Seminar 6 !Apollo and the Space Race!

Orbit Transfer, Interplanetary Travel!FRS 112, Princeton University!

Robert Stengel"

Copyright 2015 by Robert Stengel. All rights reserved. For educational use only.!http://www.princeton.edu/~stengel/FRS.html! 1!

The Shape of Things to Come !Prologue of “A Man on the Moon”!

Fire in the Cockpit!The Office!

First Around the Moon: The Decision!Impulsive Orbit Transfer"Interplanetary Travel: !"

Understanding Space, Ch 6, Sec 7.1, 7.2"

2!

March 22, 1952!

Trouble in the Spacecraft:

Ejection Capsule"

3!

Advancing Toward “MAD”"!# Jefferson: State and society natural adversaries"!# Eisenhower Republicans: Government

intervention as a necessary evil"!# Democrats: Stevenson doves and Symington

hawks"!# Warfare had become politicized and democratized"!# Nuclear weapons changed the nature of warfare

forever – did they?"!# “Mutual assured destruction” vs. survivable

nuclear war"!# Proliferation of “Think Tanks”"!# Space, a “new frontier” for strategy"

4!

Increased Government Spending"!# 1958-1961: “Reinvigoration of life” in “symphony

of protest”"!# “Intensified exploration of brainpower”"

!# Seaborg Report"!# Consensus on need for vastly increased federal

spending and power"!# Ike didn’t buy it"!# Impacts of the 1960 Presidential election"!# U-2 flights found no deployed Soviet ICBMs"!# SAC and CIA still provided defensive wall"!# Reconnaissance satellites launched in profusion"!# Project Mercury as a “stop-gap measure” before

Apollo?"!# Hardly!"

5!

Corona, Discoverer, KH-1 to KH-4"

6!https://www.youtube.com/watch?v=9jOGicfF_vQ!

7!

Implications of the “Missile Gap”"!# Follow-on to Mercury required F-1 engine (?) "

!# Hardly!"!# Project Gemini didn’t need it"

!# But F-1 engine was critical for Saturn V"!# Missile gap myth used to advantage during

“critical years”"!# After Republicans lost 1960 election,

Eisenhower"!# killed the NASA Apollo Program"!# increased funding for USAF spy satellites"

!# Importance of a non-secret civilian space program"

!# As Ike wrote his Farewell Address, JFK and staff planned for the New Frontier"

8!

USAF Reconnaissance Satellites"

9!

KH-7 Gambit 1! KH-8 Gambit 3!

KH-9 Hexagon!

Cold War vs. Open Space Policy"!# Sputnik made Cold War “total”"!# Impact confusing at first"!# Preventing military from going “hog wild”"!# Space policy should shield spy satellites,

other military systems"!# Open space policy real but disingenuous in

part"!# Flight to the Moon, a self-justifying feat"!# Big technology not inherently un-American,

inevitable replacement for individual innovation"

!# Ike: “Military hero who revolted against war”"!# Edwin Land: “More and more we tend to

resemble the Soviets”"

10!

Destination Moon"!# Kennedy men: "The generation that fought the war...”"!# Eisenhower: Little faith in centralized management"!# 1958: LBJ’s National Aeronautics and Space Council"!# Robert Kerr: senator, oil millionaire"!# Project Mercury: Weisner committee: crash program

to put man in space unjustifiable"!# NASA’s focus"!# USAF Space Study Committee"

11!

Politics and Advice"!# USAF expectations "!# Feb 1961: Webb finds BoB in dark about space

programs, returns to JFK in March"!# Mar 1961: Weisner Report "!# Lloyd Berkner: Visionary statements"!# JFK reaction to Gagarin orbit, Bay of Pigs (4/61)"!# Johnson report, only one possible conclusion "!# LBJ worked on Webb for backup "!# Webb-McNamara report"!# Health of aerospace industry"!# Congress: $20B on command technology for

political goal"

12!

All Constituencies Onboard"!# "Of all those who contributed to the moon decision, the

ones farthest in the background were the engineers of Langley and Goddard and Marshall""

!# Parallels to Constantine's conversion to Christian church"

!# Kennedy years: Space policy and image makers"!# Apollo: Greatest peace-time commitment by Congress

in history"!# McNamara imposed strict management reforms at the

Pentagon "!# Playing off NASA against the aerospace industry"!# Keeping NASA alive without paying from the DoD

budget"

13!

“We Choose to Go to the Moon …” "Rice University, Texas, September 12, 1962!

14!

Project Apollo!

15!

Pre-Lunar Module Lander Concepts"

16!

Evolution of the Lunar Module"

17!

William Michael, ‘48, *67 (1926 - )"

John Houbolt (1919 - )"

Yuri"Kondratyuk (1897-1942)"

18!

Enchanted Rendezvous*"!# Lunar Exploration Working

Group"!# Bill Michael’s (‘48) paper on

parking orbit"!# Rendezvous committees"!# Houbolt’s 1st crusade"!# Anti-lunar-rendezvous sentiment"!# Space Task Group’s skepticism"!# Mounting frustration"!# Kennedy’s commitment"!# 1st letter to Seamans"!# A voice in the wilderness"!# Decision to use LOR "

19!* NASA Monographs in Aerospace History Series #4, 1999 !

Apollo Launch Vehicles!

Sub-Orbital Test!

Sub-Orbital, Orbital Test! Orbital Test!

Lunar Missions!

20!

Little Joe II, 1963-1966!!# Unmanned test of

abort escape system"!# 5 flights"!# 9 solid-rocket motors"

!# 5 Recruit (Boost)"!# 2 Algol (Sustainer)"!# 2 Algol (2nd stage)"

!# Sub-orbital, 120,000-ft apogee"

!# One unplanned low-altitude abort when rocket disintegrated"

!# All abort tests successful"

21!

Saturn I, 1961-1965!!# Unmanned test of the

launcher"!# 10 flights"

!# 4 with live S-I 1st stage + ballast, sub-orbital"

!# 6 with S-I and S-IV 2nd stage, to orbit"

!# 8 Redstone tanks clustered around a Jupiter tank in S-1 (V-2 heritage)"

!# 5 CSM “boilerplates” orbited "

!# 3 Pegasus satellites orbited "

SA-1!

22!

Saturn IB, 1966-1975!!# 9 launches"

!# Uprated S-I and S-IV stages"!# AS-201, -202: sub-orbital"!# AS-203: orbital"!# AS-204: Apollo 1: Block 1, Jan

1967, no launch, loss of crew (Grissom, White, Chaffee)"

!# No Apollo 2 or 3"!# Apollo 5: Jan 1968, LM test

(unmanned)"!# Apollo 7: Block 2, Oct 1968, 1st

manned flight, (Schirra, Eisele, Cunningham)"

!# 3 flights to SkyLab, 1973"!# Docking with Soyuz, 1975" 23!

“Cluster’s Last Stand”" 24!

… and Saturn V 3rd stage" 25!

Saturn V, 1968-1975!!# New 1st and 2nd stages"!# S-IVB became 3rd stage"!# Apollo 4, 6: Unmanned"!# Apollo 8: 1st to the Moon"!# Apollo 9: orbital"!# Apollo 10: 2nd to the Moon"!# Apollo 11: 1st lunar landing "!# Apollo 12: 2nd lunar landing"!# Apollo 13: aborted lunar

mission"!# Apollo 14-17: successful

lunar missions"!# Skylab launch (2 stages)"

26!

Saturn V in Princeton Stadium"

27!

28!

29!

30!

31!

A MAN ON THE MOON!THE VOYAGES OF THE APOLLO

ASTRONAUTS!

32!

Charles “Pete” Conrad, ’51"(1930-1999)"

33!

Launch Complex 34"

34!

Apollo 1 (AS-204) Fire !January 27, 1967!

35!

White! Grissom! Chaffee!

Apollo 7!October 11, 1968!

36!

Eisele!Schirra!

Cunningham!

Apollo 8 !December 21-27, 1968!

Trans-Lunar Injection"

Coast"

Coast"

Reentry"

•# Originally planned to be an Earth-orbit mission"•# Repurposed to be 1st manned flight to the moon, without LM"•# 6-day mission duration"•# Free-return trajectory possible with no further propulsion

after Trans-Lunar Injection"

Moon’s"“Sphere of Influence”"

37!

Apollo 8 Entered Lunar Orbit"•# BUT a more ambitious mission was pursued"•# Service Propulsion System was fired on far side

for Lunar-Orbit Insertion; no free return"•# SPS had to fire again on far side to return to Earth"

38!

Why Was the Apollo 8 Mission Changed on Such Short Notice?!

39!

CIA KH-8 GAMBIT Reconnaissance Satellite, August 1968"

40!

Racing Apollo: The Russian Perspective!

The Odds Were Enormous!

41!

Soviet Lunar Program"!# Intense secrecy"!# Decision to build a manned Moon rocket, N-1"!# Large investment in rubles absent"!# Disarray in central planning of the project"!# Competing design bureaus wasted resources"

!# Korolev"!# Glushko"!# Chelomei"

!# Gave away their lead in rocket technology"!# Inadequate testing of the N-1 launcher"!# The down side of autocratic technocracy"

42!

Developing the N-1 Rocket"

43!

Soviet Manned Lunar Flight Program!(1961-1972)"

•# N-1 Rocket, designed by Sergei Korolev"–# 4 launches (unmanned), none successful"–# 2nd attempt produced largest non-nuclear explosion in history"

N-1!Soyuz 7K-LOK,

2-man CSM!

LK, 1-man Lunar Lander!

44!

N-1 5L Rocket Launch, July 1969"

N-1!

Oxygen pump explosion, 5-9 sec after launch"29 of 30 engines automatically shut down"

Launch pad destroyed" 45!

Impulsive Orbit Transfer and Adjustment!

46!

Scout Launch Trajectory"•# 4-stage launch to orbit!

–# Three stages burn sequentially, short coast between ignitions"–# 3rd-stage coasts to apogee = perigee of desired orbit"–# 4th-stage burn @ 3rd-stage apogee provides orbit insertion"

•# Each stage has high thrust and short burn time"•# 4th-stage burn time is short compared to orbital period"

47!

"1. BO "2. IGN "2. BO "3. IGN "3. BO "4. IGN "4. BO ""t, sec "41.3 "75.3 "115.0 "120.0 "159.4 "479.2 "520.2"v, fps "4,589 "3,932 "10,371 "10,312 "17,648 "15,974 "27,036"h, nm "9.02 "2l.40 "4l.10 "44.30 "74.10 "230.40 "230.40"

Assumptions for Impulsive Maneuver"

•# Instantaneous change in velocity vector"

•# Negligible change in radius vector"

•# Therefore, new orbit intersects old orbit"•# Velocities different at the intersection"

v2 = v1 + !v rocket

r2 = r1

48!

Geometry of Impulsive Maneuver"

49!

v1 =!x!y!z

!

"

###

$

%

&&&1

=

vxvyvz

!

"

####

$

%

&&&&1

=V cos' cos(V cos' sin()V sin'

!

"

###

$

%

&&&1

v2 =!x!y!z

!

"

###

$

%

&&&2

=

vxvyvz

!

"

####

$

%

&&&&2

=V cos' cos(V cos' sin()V sin'

!

"

###

$

%

&&&2

!v =!vx!vy!vz

"

#

$$$$

%

&

''''

=

vx2 ( vx1( )vy2 ( vy1( )vz2 ( vz1( )

"

#

$$$$$

%

&

'''''

Change in velocity magnitude, |v|, vertical flight path angle, #, and horizontal flight path angle, $!

Required #v for Impulsive Maneuver"

50!

!v =!vx!vy!vz

"

#

$$$$

%

&

''''

=

vx2 ( vx1( )vy2 ( vy1( )vz2 ( vz1( )

"

#

$$$$$

%

&

'''''

!v rocket =!Vrocket"rocket# rocket

$

%

&&&

'

(

)))=

!vx2 + !vy

2 + !vz2( )rocket1/2

sin*1 !vy!vx

2 + !vy2( )1/2

+

,--

.

/00rocket

sin*1 !vz!V

+,-

./0 rocket

$

%

&&&&&&&&

'

(

))))))))

Single Impulse Orbit Adjustment"Coplanar (i.e., in-plane) maneuvers"

•# Change energy"•# Change angular

momentum"•# Change eccentricity"

E = 12v2 ! µ r = e2 !1( )µ2 h2

h =µ2 e2 !1( )

E=

µ2 e2 !1( )v2 2 ! µ r

e = 1+ 2Eh2 µ2

vnew ! vold + !vrocket = 2 Enew + µ r( )= 2 enew

2 "1( )µ2 hnew2 + µ r#$ %&

!vrocket = vnew " vold

•# Required velocity increment"

51!

Single Impulse Orbit Adjustment"Coplanar (i.e., in-plane) maneuvers"

•# Change semi-major axis "–# magnitude"–# orientation (i.e., argument

of perigee); in-plane isosceles triangle"

anew =hnew2 µ1! enew

2

•# Change apogee or perigee"–# radius"–# velocity"

rperigee = a 1! e( )rapogee = a 1+ e( )

vperigee =µa1+ e1! e

"#$

%&'

vapogee =µa1! e1+ e

"#$

%&' 52!

In-Plane Orbit Circularization"•# Initial orbit is elliptical, with apogee radius equal to

desired circular orbit radius"Initial Orbit

a = rcir + rinsertion( ) 2

e = rcir ! rinsertion( ) 2a

vapogee =µa

1! e1+ e

"#$

%&'

vcir = µ 2rcir

! 1acir

"#$

%&'= µ 2

rcir! 1rcir

"#$

%&'= µ

rcir

•# Velocity in circular orbit is a function of the radius"–# “Vis viva” equation:"

!vrocket = vcir " vapogee•# Rocket must provide the

difference"53!

Single Impulse Orbit Adjustment"Out-of-plane maneuvers"

•# Change orbital inclination"•# Change longitude of the ascending node"•# v1, #v, and v2 form isosceles triangle

perpendicular to the orbital plane to leave in-plane parameters unchanged "

54!

Change in Inclination and Longitude of Ascending Node"(from Sellers, Understanding Space)!

Inclination! Longitude of Ascending Node!

55!

Escape from a Circular Orbit"•# Velocity in circular

orbit is a function of the radius"–# “Vis viva” equation:"

vcir = µ 2rcir

! 1a

"#$

%&'= µ

rcir

•# Minimum escape trajectory shape is a parabola"

56!

Escape from a Circular Orbit"

•# Semi-major axis goes to $"•# Total specific energy of the

parabolic orbit is zero"Epar = ! µ

2a a"#$ "$$ 0

•# Eccentricity of the parabolic orbit is one" e = 1+ 2

Epar pparµ

= 1

•# Perigee velocity of the parabolic orbit" vppar = µ 2

rppar! 1a

"

#$

%

&' = 2µ

rppa, a()

57!

Velocity Increment Required for Escape"

Velocity increment supplied by the spacecraft"

!vrocket = vppar " vcir

= 2µrcir

! µrcir

= 2 !1( ) µrcir

! 0.414 µ

rcir 58!

Two Impulse Maneuvers"Transfer to Non-

Intersecting Orbit" Phasing Orbit"

•# 1st #v produces target orbit intersection"

•# 2nd #v matches target orbit"•# Minimize (|#v1| + |#v2|) to

minimize propellant use"

•# Rendezvous with trailing spacecraft in same orbit"

•# At perigee, increase speed to increase orbital period"

•# At future perigee, decrease speed to resume original orbit"

59!

Hohmann Transfer between Coplanar Circular Orbits"(Outward transfer example)!

Transfer Orbit

a = rcir1 + rcir2( ) 2

e = rcir2 ! rcir1( ) 2a

vptransfer =µa

1+ e1! e

"#$

%&'

vatransfer =µa

1! e1+ e

"#$

%&'

vcir1 =µrcir1

vcir2 =µrcir2

Thrust in direction of motion at transfer perigee and apogee"

60!

Outward Transfer Orbit Velocity Requirements "

!v1 = vptransfer " vcir1

= vcir12rcir2

rcir1 + rcir2"1

#

$%

&

'(

!v2 = vcir1 " vatransfer

= vcir2 1"2rcir1

rcir1 + rcir2

#

$%

&

'(

vcir2 = vcir1rcir1rcir2

!vtotal = vcir12rcir2

rcir1 + rcir21"

rcir1rcir2

#

$%&

'(+

rcir1rcir2

"1)

*++

,

-..

#v at 1st Burn" #v at 2nd Burn"

Hohmann Transfer is energy-optimal for 2-impulse transfer between circular orbits"

61!

Rendezvous Requires Phasing of the Maneuver"

(from Sellers, Understanding Space) "

•# Transfer orbit time equals target’s time to reach rendezvous point"

62!

Interplanetary Travel!

63!

Launch Opportunities for Fixed Transit Time: The Synodic Period"

•# Synodic Period, Sn: The time between conjunctions"–# PA: Period of Planet

A"–# PB: Period of Planet

B"•# Conjunction: Two

planets, A and B, in a line or at some fixed angle"

Sn = PAPBPA ! PB

64!

Launch Opportunities for Fixed Transit Time: The Synodic Period"

PlanetSynodic Period with respect to Earth, days Period

Mercury 116 88 daysVenus 584 225 daysEarth - 365 daysMars 780 687 daysJupiter 399 11.9 yrSaturn 378 29.5 yrUranus 370 84 yrNeptune 367 165 yrPluto 367 248 yr

65!

Transfer Orbits and Spheres of Influence"•# Sphere of Influence (Laplace):"

–# Radius within which gravitational effects of planet are more significant than those of the Sun"

•# Patched-conic section approximation"–# Sequence of 2-body orbits"–# Outside of planet’s sphere of

influence, Sun is the center of attraction"

–# Within planet s sphere of influence, planet is the center of attraction"

•# Fly-by trajectories dip into intermediate object s sphere of influence for gravity assist"

66!

Interplanetary Mission Planning"•# Example: Direct Hohmann

Transfer from Earth Orbit to Mars Orbit (No fly-bys)"

1)% Calculate required perigee velocity for transfer orbit - Sun as center of attraction: Elliptical orbit"

2)% Calculate #v required to reach Earth’s sphere of influence with velocity required for transfer – Earth as center of attraction: Hyperbolic orbit"

3)% Calculate #v required to enter circular orbit about Mars, given transfer apogee velocity – Mars as center of attraction: Hyperbolic orbit"

67!

Solar Orbits"•# Same equations as used for earth-referenced orbits"

–# Dimensions of the orbit"–# Position and velocity of the spacecraft"–# Period of elliptical orbits"–# Different gravitational constant"

µSun =1.3327 !1011km3 /s2

68!

Solar System Spheres of Influence"

for mPlanet

mSun

<<1, rSI ! rPlanet!SunmPlanet

mSun

"#$

%&'

2 5

Planet" Sphere of Influence, km"Mercury" 112,000"Venus" 616,000"Earth" 929,000"Mars" 578,000"Jupiter" 48,200,000"Saturn" 54,500,000"

69!

70!

Hyperbolic Orbits"

E = v2

2! µr= ! µ

2a, "a < 0

Orbit Shape" Eccentricity, e" Energy, E"Circle" 0" <0"Ellipse" 0 < e <1" <0"Parabola" 1" 0"Hyperbola" >1" >0"

v r!"# !## v"

$E" = v"2

2, and v" = % µ

a or a = % µ

v"2

Velocity remains positive as radius approaches $"

71!

Hyperbolic Encounter with

a Planet "•# Trajectory is

deflected by target planet s gravitational field"

•# Velocity w.r.t. Sun is increased or decreased"

Kaplan!

! : Miss Distance, km" : Deflection Angle, deg or rad

72!

Hyperbolic Orbits"

r = p1+ ecos!

=a 1" e2( )1+ ecos!

cos! = 1ea 1" e2( )

r"1

#

$%%

&

'((

Asymptotic Value of True Anomaly!

! r"#$ %$$!#

!# = cos&1 & 1e

'()

*+,

Polar Equation for a Conic Section"

73!

Hyperbolic Orbits"

h = Constant = v!"

= µp = µa 1# e2( ) = µ2 e2 #1( )v!

2

e = 1+ 2h2E

µ2 = 1+ v!4"2

µ2

rp = a 1! e( ) = µv"2 e!1( )

e = 1+rpv!

2

µ"

#$

%

&'

Angular Momentum"

Eccentricity"

Eccentricity"

Perigee Radius!

74!

Effect of Target Planet s Gravity on Probe s Sun-Relative Velocity"

Deflection – Velocity Reduction!

75!

Effect of Target Planet s Gravity on Probe s Sun-Relative Velocity"

Deflection – Velocity Addition!

76!

Earth Escape Trajectory "•# #v to increase speed to escape velocity"•# Velocity required for transfer at sphere of

influence"

77!

Planet Capture Trajectory "•# Hyperbolic approach to planet’s sphere of influence"•# #v to decrease speed to circular velocity"

78!

Next Time:!Lunar Missions, Science, & Astronauts: "A Man on the Moon, Ch 3-6, II-IV, 4, 5, 6 "

Suggested Background Reading!Apollo: A Retrospective Analysis, NASA-SP-4503, pp

1-20"Exploration of the Moon (Wikipedia)"

"Lunar Transfer Trajectories"

Understanding Space, Sec 7.2, 7.3"Modern Spacecraft Dynamics & Control, Sec 3.5 (ER)"

79!

Supplemental Material!

80!

Army Ballistic Missile Agency Heavy-Lift Concepts, 1959!

Derivatives of concepts hatched at Peenemünde!

81!

NOT BUILT"

82!