Mark Beckman - Flight Dynamics MB-1

Lunar Flight Dynamics

Mark Beckman

July 12, 2012

LRO Mission

• Lunar Reconnaissance Orbiter (LRO) mission launched on June 18, 2009

• It is still orbiting the moon today

Mark Beckman - Flight Dynamics MB-2

30 x 216 km Quasi-frozen Orbit: up to 60 days

Lunar Orbit Insertion Sequence (4): 2-5 days 50 km Polar Mapping Orbit: at least 1 year

Minimum Energy Lunar Transfer: ~ 4 days

LRO Mapping Orbit

Mark Beckman - Flight Dynamics MB-3

How do you get to the Moon?

• Need a really big rocket to shoot you from the Earth to the Moon

• But it’s not that simple…– You must lead the Moon or when you arrive at the Moon 3-5 days

later, the Moon won’t be there anymore (must know the precise time-of-flight to get to the Moon)

– Remember that you are on a spinning sphere, so you only have one (sort of) opportunity per revolution (day) to shoot in the right direction

– You want to shoot with the minimum amount of energy that will get you there because when you get there you will have to put on the brakes to enter lunar orbit (no refueling options in space!)

Mark Beckman - Flight Dynamics MB-4

Further Complications

• To complicate things, the Moon’s orbit is not circular - it’s elliptical or elongated so the distance from the Earth to the Moon is not constant– So your minimum energy to get to the Moon is a function of how far

away the Moon is at arrival

• Additionally, this is not a 2D problem, it’s 3D– The Earth spins on an axis tilted 23.5 degrees from the ecliptic plane– The Moon’s orbit is inclined 5 degrees from the ecliptic plane– You launch from a fixed latitude on the Earth

Mark Beckman - Flight Dynamics MB-5

Opportunities to Get to the Moon

• When you solve all that, you get one fixed location per day you can insert onto your cislunar trajectory– You actually get two launch opportunities per day, both of which put

you at the same location above

• Now you have your two solutions per day to get to the Moon but there might be other constraints– You might have shadows – the spacecraft flies into the Earth’s

shadow. You might have to discard these opportunities.– The cost to insert at the Moon is a function of orbital geometry at

arrival. You might have to discard days that are too expensive fuel-wise.

– You might have restrictions on your final orbit. Lighting restrictions (ala LRO) would limit you to two chances per month, each chance being three consecutive days.

Mark Beckman - Flight Dynamics MB-6

Mark Beckman - Flight Dynamics MB-7

TLI Quadrants

Short coast solutionsfor southern latitude TLIs

Long coast solutionsfor southern latitude TLIs

Long coast solutionsfor northern latitude TLIs

Short coast solutionsfor northern latitude TLIs

Launch

MECO-1

Two TLI locationsShort/Long coast

Mark Beckman - Flight Dynamics MB-8

Short & Long Coast

LRO Images

Mark Beckman - Flight Dynamics MB-9

Shackleton Crater

Mark Beckman - Flight Dynamics MB-10

Mark Beckman - Flight Dynamics MB-11

• Beta-earth at insertion is relatively fixed (~80 deg)• Beta-sun at insertion is function of lunar phase• Sun circles moon system once/year after insertion• Two (2) extreme lighting conditions (the solstices)• Prime opportunities for looking at permanently light/shadowed regions• Need to be near beta-sun-0 at each of the solstices

Sun @ Summer Solstice1.4 deg “above” equator

PL? PS?

Sun @ Winter Solstice1.4 deg “below” equator

(South Pole Views)

Moon

Orbit Plane 1 year

Earth

1 month

Moon

Insertion Plane

Launch Window Overview

Lunar Orbit Insertion

• You have now planned how to GET TO the Moon, now you have to get into orbit about it– Lunar Orbit Insertion (LOI) is a retrograde maneuver (braking) that

removes a lot of energy– Your spacecraft’s thrusters are limited in how much braking they can

apply• This might affect your trajectory design since LOI maneuver is not

anywhere near instantaneous (called finite maneuver modeling)

– Now that you are at the Moon, the Moon itself causes problems …• Depending on your transfer trajectory, your LOI may not be visible to

Earth

• Depending on the time of year, LOI may not be in sunlight (spacecraft are almost all solar powered)

– Lastly, what do you do if something goes wrong? The entire mission success depends on achieving lunar orbit

Mark Beckman - Flight Dynamics MB-12

LRO LOI

Mark Beckman - Flight Dynamics MB-13

Mark Beckman - Flight Dynamics MB-14

10 Day Recovery Maneuver

• Deep Space Maneuver (DSM) must be performed within 10 days of lunar swingby

• Approximately 90 day transfer to 2nd lunar encounter• Additional ΔV cost: 300 m/sec• Polar orbit can be achieved

Mark Beckman - Flight Dynamics MB-15

LOI Interrupted Late

4035

30

25

20

15

10

50

Burn Time (min)

Anything > 20 min: Successful LOISmall overall ΔV penaltyNo impact to primary mission

You’re at the Moon now … but there’s more

• Once you get into a low lunar orbit, you’d think you might be done– There is no atmosphere to slow the spacecraft down– There is no oblateness which causes orbital precession around the

Earth

• But low lunar orbits are not stable, they drift– The drift is in the eccentricity or elongation of the orbit– The drift is periodic but eccentricity generally increases– Eventually, the periapsis (or closest approach to the Moon) will

impact the surface and your mission is over– So, you must routinely control your spacecraft (stationkeeping) to

maintain your orbit

Mark Beckman - Flight Dynamics MB-16

Mark Beckman - Flight Dynamics MB-17

Stationkeeping

Mark Beckman - Flight Dynamics MB-18

SK ΔV 1SK ΔV 2

Point every ascending nodeLunar longitude labeled

Stationkeeping Phase Plot

LRO Low Periapsis Cycle

Mark Beckman - Flight Dynamics MB-19

LRO-LCROSS

Mark Beckman - Flight Dynamics MB-20

Lunar CA

Mark Beckman - Flight Dynamics MB-21

LRO MOC

Mark Beckman - Flight Dynamics MB-22

References

• http://lunar.gsfc.nasa.gov/• http://nssdc.gsfc.nasa.gov/planetary/lunar/• http://lcross.arc.nasa.gov/• http://www.nasa.gov/mission_pages/LADEE/main/• http://science.nasa.gov/missions/grail/

Mark Beckman - Flight Dynamics MB-23