 10.1016/j.pss.2012.06.008.

2. Método de determinación de coordenadas a partir de los datos de observación de eclipses

Barderas, G., Romero, P., 2012. Inverse Problem of Determining Mars Landers Coordinates Using Phobos Eclipse Observations. Planetary and Space Science, (aceptado)

Page 23: Panoramic Issues of the Martian Exploration Luis Vázquez Departamento de Matemática Aplicada Facultad de Informática Universidad Complutense de Madrid.

• MOLA: Oberst et al. (1998) and Standish and Williams (2009), mean offset less than 3s;• MOLA: Chapront-Touzé (1990), Standish et al. (1992) and Allison and McEwen (2000), less

than 1 s;• MERs: Burkhart (2006), Standish and Williams (2009) and Archinal et al. (2011), nearly null

mean offset.

VERIFICACION DE LOS PARAMETROS UTILIZADOS

Page 24: Panoramic Issues of the Martian Exploration Luis Vázquez Departamento de Matemática Aplicada Facultad de Informática Universidad Complutense de Madrid.

Determinación de coordenadas a partir de los datos de observación de eclipses

Se ha resuelto el problema nolineal de mínimos cuadrados sin constreñimientos asociado:

min con vi residuales.

La búsqueda del mínimo se realiza mediante un proceso iterativo basado en el método de Levenberg-Marquardt:

donde J es la matriz jacobiana y el factor de amortiguamiento. La convergencia del se acelera mediante un método de relajación por bloques.

El problema de determinar la latitud y la longitud de un observador mediante los datos temporales de observación de eclipses se corresponde a la inversión de:

Donde c(ti) representan las efemérides del Sol y Fobos y d sus modelos de tamaño y forma. ti es el instante central del tránsito y ti la duración, para los eclipses i= 1, .., n.

Page 25: Panoramic Issues of the Martian Exploration Luis Vázquez Departamento de Matemática Aplicada Facultad de Informática Universidad Complutense de Madrid.

RESULTADOS NUMÉRICOS

Los resultados numéricos muestran como después de 4 días de observaciones, con un minuto de observaciones cada día para una incertidumbre en elipse de aterrizaje de 25x20 kilómetros, la posición de un módulo marciano puede limitarse a una elipse de 40x60 metros para incertidumbres en la observación de eclipses de 1 segundo. Si una precisión de 0.1 segundos fuera posible, el posicionamiento podría restringirse a 20x15 metros.

Numerical test to study the sensitivity of the observed contact times precision to the coordinate determination

Page 26: Panoramic Issues of the Martian Exploration Luis Vázquez Departamento de Matemática Aplicada Facultad de Informática Universidad Complutense de Madrid.

REFERENCIAS

MODELIZACION DE LOS ECLIPSES DE FOBOSBarderas, G., Romero, P., 2012. Observations of Phobos shadow: Analysis of parameters connecting Earth-Mars reference frames. Planetary and Space Science, 10.1016/j.pss.2012.06.008.Barderas G., Romero P. and Vazquez L, 2012. Phobos Eclipse Observation Opportunities with the Mars Science Laboratory, EPSC Abstracts, Vol. 7 EPSC2012-326. European Planetary Science Congress 2012.Harri A., Schmidt W., Romero P., Vazquez L., Barderas G., Kemppinen O., Aguirre C., Vazquez-Poletti J., Llorente I., Haukka H., Paton M. , 2012. Phobos eclipse detection on Mars: theory and practice. In Reports 2012:2, Finnish Meteorological Institute.Romero, P., Barderas, G., Vazquez-Poletti, J., Llorente, I., 2011. Spatial chronogram to detect Phobos eclipses on Mars with the MetNet Precursor Lander. Planetary and Space Science 59, 1542–1550. Vazquez-Poletti, J.L., Barderas, G., Llorente, I.M., Romero, P., 2010. A model for efficient onboard actualization of an instrumental cyclogram for the Mars Metnet mission on a public cloud infrastructure. In: PARA 2010: State of the Art in Scientific and Parallel Computing. Lecture Notes in Computer Science. Elsevier, 2010.G. Barderas, P. Romero L. Vazquez, J.L. Vazquez-Poletti, and I.M. Llorente. 2012. Phobos Eclipse Observation Opportunities with the Mars Science Laboratory. Mon. Not. R. Astron. Soc.496, 3195-3200 (2012).

APLICACIONES DE LOS ECLIPSES DE FOBOSBills, B., Neumann, G.A., Smith, D., Zuber, M., 2005. Improved estimate of tidal dissipation within Mars from MOLA observations of the shadow of Phobos. Journal of Geophysical Research 110 (E07004). Murray, B., Naraeva, M., Selivanov, A., Betts, B., Svitek, T., Kharlamov, V., Romanov, A., Santee, M., Gektin, X., Fomin, D., Paice, D., Panfilov, A., Crisp, D., Head, J., Murchd, S., Martin, T., 1991. Preliminary assessment of Termoskan observations of Mars. Planet Space Science 39, 237–265. Christou, A.A., 2002. Lander position determination on Mars using Phobos transits: application to Beagle 2. Planetary and Space Science 50, 781–788. Haberle, R.M., 1991. Atmospheric effects on the remote determination of thermal inertia on Mars. Icarus 90, 187–204. Willner, K., Oberst, J., Wählisch, M., Matz, K.D., Roatsch, T., 2007. Observations of Phobos and its shadow: implications for the Phobos orbit. In: SPP 1115 Colloquium 2007 (4 Colloquium).

Page 27: Panoramic Issues of the Martian Exploration Luis Vázquez Departamento de Matemática Aplicada Facultad de Informática Universidad Complutense de Madrid.

MARS GLOBAL SURVEYOR

Page 28: Panoramic Issues of the Martian Exploration Luis Vázquez Departamento de Matemática Aplicada Facultad de Informática Universidad Complutense de Madrid.

MARS EXPRESS (Cámara estereoscópica HRSC , 2-10 m/pixel) Collapse in en Meseta “Hebes Chasma”

Page 29: Panoramic Issues of the Martian Exploration Luis Vázquez Departamento de Matemática Aplicada Facultad de Informática Universidad Complutense de Madrid.

General Data Basis

29

Page 30: Panoramic Issues of the Martian Exploration Luis Vázquez Departamento de Matemática Aplicada Facultad de Informática Universidad Complutense de Madrid.

Some Remarks about the Data

• Data of Pathfinder as a good Laboratory

• Eclipses of Phobos: MetNet, Viking, Pathfinder, Phoenix.

• Viking Data. MSL. ExoMars 2018

• Cloud Computing: Transversal instrument• European Project

Page 31: Panoramic Issues of the Martian Exploration Luis Vázquez Departamento de Matemática Aplicada Facultad de Informática Universidad Complutense de Madrid.

Format of the Data• The good news.

– Huge amounts of data are readily avalable.– Data is well documented and ordered.– Data is easily readable (plain text files).

• The bad news– Data is spreaded over many files.

• A Mars day is stored in several files placed usually in several different folders (sessions).

– Data is not uniquely sampled. • Sampling rate can vary from 1 to 4 seconds.

• Tools has been developed to manage these data sets• Extracting usable time scales (Sun, hour)• Unify sampling rates (by average of higher rates).• Compute relevant quantities.

Page 32: Panoramic Issues of the Martian Exploration Luis Vázquez Departamento de Matemática Aplicada Facultad de Informática Universidad Complutense de Madrid.

Example

Pressure in Millibars. Duration 15 mins, one sample per second.

Page 33: Panoramic Issues of the Martian Exploration Luis Vázquez Departamento de Matemática Aplicada Facultad de Informática Universidad Complutense de Madrid.

Data Analysis

• Three main sets of analysis are being applied.– Data adjust to a given partial differential

equation.– Statistical Analysis– Spectral, Wavelet and Tomographic analysis.

Page 34: Panoramic Issues of the Martian Exploration Luis Vázquez Departamento de Matemática Aplicada Facultad de Informática Universidad Complutense de Madrid.

Adjust to a given partial differential equation

• We are now focusing on this method.

• We assume that the data can be modelled by a known homogeneous partial differential equation with unknown parameters.

• Following a finite difference scheme this parameters can be stimated by an highly overdimensionated linear equations system.

Page 35: Panoramic Issues of the Martian Exploration Luis Vázquez Departamento de Matemática Aplicada Facultad de Informática Universidad Complutense de Madrid.

Statistical Analysis• The usual techniques of statitiscal analysis will

be taken in account.– Reduction of dimensionality (PCA).– Linear Modelling (ARIMA Models)– Linear and Nonlinear Regression

• Previous studies carried by us show that data is most nonlinear, showing to fit better to a cubic approximation.

– And many others.

• But with a difference….– Existing statistical packages (R, SPSS, Matlab) are

not suitable for cloud computing, we are developing our own methods and routines.

Page 36: Panoramic Issues of the Martian Exploration Luis Vázquez Departamento de Matemática Aplicada Facultad de Informática Universidad Complutense de Madrid.

Spectral, Wavelet and Tomographic Methods

• Analysis of stationarity, frequency and resolution.– Previous studies show that data are mainly

nonstationary and multi resolution.

• The use of a tomographic analysis of the data.– Tomographic analysis consists on using as

projecting basis the eigenvectors of linear combinations of operators (time-frequency, time-resolution, time-conformal).

• Dust Devils and plasma effects: size and duration

Page 37: Panoramic Issues of the Martian Exploration Luis Vázquez Departamento de Matemática Aplicada Facultad de Informática Universidad Complutense de Madrid.
Page 38: Panoramic Issues of the Martian Exploration Luis Vázquez Departamento de Matemática Aplicada Facultad de Informática Universidad Complutense de Madrid.
Page 39: Panoramic Issues of the Martian Exploration Luis Vázquez Departamento de Matemática Aplicada Facultad de Informática Universidad Complutense de Madrid.

www.hpcinthecloud.com

Page 40: Panoramic Issues of the Martian Exploration Luis Vázquez Departamento de Matemática Aplicada Facultad de Informática Universidad Complutense de Madrid.

2030: LANDING A HUMAN ON MARS?Historical Periodicity over the last 500 years:

Major new steps in exploration seem to take place in approximately 60-year intervals

• 1492: America• 1550: Pacific Islands• 1610: Japan• 1670: Australia• 1730: Siberia• 1790: Himalayas• 1850: Africa• 1910: Poles Polos • 1969: Moon

2030: Mars?

“Towards Mars” Raud Publishing (2006)

Page 41: Panoramic Issues of the Martian Exploration Luis Vázquez Departamento de Matemática Aplicada Facultad de Informática Universidad Complutense de Madrid.

2030: LANDING A HUMAN ON MARS?Historical Periodicity over the last 500 years:

Major new steps in exploration seem to take place in approximately 60-year intervals

• First manned space flight in 1961.

• 1961: President J.F. Kennedy declared that the USA would land a human on the Moon before the start of 1970.

• MARS: We have twice as much time for preparing for the launch as was ever allocated in the Apollo Moon programme. We have more experience in flights.

Page 42: Panoramic Issues of the Martian Exploration Luis Vázquez Departamento de Matemática Aplicada Facultad de Informática Universidad Complutense de Madrid.

Mars, Solar System, Milky Way, 2132

Dear Mom and Dad,

Greetings from the red planet ! I am having a wonderful time. Yesterday we

had to go 2 meters underground for a couple of hours due to a « solar proton

event ». Very cool !!!

The hotel was super professional about security procedures and organized a

special dinner for us.

Wish you were here.

Love, Susie

P.S.: Please can you wire me some more money. I would liketo perform an EVA

next week, but the price is a bit higher than what I thought it would be.

Thanks.

EVA = Extra Vehicular Activity

Page 43: Panoramic Issues of the Martian Exploration Luis Vázquez Departamento de Matemática Aplicada Facultad de Informática Universidad Complutense de Madrid.

Thank You Very Much !