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Broseidon: Mission to Mars

(Design Project for MAE146: Planning an Interplanetary Mission)

Design Team Members:

Nicholas Cordero

George Ramos

Teory Gonzalez

Table of Contents Mission Overview .................................………………………..........................................…........2

Spacecraft and Launch .........................................………………………..........................…........3

Parameters.................................………….……………………..........................................…........4

Equations .................................………………………..………..........................................…....5-6

Calculations ................................………………………....................................................….....6-7

Launch Window, Site, and Geometry.…………………….................................................…........7

Interplanetary Transfer ....................………………………................................................…........8

Mission Summary .................................………………………..........................................…........9

Sources and Team Member Contributions ………..............................................….....................10

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Mission Overview

Objective: As the Mars One mission approaches, human settlement on Mars will begin taking

place as early as 2024. In anticipation of mankind's next big leap, many studies and preparations

are in the works including the Broseidon Orbiter mission.

The Broseidon Orbiter, based on the Mars Reconnaissance Orbiter, will be designed and

scheduled to last 2 years upon its arrival on June 13, 2015. The mission’s main goals are to

landscape the terrain for possible settlement sites and collect information regarding Martian

climate including weather and atmospheric conditions in search for hospitable living conditions.

Upon completion of its data collection, the Broseidon Orbiter will serve as a communication

base and navigation system for future landers and atmospheric probes.

Assumptions: For simplification purposes, we will assume that the orbits of Earth and Mars

around the Sun are circular (e=0) and co-planar (i=0º). The method of patched conics and the

two-body theory will be used for the calculations for the interplanetary transfer. We are using a

Hohmann Transfer since this is the most energy efficient transfer, which will require the least

amount of propellant. We are also assuming that the upper stage centaur rocket with the attached

spacecraft is already in a circular orbit; therefore it is not necessary to know the total mass at

launch or compute the required to enter the particular circular orbit. We will assume that the

payload fairing, protecting the spacecraft from the impact of dynamic pressure and aerodynamic

heating during launch through the atmosphere, along with the short interstage adapter has already

been jettisoned and that we do not have to account for these extra masses. (See Figure 1.) The

mass of propellants was always rounded up to the nearest whole number to ensure that there will

be enough propellant for the ∆ burns.

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Spacecraft and Launch Vehicle

Spacecraft: Orbiter based off the Mars Reconnaissance Orbiter

Science Payload: Consists of High Resolution Color Camera, Shallow Subsurface Radar,

Thermal Emission Imaging System, and Climate Sounder.

Engine Isp: 451s using Liquid Hydrogen and Liquid Oxygen

Mass: The amount of propellant needed for the insertion into the Mars circular parking orbit

must be = 37.8% of the total mass of the spacecraft, which was calculated using Equation 8.

Therefore, the total mass at launch for the orbital insertion is 1608 kilograms, consisting of a

200-kilogram science payload, 800 kilograms other dry weight, plus 608 kilograms of propellant.

Launch Vehicle: Atlas V 401 with Centaur Upper Stage

Figure 1.

Engine Isp 2: 451s using Liquid Hydrogen and Liquid Oxygen Mass 2: The amount of propellant needed for the departure from the Earth circular orbit must be

= 55.68% of the total mass of the upper stage centaur and spacecraft, which was calculated

using Equation 7. The upper stage centaur inert mass 2,243kg along with the spacecraft mass of

1608 kilograms leads to total mass of 3,851 kilograms, which means that the propellant mass

must be 4838 kilograms. Therefore, the total mass at launch for departure from the circular

parking orbit is 8689 kilograms.

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Parameters

µM (Gravitational Parameter for Mars) = 42828 km3/s2

µE (Gravitational Parameter for Earth) = 398600 km3/s2

µSun (Gravitational Parameter for Sun) = 132.7x109 km3/s2

RE (Orbital Radius of Earth, i.e., distance from Sun to Earth) = 149.6x106 km

RM (Orbital Radius of Mars, i.e., distance from Sun to Mars) = 227.9x106 km

NM (Mean motion of Mars) = 1.06x10-7

radians/second

NE (Mean motion of Earth) = 1.99x10-7

radians/second

RCPOE (Circular Parking Orbit for Earth) = 6628 km → Corresponds to an altitude of 250 km

RCPOM (Circular Parking Orbit for Mars) = 3640 km → Corresponds to an altitude of 250 km

Direction of hyperbolic asymptote:

RA (Right Ascension) = 12:15:04.63 [HMS]

Declination = 55.9o

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Equations

Equation 1: ϕ (Angular separation required for Hohmann Transfer) = Π-NM*(TH); where

TH (Period for Hohmann Transfer) = and

A (Semi-major axis for Hohmann Transfer) = (RM+RE) / 2

Equation 2: V∞D (Hyperbolic excess speed at departure) = VD – VE; where

VD (Heliocentric velocity of spacecraft at Earth Departure) = and

VE (Velocity of Earth around Sun) =

Equation 3: V∞A (Hyperbolic excess speed at arrival) = VM – VA; where

VA (Heliocentric velocity of spacecraft at Mars Arrival) = and

VM (Velocity of Mars around Sun) =

Equation 4: Δ D (∆ needed for interplanetary departure) = PhypD - VCPOE; where

VPHypD (Periapsis speed of hyperbolic trajectory orbit at departure) = and

VCPOE (Velocity of Circular Parking Orbit for Earth) =

Equation 5: Δ A (∆ needed for interplanetary) = PhypA - VCPOM; where

VPHypA (Periapsis speed of hyperbolic trajectory orbit at arrival) = and

VCPOM (Velocity of Circular Parking Orbit for Mars) =

Equation 6: Δ (Aiming radius) = RCPOM 1+2mM

RCPOMV¥A2

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Equation 7: = *100 % (Percentage of propellant mass needed for Δ D with

upper stage plus spacecraft mass)

Equation 8: = *100 % (Percentage of propellant mass needed for Δ A with

spacecraft mass)

Equation 9: t = q1E -q 2M -f

NE -NM; where

1E (The true anomaly of Earth on March 12, 2014 at 0:00:00: CT) = 1.2113 radians and

2M(The true anomaly of Mars on March 12, 2014 at 0:00:00: CT) = 3.6643 radians

Equation 10: cos(i) = cos(Lat)*sin(Az); where

i (the inclination of the orbit plane which was arbitrarily chosen),

Lat (The latitude of the launch site) = 28.5° and

Az (The azimuth angle) = 44.975°

Equation 11: β (Location of periapsis for departure hyperbola) = cos-1 1

1+RCPOEV¥D

2

mE

æ

è

çççç

ö

ø

÷÷÷÷

Calculations

Equation 1: A=18876x104km, TH=22365247.1s =258.857 days → Φ=44.168

°

Equation 2: VD=32.73km/s, VE=29.78km/s → ∞D=2.943km/s

Equation 3: VA=21.48km/s, VM=24.13km/s → ∞A=2.648km/s

Equation 4: VPHypD=11.35km/s, VCPOE=7.755km/s → Δ D=3.6km/s

Equation 5: VPHypA=5.528km/s, VCPOM=3.43km/s → Δ A=2.10km/s

Equation 6: Δ=7592.6km

Equation 7: = 55.68%

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Equation 8: = 37.8%

Equation 9: t 18067991 41 s 209 12 days 0 5725 years

Equation 10: Lat = 28.5°, Az = 44.975

° → i = 51.6

°

Equation 11: β (Location of periapsis for departure hyperbola) = 29.06°

Launch Window, Site, and Geometry

The date of Broseidon’s departure is scheduled for September 27, 2014 (12:00:00 CT),

launching from the Eastern Test Range (ETR) at the Kennedy Space Flight Center (KSC) in

Cape Canaveral, Florida. This date was chosen by applying Equation 9 to an arbitrary date of

March 12, 2014, obtaining Earth’s and Mars’ true anomalies using JPL’s “Horizons Web-

Interface” website, and adding the resulting time to our initial March 12th date. The launch date

calculated with this method was October 7, 2014. However, the angular separation of October

7th was 51o using JPL’s “Horizons Web-Interface” website, resulting in an 87% match with

Equation 1’s 44.17o angular separation. Using October 7, 2014 as a reference date, a better

launch date of September 27, 2014 (12:00:00 CT) was found to have an angular separation of

49.37o resulting in a 90% match with Equation 1.The angular separation is not the 44.17

o

calculated in Equation 1, but that is due to our assumptions dealing with circular orbits, rather

than a more realistic elliptical orbit.

The KSC lies on a latitude of 28.5o, meaning that the minimum orbit inclination that the

Broseidon Orbiter can experience without a phase change is 28.5o. Using knowledge that the

International Space Station orbits in a plane with an inclination of 51.6o and by applying

Equation 10, an azimuth angle of 44.975o was found for departure in order to be in the same

orbital plane as the International Space Station. The resultant azimuth angle lies within the safety

considerations of launch procedures for a spacecraft leaving from the ETR. The angle of

inclination was chosen due to the already successful missions to the International Space Station,

thus knowing that angle would lead to a feasible azimuth angle.

The direction of hyperbolic asymptote was found using JPL’s “Horizons Web-Interface”

website and changing the settings to generate an ephemeris for both Earth and Mars with an

observer in a geocentric location. The result of the ephemeris led to a Right Ascension of

12:15:04.63 [HMS] and a Declination of 55.9o. The location of periapsis for the departure

hyperbola is β = 29.06° which was calculated using Equation 11.

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Interplanetary Transfer

The Hohmann transfer to Mars will take approximately 258.857 days, or eight and a half

months, departing on September 27, 2014 and arriving on June 13, 2015. Using the patched

conics method, the interplanetary trajectory is divided into three phase which include the

hyperbolic trajectory relative to Earth, the cruise ellipse relative to the sun, and the hyperbolic

trajectory relative to Mars. In the first phase, the required hyperbolic excess speed needed to

escape Earth's sphere of influence and go to Mars is V∞D = 2.943km/s, which was calculated

using Equation 2. With this V∞D, the required delta V needed by the upper stage Centaur to go

from the 250 kilometer altitude circular parking orbit to Mars is Δ D=3.6km/s, and was

calculated using Equation 4. This delta V would also be a prograde burn. The upper stage centaur

will perform this delta V and then jettison, leaving the spacecraft on a cruise ellipse relative to

the sun, which is the second phase. During the second stage, the spacecraft will unfold its solar-

array panels and release its high-gain antenna in order send signals back to Earth reassuring us

that everything on the spacecraft is working fine. There will be no delta V during this second

cruise phase until we reach Mars’s sphere of influence, which is the third phase. The required

hyperbolic excess speed needed to arrive at Mars’s sphere of influence is ∞A = 2.648km/s,

which was calculated using Equation 3. Since the target circular orbit required for the mission is

an altitude of 250 kilometers from Mars surface, the aiming radius required must be

Δ=7592.6km which was calculated using Equation 6 and the delta required from the spacecraft

is Δ A = 2.10km/s which was calculated using Equation 5. Since the spacecraft is going faster

than Mars, a retrograde burn is needed for this particular insertion. Once the spacecraft is in orbit,

the interplanetary transfer will finally be complete and the spacecraft will start its data

acquisition.

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Mission Summary

The Broseidon Orbiter will serve as a remote observer to better our understanding of

Martian climate and geology. More specifically enabling us to find the best possible location for

the future Mars One mission. The mission will last 2 Martian years to later serve as a

communication base and telecommunication system for upcoming Mars missions.

The launch window for the Broseidon mission is limited due to the synodic period of

Mars. Approximately only every 2 Earth years is a mission of this magnitude possible. The

Broseidon Orbiter is set to launch on September 27, 2014 and arrive 259 days later on June 13,

2015. The orbiter will depart using an Atlas V-Centaur launch vehicle. To successfully reach our

target, the Broseidon Orbiter mission will use the energy efficient interplanetary Hohmann

transfer. Assuming simple circular and co-planar orbits, for both Earth and Mars, the mission

trajectory is split into 3 phases: the hyperbolic trajectory relative to the earth, the cruise ellipse

relative to the sun and the hyperbolic trajectory relative to Mars. Upon its arrival the orbiter will

have a circular parking orbit 250 km above the surface of Mars where it will execute its purpose.

Broseiden Orbital Table

Launch Departure Date September 27, 2014

Launch Arrival Date June 15, 2015

Target Orbit 250 kilometers above Mars surface

Total Mass at Departure 8689 kilograms

Total Mass at Arrival 1608 kilograms

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Sources

http://solarsystem.nasa.gov/missions/profile.cfm?Sort=Target&Target=Mars&MCode=Odyssey

&Display=ReadMore

http://solarsystem.nasa.gov/missions/profile.cfm?Sort=Target&Target=Mars&MCode=MRO&D

isplay=ReadMore

http://ssd.jpl.nasa.gov/?horizons

https://www.mars-one.com/

http://www.spaceflight101.com/atlas-v-401.html

http://www.universetoday.com/14889/mars-rotation/

http://nssdc.gsfc.nasa.gov/planetary/factsheet/marsfact.html

http://www.jpl.nasa.gov/news/press_kits/mro-arrival.pdf

http://www.jpl.nasa.gov/news/press_kits/odysseylaunch.pdf

http://www.orbiterwiki.org/wiki/Launch_Azimuth

http://books.google.com/books?id=vpilMLP7OHQC&pg=PA55&lpg=PA55&dq=cape+canavera

l+launch+azimuth&source=bl&ots=8J4vWvSxaf&sig=ZsA_g0qfAXIgwKp5UNa8TqQrmBY&h

l=en&sa=X&ei=zloeU-

yZAYf2oAS1sYCACg&ved=0CEcQ6AEwAw#v=onepage&q=cape%20canaveral%20launch%

20azimuth&f=false

Team Member Contributions

*Nicholas Cordero – Worked on the interplanetary transfer and on the masses of the spacecraft,

centaur, and the amount of propellant needed. Inserted pictures, equations, and the parameters

needed along with the assumptions; writing of mission report

*George Ramos – Research on mission objectives and design; Research and calculations for the

launch window, site, and geometry; Writing of mission report. Worked on the table of contents

and organization of the report.

*Teory Gonzalez – Worked on the objective and mission summary. Also worked on the launch

window, site, and geometry; writing of mission report. Drew the interplanetary picture

containing the Sun, Earth, Mars, and the trajectory for the Hohmann transfer.