5A_Celestial & Inertial Navi

5ECEA

Lapus, Aja LorenzoLlanera, Ian Carlo

Lopez, John GregoryMagsino, Chermaine

Manrique, Dianne StephanieMateo, Ma. Khristina

Matira, EmersonNarciso, Ma. Kristina

AN INTRODUCTION AND A PEEK AN INTRODUCTION AND A PEEK ON ITS HISTORY...ON ITS HISTORY...

INTRODUCTION

CELESTIAL NAVIGATION - the art of finding one's way with reference to the Sun, the Moon and the stars.

celestial bodies obey certain behavior and the cycles repeat over a period of time.

HISTORY

in the late 15th century the Portuguese and the Castillians (Spanish) started their voyages of discovery their instruments of navigation were: Chip log and hour glass to determine speed and

dead reckoning Sounding lead to determine depth and nature of

bottom Magnetic needles floating on bit of cork to

determine orientation Astrolabe to measure the height of a celestial

body above the horizon (H).

HISTORY

Astrolabe - used to determine latitude by a sight of Polaris or the meridian passage of the Sun. invented by the Arabs.

cross staff – an “improvement” of the astrolabe. had to be aligned simultaneously (and therefore view simultaneously) one end of the cross-staff with the horizon and the other with the Sun or other celestial body. Highly impractical.

HISTORY

backstaff – invented in 1590 by davis(also called Davis' octant)

The observer, with his back to the Sun, aligns the shadow of the Sun with the horizon therefore maintaining one single line of sight.

Sextant – invented around 1750. it allowed a more precise measurement of H and

has remained basically unchanged to these days.

telescope and subsequent astronomical research allowed accurate prediction of the position of celestial bodies

in the latter part of the 18th century the British Royal Observatory started publishing the Nautical Almanac.

The first systems devised to determine GMT were by observing celestial movements which were quite fast and predicted in the almanac.

Lunar distance method○ By measuring the angular distance between the

moon and a star near the ecliptic, one determines the Moon's SHA and, with that, GMT.

Another method of determining GMT was by observing the fast movement of the four planets of Jupiter in their orbits and their eclipses.

John Harrison coupled the pendulum with an escapement of his invention and produced the first useful chronometers during the 18th century. The first one weighed 65 pounds.

In 1837 Capt. Sumner – invented the line of position (LOP).

19th century, Capt. Marcq St. Hilaire invented the intercept method

Around 1930, Ageton, then a student at the Naval Academy in Annapolis, invented the method that bears his name and which has later been known under other names such as HO211 and Bayless

This method uses a short table of logarithmic functions and is still useful today. It truly simplified the intercept method. Later, other similar methods have been proposed and one of them known as the Compact or Davies method is included in the Nautical Almanac

This system and tables evolved in the 50s into HO249 for air navigators and later HO229 for marine navigators. Both are essentially the same but HO229 give more precision, are bulkier and a bit slower to use.

CELESTIAL COORDINATE SYSTEM... position of an object uses a sphere (celestial sphere) as its

reference body use of the fact that there are 360

degrees in a circle coordinates are usually written in

degrees, minutes, and seconds

CELESTIAL COORDINATE SYSTEM...

1. Equatorial Coordinate System 2. Horizon Coordinate System

CELESTIAL SPHERE...

a huge, transparent imaginary rotating sphere of "gigantic radius", concentric and coaxial with the Earth

all objects in the sky can be thought of as lying upon the sphere

Projected from their corresponding geographic equivalents are the celestial equator and the celestial poles.

CELESTIAL SPHERE...

contains any number of large circles called great circles

any great circle intersecting the celestial poles is called an hour circlecelestial sphere is divided by hour circles

into 24 sectionsdistance between each hour circle is 15

degrees.

CELESTIAL SPHERE...

CELESTIAL SPHERE... divided by projecting the equator into

space; north celestial hemisphere and the south celestial hemisphere

ecliptic - a great circle on the plane of the earth’s orbit

celestial equator - the great circle where the plane of the equator intersects the celestial sphere. It is inclined by 23.5 degrees to the ecliptic

celestial poles - the points where the line making up the axis of the earth meets the sphere

CELESTIAL SPHERE...

CELESTIAL SPHERE... Zenith - point where a line extending from the

center of the earth through the point and out into space meets the celestial sphere

Nadir - the opposite side of the earth (in reference to zenith) where a line extending from the center of the earth through the point and out into space meets the celestial sphere

Zenith-Nadir axis - line connecting the zenith to the nadir

astronomical horizon - a great circle on the celestial sphere which is perpendicular to the zenith-nadir axis

CELESTIAL SPHERE... celestial meridian - a great circle which

intersects the zenith, the nadir, and the celestial poles

cardinal points - four points in the astronomical horizon which correspond to the directions of a compass

North (N) and South (S) points - two points which lie on the intersection of the celestial meridian

East (E) and West (W) points – two points which lie at the intersections of the horizon and the celestial equator

CELESTIAL SPHERE...

Zenith – Nadir axis

Astronomical horizon(Celestial horizon)

CELESTIAL SPHERE...

CELESTIAL SPHERE...

All parts of the celestial sphere: The horizon, zenith, nadir, celestial meridian, celestial poles, celestial equator, and cardinal points.

EQUATORIAL COORDINATE SYSTEM alternatively known as the 'RA/Dec coordinate

system' uses the celestial equator, the hour lines, and the

vernal equinox to describe the position of stars Vernal equinox - point where the Sun crosses from the

south to the north of the celestial equator. It occurs around March 21 every year.

independent of the observer's location and the time of the observation only one set of coordinates is required for each object same coordinates can be used by observers in different

locations and at different times

EQUATORIAL COORDINATE SYSTEM origin: vernal equinox (zero point for the hour

circles)also known as the First Point of Aries, since about

2,000 years ago, the intersection point on the celestial sphere where the ecliptic and celestial equator

the time at which the apparent longitude of the Sun is 0°.

primary reference circle: the celestial equator secondary reference circles: hour circles two coordinates: the right ascension (RA)

point and declination (DEC) point

EQUATORIAL COORDINATE SYSTEM

EQUATORIAL COORDINATE SYSTEM Declination (Dec) point, δ

analogous to the latitude coordinate on Earth angular distance above or below the celestial

equatormeasured in degrees, minutes, and seconds

from -90 to +90 degrees with ZERO (0) being on the celestial equator○ Note:

negative degrees - point is south of the celestial equator; positive degrees – point north of the celestial equator

stars on the celestial equator : Dec=0o

stars at the south celestial pole : Dec= -90o

stars at the north celestial pole : Dec=+90o.


An object's position is given by its RA (measured east from the vernal equinox) and Dec (measured north or south of the celestial equator).

REMINDERS:

The equatorial coordinate system is tied to the orientation of the Earth in space

Earth’s orientation changes over a period of 26,000 years due to the precession of the Earth's axis. Precession - refers to the movement of the

rotational axis of a body, such as a planet

consider EPOCH!!!

REMINDERS:

Epoch a moment in time used as a reference for the

orbital elements of a celestial bodyeither the moment an observation was made or

the moment for which a prediction was calculated

Julian years - a year of exactly 365.25 days○ Ex. J2000.0 coordinates

Besselian years - beginning of a Besselian year to be the moment at which the mean longitude of the Sun is exactly 280 degrees○ Ex. B1900.0 coordinates, B1950.0 coordinates


Example: Star = Einstein CrossRA = 22h 37m Dec = +03o05' (according to B1950.0 coordinates)RA = 22h 37m Dec = +03o 21' (according to J2000.0 coordinates)

NAUTICAL ALMANAC...

a publication describing the positions and movements of celestial bodies for the purpose of enabling navigators to use celestial navigation to determine the position of their ship while at sea including the sun, moon, planets, and 57 stars chosen for their ease of identification and wide spacing.

specifies for each whole hour of the year the position on the Earth's surface at which each body is directly overhead.

CELESTIAL COORDINATE SYSTEM... 1. Equatorial Coordinate System

2. Horizon Coordinate System

HORIZON COORDINATE SYSTEM Also called as horizontal coordinate system Measured in relation to the zenith Time and date dependent uses the zenith, the horizon, and the

cardinal points to describe the position of the stars

Primary reference circle: horizon Secondary reference circle: vertical circles

Vertical circles – perpendicular to the horizon and intersect the zenith

HORIZON COORDINATE SYSTEM Coordinates: the altitude and the

azimuth of a point Altitude – angular distance above or

below the horizon Zenith distance – angular distance

between the zenith and the point Azimuth – angular distance between the

north point and the vertical circle which intersects the point

HORIZON COORDINATE SYSTEM

TRANSFORMATION OF COORDINATES

Horizon to Equatorial Coordinates

D. α = GST – H (if negative, add 24)Where: α = right ascension (a) aka RA

δ = declination (d) aka Decφ = observer's geographic latitudeA = azimutha = latitudeH = hour angle

A.

B.

C.

TRANSFORMATION OF COORDINATES Example:

Horizon to equatorial transformation. Convert horizon coordinates azimuth= 283°16'16" and latitude = 19°20'04" to equatorial coordinates.

The observer is at the Greenwich meridian, 52° N, and GST (Greenwich Sidereal Time) is 0h24m05s.

TRANSFORMATION OF COORDINATES Answer:

Steps:To find δ (Dec):1. convert azimuth and altitude to decimal degrees2. find δ using eqn .A3. convert δ in degrees, minutes, and seconds formTo find α (RA):1. find H using eqn.B (answer is in degree hours)2. convert degree hours H to decimal hours 3. convert GST to decimal hours4. find α using eqn.D (answer in decimal hours)5. convert decimal hour to hours, minutes, seconds

form

TRANSFORMATION OF COORDINATES

Equatorial to Horizon Coordinates

Where: α = right ascension (a) aka RAδ = declination (d) aka Decφ = observer's geographic latitudeA = azimutha = latitudeH = hour angle

A.

B.

C.

TRANSFORMATION OF COORDINATES Answer:

Steps:

1.Convert H to decimal hours. 2.Convert H to degrees. 3.Convert δ to decimal degrees. 4.Find sin α. 5.Find sin-1 to find α. 6.Find cos A. 7.Find cos-1 to find A'. 8.Find sin H (if positive, A = 360 – A', else A = A'). 9.Convert a and A to hour angle form.

THE CELESTIAL (ASTRONOMICAL) TRIANGLE

The terrestrial, celestial, and horizon coordinate systems are combined on the celestial sphere to form the astronomical or celestial triangle.

COORDINATE SYSTEM COMPARISON

COMPASS

Compass was first used in China in the 400 BC in Feng Shui (geomancy). The first Compass was a simple piece of lodestone floating on water that pointed South.

COMPASS

The magnetic field of Earth is not uniform and varies at different latitudes of the planet. The Compass needle is attracted by magnetic force and therefore, it is fluctuating too. When the needle reads North, it is actually the direction of the magnetic North Pole. There is a slight deviation from true North and this phenomenon is called declination

QUADRANT

The Quadrant was the first altitude-measuring instrument developed for use in celestial navigation, dating back to the 15th century. Its first recorded use at sea was by Diego Gomes in 1461.

QUADRANT

The Quadrant does not require the view of the horizon to find altitude unlike most other instruments used to find altitude.

CROSS STAFF

Cross-staff is restricted from around 20° to 60°. therefore it is impossible to use the Cross-staff in low latitude regions.

ASTROLABE

The Mariner's Astrolabe (left) is the adapted version of the Astrolabe used solely for navigation

MARINER’S ASTROLABE

It is a much simpler device compared to the typical Astrolabe, consisting of a heavy ring suspended from a thumb ring. The circumference of the ring is marked in degrees and the alidade is pivoted in the center of the ring with pointers against the scale for measuring celestial altitudes.

Using the thumb ring, the astrolabe is held above eye level. The alidade is then rotated until the Sun or star is visible and the altitude is then read off the scale

SEXTANT

SEXTANT PARTS

Sextant: a navigation instrument that is used to establish position by measuring the height of stars from the horizon.Index mirror: large polished plate that reflects light.Telescope: optical instrument made of lens that magnifies objects.Telescope clamp: reinforcing circle.Eyepiece: lens the user looks through.Telescope printing: lens adjustment.Frame: structure that serves as the base for the different parts of the sextant.Graduated arc: graduated edge of the arc.Locking device: apparatus that holds the sextant in place.Drum: graduated button used to take measurements.Index arm: type of ruler that determines direction or measures an angle.Screw to regulate small mirror: piece of metal used to adjust the horizon mirror.Glass filter: colored transparent substance.Horizon mirror: small polished glass plate that reflects light.Glass filter: colored transparent substance.

SEXTANT

BACK-STAFF : ORIGIN

Circa 1594 Intention: Improvement over

Mariners’ QuadrantsAstrolabesCross-staves

BACK-STAFF : CONSTRUCTION graduated staff a half-cross in the shape of an arc of a

circle on the radius of the staff with a fixed vane

a brass horizon vane with a slit in it at the fore-end of the staff.

BACK-STAFF : USAGE

The observer places the staff on his shoulder and stand with his back to the sun.

With the horizon vane lined up with the horizon, he slides the half-cross back and forth until the shadow of its vane falls across the slit in the bottom vane while the horizon remains visible through the slit.

BACK-STAFF : ILLUSTRATION

BACK-STAFF : REMARKS

The observer is able to sight both the sun and the horizon while his back is towards the sun.Eliminated problems from Cross-staff

○ Ocular parallax○ Eye damage from looking directly at the Sun

Can only be used to measure the altitude of the Sun and not other celestial bodies.

OCTANT : ORIGIN

Around late 1600s and early 1700s Shifted to optical systems based on

mirrors and prisms Independent & almost simultaneous

developmentJohn Hadley, an EnglishmanThomas Godfrey, a Philadelphia glazierAbout 1731

OCTANT : CONSTRUCTION

a frame (one eighth of a circle) an index arm two mirrors an eyepiece

Illustration:

OCTANT : USAGE

index arm is pivoted at the circle’s center and moving over the graduation on the arc

the index glass, fully reflecting, is placed on the index arm exactly above the pivot

the horizon mirror, half-silvered, is placed on one radius of the octant

the eyepiece is placed upon the other radius, opposite to the horizon mirror

OCTANT : USAGE

Horizon is viewed through the horizon mirror

Index glass reflects light from celestial body, then by the horizon mirror to the eyepiece

Navigator must align the horizon to the reflection of light and the scale would follow

The angle measured is transferred to the lunar table whereby the longitude of the observer will be known

OCTANT : BASIS

Law of reflection of lightthe angle of incidence is equal to the angle

of reflection for a plane mirrorIt follows that if the mirror is moved so that

the angle of incidence is altered, the angle at which the emergent ray is reflected will be altered by an angle twice that through which the mirror has been moved.

OCTANT : COMPARISON

To the Sextant:Same operation/usageReduction in radius helps reduce weight

OCTANT : REMARKS

One of the first instruments that could measure angle with sufficient accuracy

The observer need only to look at one place while adjusting the instrument Prevents ocular parallax

Reading is not affected by the rolling and pitching of the ship

Glare from the sunlight is reduced when observing the Sun using the Octant (compared to the Quadrant or the Cross-staff)

OCTANT : REMARKS

Difficult to use at nightHorizon is invisiblePeople tried to make use of artificial horizon

○ Bubble Sextant (spirit level)

More complex construction

SUNDIAL : ORIGIN

More than 3500 years agoUsed the Sun to tell the timeStarted to construct sundials

SUNDIAL : USAGE

Set in direct sunlightMagnetic compass needed

Set in cloudless nightLine up with Polaris

SUNDIAL : ILLUSTRATION

SUNDIAL : REMARKS

very simple to make and to use no longer accurate after a month

obliquity of Earth causes the 'path' of the Sun to change over the months

The same Sundial cannot be used in two different placesThe Sun has different 'paths' for two

different places

NOCTURNAL : ORIGIN

AKA Nocturlabe 1272 Calculates the time at night

NOCTURNAL : BASIS

works on the principle that stars close to the Celestial Poles are circumpolar

Circumpolar, adj. Denoting a star that from a given observer's latitude does not go below the horizon.

NOCTURNAL : CONSTRUCTION several pieces of metal or wood

attached at the center so they can rotate relative to one another

at the axis of rotation is a hole

NOCTURNAL : USAGE

Held upright by the handle until the Polaris can be sighted through the hole

The long arm of the device is then turned until it lies along the line made by the two brightest stars in the constellation Ursa Major.The bright star in the Ursa Minor can be

used in the same way.

NOCTURNAL : USAGE

If Ursa Minor is used, the inner dial would be turned so that the pointer marked "LB" would lie against the date on which the observation is being made.

If the Ursa Major is chosen as a reference, the procedure is the same, except that the small pointer marked "GB" is set against the date

By doing this, the correction from sidereal time to solar time is automatically corrected.

NOCTURNAL : REMARKS

Could only be used in the northern hemisphere because it requires the user to be able to see Ursa Major or Ursa Minor, which lie near the North Celestial Pole

CHRONOMETER : ORIGIN

Idea: circa 13th century Invention: 18th century English clock-maker, John Harrison Brothers John and James made two

clocks that lost no more than a second per monthRemarkable at the year 1726

AKA sea-clock

CHRONOMETER : H1

Harrison Number 1 1735 Balance ring with two 5-pound weights

connected by brass arcs replace the pendulumWeights balances the spring during tilts and

turns by the sea Total weight: 72 pounds

CHRONOMETER : H1

CHRONOMETER : H2

Harrison Number 2 1739 Tall and heavier, but took up less space Innovation: The remontoire mechanism

ensures that the force on the escapement is constant, thus improving the accuracy of the clock

CHRONOMETER : H2

CHRONOMETER : H3

Harrison Number 3 1741 Similar to H2, but smaller, lighter, had

circular balances instead of dumbbell shapes

A bi-metallic curb was used to allow for variations in temperature

Impossible to adjust without dismantling and re-assembling

CHRONOMETER : H3

CHRONOMETER : H4

Harrison Number 4 Breakthrough: 5.25 inches Oil was used as lubricants

to minimize the problems of ageing oil, Harrison used wheels and pinions with a great number of teeth that increased the efficiency of the clock

lost 5 seconds in 2 monthscorresponded to an error in longitude of only

1.25 minutes

CHRONOMETER : H4

CHRONOMETER : H5

Harrison Number 5 1772 Harrison’s final longitude time-keeper Mechanically very similar to H4.

INERTIAL NAVIGATION SYSTEM

A self-contained navigation technique in which measurements provided by accelerometers and gyroscopes are used to track the position and orientation of an object relative to a known starting point, orientation and velocity

Inertial navigation is used in a wide range of applications including the navigation of aircraft, tactical and strategic missiles, spacecraft, submarines and ships

1

2

Inertial measurement units (IMUs)

Contain three orthogonal rate-gyroscopes and three orthogonal accelerometers, measuring angular velocity and linear acceleration

By processing signals from these devices it is possible to track the position and orientation of a device

and...

INERTIAL NAVIGATION SYSTEM

INERTIAL SYSTEM CONFIGURATION

Stable Platform Systems


- the inertial sensors are mounted on a platform which is isolated from any external rotational motion. In other words the platform is held in alignment with the global frame



- this is achieved by mounting the platform using gimbals (frames) which allow the platform freedom in all three axes



- the platform mounted gyroscopes detect any platform rotations. These signals are fed back to torque motors which rotate the gimbals in order to cancel out such rotations, hence keeping the platform aligned with the global frame



- to track the orientation of the device the angles between adjacent gimbals can be read using angle pick-offs. To calculate the position of the device the signals from the platform mounted accelerometers are double integrated



Strapdown Systems

- the inertial sensors are mounted rigidly onto the device, and therefore output quantities measured in the body frame rather than the global frame


Strapdown Systems


- to keep track of orientation the signals from the rate gyroscopes are ’integrated’. To track position the three accelerometer signals are resolved into global coordinates using the known orientation, as determined by the integration of the gyro signals. The global acceleration signals are then integrated as in the stable platform algorithm.

Strapdown Systems


Stable platform and strapdown systems are both based on the same underlying principles. Strapdown systems have reduced mechanical complexity and tend to be physically smaller than stable platform systems. These benefits are achieved at the cost of increased computational complexity. As the cost of computation has decreased strapdown systems have become the dominant type of INS.


GYROSCOPE

device for measuring or maintaining orientation based on the

principles of angular momentum

defy gravity

GYROSCOPE: HISTORY

1817 it simply called the "Machine.“ by Johann Bohnenberger

Recommended the machine for use as teaching aid

by French mathematician Pierre-Simon Laplace

In 1852, it was used for an experiment involving the rotation of the Earth by Foucault, he was also the one who gave

the device its modern name (Greek skopeein, to see) the Earth's rotation

(Greek gyros, circle or rotation)

GYROSCOPE: HISTORY

1860s, electric motors made the concept feasible, leading to the first prototype gyrocompasses

the first functional marine gyrocompass was developed between 1905 and 1908 by German inventor Hermann Anschütz-Kaempfe

The American Elmer Sperry followed with his own design in 1910, and other nations soon realized the military importance of the invention

The Sperry Gyroscope Company quickly expanded to provide aircraft and naval stabilizers as well, and other gyroscope developers followed suit.

GYROSCOPE: HISTORY

In 1917, the Chandler Company created the "Chandler gyroscope," a toy gyroscope with a pull string and pedestal

MEMS (Micro Electro-Mechanical System)idea of the Foucault produce by Systron Donner Inertial (SDI).

GYROSCOPE: HISTORY

GYROSCOPE

ACCELEROMETER

a device that measures non-gravitational accelerations non-gravitational acceleration is produced

by forces other than gravity or inertial/fictitious forces

simple mechanical forces, these are transmitted to the accelerometer device through mechanical stress on its mounting.

ACCELEROMETER

expressed in SI units (m/s2) or popularly in terms of g-force

does not measure the "acceleration" due to gravity

in free fall in a gravity field, even though being accelerated, will read "zero" uses in an earth orbiting spaceship.

ACCELEROMETER: HISTORY

micro electro-mechanical systems (MEMS)

consisting of little more than a cantilever beam with a proof mass (also known as seismic mass).

ACCELEROMETER

5A_Celestial & Inertial Navi

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