Powered Space Flight - 東京大学PoweredSpaceFlight).pdfPropulsion and Energy Systems; Dec. 7th...

Propulsion and Energy Systems; Dec. 7th (2015)

Powered Space Flight KOIZUMI Hiroyuki

(小泉宏之)

Graduate School of Frontier Sciences, Department of Advanced Energy

& Department of Aeronautics and Astronautics

(基盤科学研究系先端エネルギー工学専攻，工学系航空宇宙工学専攻兼担)


1. Introduction

2. Fundamentals of orbit

Purpose of today’s lecture

Scope of Today’s Lecture

to learn “Powered Space Flight” using electric propulsion by actual orbit examples

3. Examples of powered flights

3.1 HAYABUSA

3.2 DAWN

3.3 Boeing 702SP

Contents

What is

“Powered Space Flight” ?


How to change orbits ?

Adding energy (or velocity) changes the orbits

Energy: depends on the mass

Velocity: as specific energy

Velocity increment, Delta-V (ΔV), is the index of Powered Space Flight

©JAXA

Powered space flight is flight using a propulsion device to control the trajectory by ΔV maneuvers

Propulsion is a device to provide ΔV


Chemical & Electric Propulsion

Chemical propulsion

Electric Propulsion

Chemical E (inside propellant) → Kinetic E

Propulsive device = Device exhausting propellant by adding energy on it = Energy converter (from any source to kinetic energy)

Electrical E (Solar, Nuclear) → Kinetic E

Exhaust V：1 – 4 km/s

Exhaust V：10 – 50 km/s


Chemical & Electric Propulsion

Chemical propulsion

Electric Prouplsion

ΔV: 4– 5 km/s

Exhaust V：3 km/s

Exhaust V：30 km/s

Propellant

Payload = 200–400%

Propellant

Payload = 14–18%

1 ton Car + 150 kg gas

+ 3 ton gas 1 ton Car

1exp

Exhaust

PayloadPropellantv

VMM


Saving propellant

Low cost by decreasing S/C weight

High quality by increasing equipment

Merit of EP 1)


Merit of EP 2)

Electric propulsion gives us freedom to travel

Chemical propulsion

Your journey (orbit) is pre-fixed

You can freely change the journey as you do in the journey on the ground

Electric propulsion

Flexibility & Redundancy are increased

Excessive propellant

My opinion: “True” powered space flight needs

Electric Propulsion


1. Introduction






3.1 HAYABUSA

3.2 DAWN

3.3 Boeing 702SP

Contents


Motion in space

on the ground in space

Free-form path governed by celestial bodies

©JAXA


Equation of Motion

M>>m

Position of the S/C

Thrust

Standard gravitational parameter: 𝐺𝑀

Massive body Spacecraft

: thrust

𝑑2

𝑑𝑡2𝒓 = −

𝜇

𝑟2𝒓 +

𝑭 𝑡

𝑚

𝑀

𝑟

𝑚

𝑭(𝑡)


Two-body Problem w/o thrust

Ellipse Hyperbola Parabola

Three types


Orbit Terminology Apoapsis

Periapsis

a: Semi-major axis

Perigee

Semi-minor axis

Apogee

Apolune Perilune

Perihelion Aphelion

e: Eccentricity ea

Focus Peri Apo

Sun

Earth

Moon


Initial velocity and its orbit

V: small

V: middle

V: large

Ellipse (from apoapsis)

Circle

Ellipse （from periapsis)


Typical trajectory by CP

Orbital period >> Thrusting time

Impulse approximation

Connect the analytical solutions of I.C. problem of Momentum eq.

©JAXA


Typical Trajectories of EP ; Spiral

Tangential thrust

Spiral orbit

Gradual orbit raising/lowering

T = 25 mN Msc = 500 kg 1000 days


Typical Trajectories of EP ; Deform.

Constant Thrust

Eccentricity change

Earth gravity assist Ellipse to/from Circle

T = 25 mN Msc = 500 kg 1000 days

Orbit raising and lowering


1. Introduction






3.1 HAYABUSA

3.2 DAWN

3.3 Boeing 702SP

Contents


HAYABUSA

Feature： Return trip using electric propulsion

Mission: Sample return of a small asteroid

©JAXA


ITOKAWA (small asteroid)

500 m

Orbit specifications

Semi-major axis: Aphelion: Perihelion: Eccentricity: Inclination:

35,000,000 ton

ITOKAWA; the asteroid

1.32 AU 1.70 AU 0.95 AU 0.28 1.6 deg

©JAXA


HAYABUSA’s journey

2003-2004 Delta-V for Earth Gravity Assist

2004-2005 Delta-V for rendezvous with ITOKAWA

2007-2010 Delta-V for reentry to the Earth

ITOKAWA touch down

Some troubles


Trajectory from Earth to ITOKAWA

Earth HAYABUSA

ITOKAWA

Departure (2003, May 9th)

Earth gravity assist (2004, May 19th)

Sun


In the case of free flight

HAYABUSA was launched with hyperbolic excess velocity: 3.2 km/s

Sun orbital velocity: 29.8 km + Initial ΔV 3.2 km/s

Departure

Earth

Spacecraft

Unit is AU (astronomical unit) 1 AU = Sun-Earth distance

= 150 Million km



HAYABUSA orbit on

Earth

Spacecraft

Sun direction

Unit is AU (astronomical unit) 1 AU = Sun-Earth distance

Spacecraft does not meet with the Earth



Earth

Thrust off

Sun direction

With thrust (18 mN average)

Thrust on

HAYABUSA orbit on

Spacecraft meets with the Earth

Gravity assist


Real HAYABUSA orbit

©JAXA

June 24th

July 29th

Aug. 4th

Sep. 3rd

Oct. 2nd

Oct. 29th

Dec. 3rd

in 2003

©JAXA


Earth Gravity Assist

Velocity increment: 4 km/s

Alt. 3700 km

Required accuracy is Position: 1 km Velocity: 1 cm/s

©JAXA


Gravity Assist; Principle

Moving wall


Hyperbolic Trajectory

Hyperbola

ui

uf = R(θ*)ui

θ* Scattering angle

Collision parameter b

bu22

*tan


GA = Velocity Rotation

θ*

ui

Vp

vsc,i

vsc,f

β

ui = vsc,i - Vp

Red arrows: S/C inertial velocity

Black arrows: S/C relative velocity

uf

Green arrow: Planet inertial velocity


Accurate Trajectory Control for GA

Collision parameter: b

Scattering angle: θ*

Gravity assist

Planet velocity

Spacecraft velocity

Orbit scale

Planet scale

1 AU = 150,000,000 km

To get 90 deg scattering b = 4,4000 km (relative V : 3 km/s, Earth)

Accurate Orbit Control is required


Trajectory from Earth to ITOKAWA

Earth HAYABUSA

ITOKAWA

Departure (2003, May 9th)

Earth gravity assist (2004, May 19th)

Sun

©JAXA


Toward the ITOKAWA

Rendezvous

Position & Velocity must be matched

Orbits of two objects must be matched


Toward the ITOKAWA

The semi-major axes

ITOKAWA: 1.32 AU

Hayabusa :1.37 AU (after the GA)

Earth: 1.00 AU

Ion thruster Delta-V : reducing the perihelion (deceleration)

Aphelion matching


Return to Earth

Outward journey

Homeward journey

Rendezvous with ITOKAWA

Reentry to the Earth

Position & velocity must be exactly matched

Only position must be matched

Delta-V requirement is lower Troubles


1. Introduction






3.1 HAYABUSA

3.2 DAWN

3.3 Boeing 702SP

Contents


DAWN

Weight：1250 kg

by NASA JPL DAWN

NSTAR

90 mN ion thruster

3 kW

3100 s

Mission: rendezvous with asteroids

ΔV : 11 km/s (Ion propulsion)

Propellant: 400 kg

©NASA


NSTAR ion engine (NASA)

Deep Space 1(1998): Flyby of comet

Single NSTAR

Demonstration of NSTAR (16 k-hours operation)

DAWN(2007-): Asteroid probe

Three NSTARs NSTAR engine

Thrust 93 mN

Isp 3100 s

Power 2550 W

Efficiency 62 %

Beam D. 29 cm

©NASA

©NASA


Spiral orbit raising

Launch, 2007 Sept.


Earth

Ceres

Vesta Thrust on

Thrust off



・Tangential thrust to the orbit ・Assuming the circular orbit

FVdt

dE

r

μm

r

μmmVE

22

1 2

r

μF

dt

dr

r

μm

22 )/)(( 12

21

mttFV

VVV

Spiral orbit raising requires ΔV equal to the difference between the initial orbit and the final orbit

©JAXA


Let’s estimate the thrust of DAWN

Spacecraft momentum change = given impulse

FTVM SC

DAWN wet mass = 1250 kg Xenon propellant = 425 kg

Get from the orbit and events

kg 1000SCM

km/s 9.11V

? T


Phase-1; from Earth to Mars

Earth

Three thrusting phases

1. Earth departure – Mars gravity assist

600 days = Mars GA (Feb 2009) - Launch (Oct 2007) - Mars period／6

687 days


Phase-2; from Mars to Vesta

Earth


2. Mars gravity assist – Vestra arrival

550 days = Vesta arv. (July 2011) - Mars GA (Feb 2009) - Mars period／6


Phase-3; Vesta to Ceres

Earth


3. Vesta departure – Ceres arrival

950 days = Vesta dept. (July 2012) - Ceres arrv. (Feb 2015)


Let’s estimate the thrust of DAWN

FTVM SC

S/C mass (average)：1000 kg

Estimate: 65 mN

Thrusting time：2100 days (550 + 600 + 950)

ΔV：11.9 km/s

「 John R. Brophy et al.,J. Propul. Power 25(2009)」

Actual: 91 mN


Solar power is decreasing

Earth：1 AU

Ceres： 2.8 AU

Solar power at Ceres is

1/2.82 (= 13%) of Earth

Solar power averaged from Earth to Ceres is 57% of Earth

Estimated: 65 mN

Actual: 91 mN

70% Good estimation!


Very low power near Ceres

Earth

Phase 1+2 (Earth to Vesta)

Phase 3 (Vesta to Ceres)

Spiral ΔV = 1.5 km/s

Period = 950 days

Spiral ΔV = 10.4 km/s

Period = 1150 days

Estimated F = 105 mN

Estimated F = 18 mN

Over 90 mN is caused by initial dV & Mars GA


1. Introduction






3.1 HAYABUSA

3.2 DAWN

3.3 Boeing 702SP

Contents


GEO: Geostationary Earth Orbit

24 hrs/cycle

90 min/cycle

600 km 36000 km

Communication satellite

Broadcasting satellite

©JAXA


Disturbances from Sun and Moon

GEO：on equatorial plane

Sun, moon, planets: on ecliptic plane

Sun and Moon gravity forces are disturbances to GEO S/C


North South Station Keeping

Maintaining the orbit plane requires ΔV of 50 m/s per year

(NSSK: north south stationkeeping)

Eelectric（3000 s）

Chemical (200 s）

Propellant: 50 kg

Propellant: 850 kg

3 ton＋10 year operation


By all EP, mass becomes half

ΔV = 500 + 1500 m/s

1expSatPropellant

eu

VMM

Msat = 2.0 ton

MPropellant = 1.9 ton

MPropellant = 0.14 ton

by Chemical

by Electric


1. Introduction






3.1 HAYABUSA

3.2 DAWN

3.3 Boeing 702SP

Contents

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