Celestial NavigationCelestial Navigation

Getting StartedGetting Started

Amy Hopkins

MaterialsMaterials

Sextant Sextant Watch Watch Nautical AlmanacNautical Almanac HO 249 or HO 229HO 249 or HO 229 Planispheric AstrolabePlanispheric Astrolabe

What We Want to What We Want to KnowKnow

Our location on EarthOur location on Earth

What We ObserveWhat We Observe

Predetermined location of one of Predetermined location of one of the 57 bodies in Space using the the 57 bodies in Space using the Nautical AlmanacNautical Almanac

The exact time using a watchThe exact time using a watch The The altitudealtitude of the astronomical of the astronomical

body using the sextantbody using the sextant

What a Sextant Tells What a Sextant Tells UsUs Sextant Measures an AngleSextant Measures an Angle Breaks those angle measurements into degrees, Breaks those angle measurements into degrees,

minutes, and seconds (1/10)minutes, and seconds (1/10) Each Degree represents 60 minutesEach Degree represents 60 minutes If we take each minute and break it down further into If we take each minute and break it down further into

seconds (60mins x 60seconds) the sextant can give us seconds (60mins x 60seconds) the sextant can give us up to 3600 different readings within any degree.up to 3600 different readings within any degree.

The reading of a Sextant will look like the followingThe reading of a Sextant will look like the following 45˚ 20.2 minutes45˚ 20.2 minutes We call this We call this sexagesimal notation.sexagesimal notation. Take a minute and turn your sextant to this Take a minute and turn your sextant to this

measurement.measurement.

The Light House The Light House ExampleExample

Zenith as a Zenith as a reference pointreference point

DistanceDistance 90˚ 0.090˚ 0.0

TangentTangent

A line which touches A line which touches a circle or ellipse at a circle or ellipse at just one point. just one point.

The blue line is a The blue line is a tangent to the circle.tangent to the circle.

Note the radius to the Note the radius to the point of tangency is point of tangency is always perpendicular always perpendicular to the tangent line (a to the tangent line (a 90 degree angle). 90 degree angle).

How it WorksHow it Works

Must calculate Must calculate tangent h.tangent h.

The lighthouse is The lighthouse is H tall.H tall.

I am standing a I am standing a particular D particular D (distance) away.(distance) away.

So tangent h or So tangent h or tanh = H/Dtanh = H/D

The ChallengeThe Challenge

Why Two ShotsWhy Two Shots

This is why we This is why we need two need two measurements.measurements.

From two From two different celestial different celestial bodiesbodies

We create our We create our lines of position.lines of position.

The SolutionThe Solution

Altitude InterceptAltitude Intercept11stst Coordinate System Coordinate System We only have our measurement of We only have our measurement of

altitude and time.altitude and time. Now we make one nautical mile the Now we make one nautical mile the

length of time it takes to see the length of time it takes to see the astral body change one MINUTE of astral body change one MINUTE of altitude (as measured on the sextant)altitude (as measured on the sextant)

This gives us our intercept!!!!This gives us our intercept!!!!

Practical ApproachPractical Approach

If you are at 38degrees and 32.6 minutes

I am at 38 degrees and 42.8 minutes

We just need to find the difference.

We are 10.2 nautical miles away or 10.2 minutes difference on our sextant.

Intercept MethodIntercept Method

Reading 1 - Calculate and plot Reading 1 - Calculate and plot your assumed location or your assumed location or deduced reckoning. deduced reckoning.

Reading 2 – Calculate your Reading 2 – Calculate your location using your celestial location using your celestial navigation tools.navigation tools.

When you compare these two plot When you compare these two plot lines they will give you only one lines they will give you only one of 3 possible results. of 3 possible results.

More ComplicationsMore Complications

Let’s redesign the lighthouse to be the Let’s redesign the lighthouse to be the sun, moon, or stars. sun, moon, or stars.

Sun, Moon, and Stars have a complex Sun, Moon, and Stars have a complex pattern of movement.pattern of movement.

We don’t know how "tall" these We don’t know how "tall" these astronomical bodies are.astronomical bodies are.

We need the height to find our tangent We need the height to find our tangent h. h.

Earth is round, not flatEarth is round, not flat The sky is dome shapedThe sky is dome shaped

Map DistortionMap Distortion

Serious issue for Serious issue for navigationnavigation

Where is the map Where is the map most distorted?most distorted?

How do each of How do each of these maps these maps counteract the counteract the distortion?distortion?

Practical ApproachPractical Approach

If you are at 38degrees and 32.6 minutes

I am at 38 degrees and 42.8 minutes

We just need to find the difference.

We are 10.2 nautical miles away or 10.2 minutes difference on our sextant.

Result AResult A

If the observed altitude is exactly If the observed altitude is exactly the same as your computed the same as your computed altitude then you are standing on altitude then you are standing on exactly the same “circle of exactly the same “circle of altitude” as our deduced altitude” as our deduced reckoning.reckoning.

Result BResult B

Our observed altitude is less than Our observed altitude is less than our computed altitude. We must our computed altitude. We must be farther away from the circle of be farther away from the circle of altitude.altitude.

Result CResult C

If the observed altitude is more If the observed altitude is more than the computed altitude than than the computed altitude than we must be closer to the center of we must be closer to the center of our circle of altitude or our our circle of altitude or our assumed or dead reckoned assumed or dead reckoned position.position.

Keeping it Real!Keeping it Real!

http://http://aa.usno.navy.mil/data/docs/celnaaa.usno.navy.mil/data/docs/celnavtable.phpvtable.php offers an online Intercept Method offers an online Intercept Method calculatorcalculator

Putting it TogetherPutting it Together

If we are in the If we are in the middle…middle…

We use our dead We use our dead reckoning to get reckoning to get an assumed lat an assumed lat and long.and long.

Quick Chart ReviewQuick Chart Review

ScaleScale LegendLegend DepthDepth DeclinationDeclination

ScaleScale

LegendLegend

DepthDepth

The numbers of The numbers of depth are for low depth are for low tide.tide.

White colors White colors indicate deeper indicate deeper water.water.

Compass RoseCompass Rose

A compass rose is used to A compass rose is used to measure directions using measure directions using true or magnetic bearing. true or magnetic bearing.

True direction is printed True direction is printed around the outside around the outside

magnetic is printed magnetic is printed around the inside. around the inside.

Variation is the difference Variation is the difference between true and between true and magnetic north for the magnetic north for the covered area. covered area.

It is printed with annual It is printed with annual change in the center of change in the center of the compass rose.the compass rose.

Celestial MechanicsCelestial Mechanics22ndnd Coordinate System Coordinate System Celestial Mechanics is the study Celestial Mechanics is the study

of the movements of the celestial of the movements of the celestial bodies. bodies.

Or rather our view of the celestial Or rather our view of the celestial bodies as the earth rotates.bodies as the earth rotates.

Sketching the HeavensSketching the HeavensNorth and SouthNorth and South Let’s create a vast celestial sphere. Let’s create a vast celestial sphere.

Above the north pole we will name Above the north pole we will name Polaris as the north celestial sphere Polaris as the north celestial sphere and 180 degrees away would be the and 180 degrees away would be the South Celestial SphereSouth Celestial Sphere

Now let’s create a celestial equatorNow let’s create a celestial equator This measurement of degrees is called This measurement of degrees is called

DeclinationDeclination The declination information is The declination information is

contained in the Nautical Almanaccontained in the Nautical Almanac

Sketching the HeavensSketching the Heavens

First we must First we must pick a zero or pick a zero or beginning pointbeginning point

We call that the We call that the First Point of First Point of AriesAries

Point of AriesPoint of Aries

At a right angle to the celestial At a right angle to the celestial equator at the point of Aries equator at the point of Aries becomes zerobecomes zero

This is not a meridian line but rather This is not a meridian line but rather an hour circle or as zero is calledan hour circle or as zero is called

HOUR CIRCLE OF ARIESHOUR CIRCLE OF ARIES This is the celestial equivilent of the This is the celestial equivilent of the

Prime Meridian and it becomes zeroPrime Meridian and it becomes zero

Sidereal Hour Angle Sidereal Hour Angle SHASHA This is the measurement of the This is the measurement of the

meridian lines that span the meridian lines that span the celestial heavenscelestial heavens

Then only span westward 0-360˚Then only span westward 0-360˚ We only measure in one direction We only measure in one direction

so east and west are no longer so east and west are no longer necessarynecessary

Declination N SDeclination N SSidereal Hour Angle WSidereal Hour Angle W

This is the coordinate This is the coordinate system used for system used for celestial navigationcelestial navigation

The nautical almanac The nautical almanac tabulates the positions tabulates the positions of stars in SHAof stars in SHA

Based on GHA or Based on GHA or Greenwich Hour Angle Greenwich Hour Angle or LHA Local Hour or LHA Local Hour AngleAngle

The Almanac is in GHAThe Almanac is in GHA

Altitude AzimuthAltitude Azimuth33rdrd Coordinate System Coordinate System Your zenithYour zenith 180 degrees from you zenith is Nadir 180 degrees from you zenith is Nadir

directly on the other side of earthdirectly on the other side of earth We can only see the things above our We can only see the things above our

horizon linehorizon line Anything below our horizon line is Anything below our horizon line is

denoted as negative altitudesdenoted as negative altitudes We need more than altitude to place a We need more than altitude to place a

pinpoint a celestial body in our skypinpoint a celestial body in our sky We need an AsimuthWe need an Asimuth

Azimuth ZnAzimuth Zn

We measure in reference to the We measure in reference to the horizon such as 0 degrees at true horizon such as 0 degrees at true northnorth

Runs clockwise up to 360 degreesRuns clockwise up to 360 degrees

Altitude Azimuth Altitude Azimuth

Uses the altitude in horizontal circlesUses the altitude in horizontal circles– Principal verticle circle (due north and Principal verticle circle (due north and

south)south) Azimuth in vertical circlesAzimuth in vertical circles

– Each has an upper branch and a lower Each has an upper branch and a lower branchbranch

– Prime VerticalPrime Vertical Passes through 90 (which would be due Passes through 90 (which would be due

east) 270 (which would be due west)east) 270 (which would be due west)