275 l2 observations

8/6/2019 275 L2 Observations

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Lecture 2: Observing the Sky

Phys 275 Astrophysics I - Planets and Stars Lecture 2 January 6th 2011



The Local Sky: our simplest reference frame

To locate celestial objects, we can

define a set of coordinates called thelocal sky.

Reference points include the zenith

(the point straight up from our location),

the horizon (the circle where the

hemisphere of the sky intersects the

Earth, as seen from our pos ition), and

cardinal points (N, S, E, W) on the

horizon. Of these, our meridian is the

arc of circle passing from the northpoint on the horizon through the zenith

to the south point. (Waterloo’s

meridian: 80o 31’ West)

Formally, any point on the sky can be

located by its azimuth (or direction

)

and its altitude, or angle from the

horizon up towards the zenith.Telescopes often use “alt-az” settings.

All these coordinates are purely local,

have been understood since ancient

times , and imply no further knowledge

about the shape or s ize of the Earth, the

Solar System, etc. All celestial objects

are imagined to sit on a celestial

sphere at a single (arbitrary) distance⇒ 2D (spherical) coordinate system.

(Nadir)

Elements of the Local Sky, the simplest

spheric al c oordina te system on the sky



The most obvious fixed features in the sky (assuming you observe long enough) are the celestial poles.

All objects beyond the Earth appear to rotate around them, as discussed in the last lecture. Only one

pole (north or south - NCP or SCP) is visible unless you are exactly on the Earth’s equator; the line in

the sky equidistant from the poles is called the celestial equator .

Celestial Poles

Time lapse image showing the North Celestial Pole (NCP)

and the northern lights



Locating the Celestial Poles

In the northern hemisphere, the bright star Polaris is currently quite close (separation ~45 arcminutes)

to the north celestial pole. There is no bright star close to the southern celestial pole at the moment.

Hubble observations of the multiple components of Polaris (NASA)

Time lapse imageshowing the offset of

Polaris from the NCP



Locating the Celestial Poles

There is no bright star close to the south celestial pole at the moment, but the long arm of the

Southern Cross can be used to estimate its position.

Time lapse image of the SCP from the Anglo-Australian

Observatory at Siding Spring, Australia

Locating the South Celestial Pole (SCP)

using the Southern Cross



Locating the poles during the day

The location of the celestialpole can also be determined

during the day from the Sun’s

rotation. The altitude of thesun at noon (when it crosses

the meridian) varies

seasonally, but the pole

remains the same.

(When the sun is half way

between successivepassages overhead, we call

it midnight.)

The motion of the Sun

distinguishes East from

West: it rises in the East and

sets in the West, as do m ost

celestial objects. At special

times called equinoxes, itrises (at dawn) and sets (at

dusk) exactly at the Eas tern

and Western cardinal pointsrespectively.

The daily path of the Sun across the sky at different

times of year (as seen from a latitude of ~45o North)



Poles and Circumpolar Objects

Stars close to the north

celestial pole are

circumpolar (that is

they never set) in the

northern hemisphere,

whereas those close tothe south celestial pole

are circumpolar in the

southern hemisphere.

Examples at our

latitude include the

stars of the Big Dipper



A puzzle: does the sky rotate, or does the Earth?

Given all the stars move

together, how could we tell

the difference?

Some ancient astronomers

considered the possibility

that the Earth rotated (e.g.

Aristarchus of Samos

around 310-230 BC), butmost rejected the idea since

it was not clear what would

counter the centripetal force

Fc = m V2/R outwards

(compare this to

gravitational force)

(nor was its curvature in the

East-West direction obvious)

Actual rotation speed of different points at the surface of the

Earth, in km/hr

1670 km/hr = 463 m/s R = 6378 km = 6.3 x 106 m



Locating objects in the sky at night: the constellations

To locate objects at night,we can also use the

constellations,

traditional groupings of

bright stars related to

objects or figures from

mythology.

The International

Astronomical Union has

established an official set

of boundaries to the

constellations such that

the span the entire sky.

Note some larger patterns (the winter

triangle shown here, or a

similar “summer triangle”)

are not constellations.



N.B. constellations only 2-dimensional

The members of a constellation are not necessarily at thesame distance in space; in fact the bright stars we see in

the sky are spread over a large area around us in the

Milky Way.

This was not known until the 19th century due to the

difficulty of measuring stellar distances.

Distances are often difficult to measure in astronomy, sowe often talk about the angular separation (or angular

distance) between objects instead.



Measuring angular separation on the sky

Angular separation can be measured exactly using shadows (e.g sundials), pointers,

protractors, astrolabes or various other simple devices.

It can also be estimated roughly by comparing to various parts of the hand held at

arm’s length:

Finger tip ~ 1 degree

Four fingers together ~ 5 degrees

Fist ~10 degrees

Hand ~ 15 degrees

Widest span of fingers ~ 20 degrees

These provide a simple method for measuring time.



Measuring Angular Separation on the Sky

Some angular sizes of objects in the sky:

Sun ~ Moon ~ 0.5 degrees (in diameter)for other objects, we need subdivisions of a degree:

Mars 3-25’’ Neptune 2’’Venus 10-66’’ Pluto 0.06-0.1’’

Mercury 4-13’’ Ceres 0.3-0.8’’

Jupiter 29-50’’ Alpha Centauri A 0.007’’

Saturn 14-20’’ Deneb 0.002’’

Note the resolution of the naked eye is about 1’-2’, or 60’’-120’’

units of angular size:

1 circle = 360 degrees (abbreviation o )

1 degree = 60 minutes (of arc, or arcminutes, abbreviation′

)1 minutes = 60 seconds (of arc, or arcseconds, abbreviation″)

(Confusingly, similar-sounding units of time are also used to measure East-West

angles (Right Ascension):

1 hour = 15 degrees of arc,

1 minute of time = 15 minutes of arc, etc.)



The small angle formula

Converting to degrees, this gives the small-angle formula

(valid only for small angles, e.g. less than 5-10 degrees):

D

δθ

L

Normally, L = D tan( δθ )

But tan(x) ~ x

so L ~ D δθ or δθ ~ L/D (for δθ measured in radians)

(Try estimating the physical diameter of the Sun using this formula.)



Spherical coordinate systems: e.g. on the Earth

To locate points preciselyon the surface of the

Earth, we need two

coordinates, for instance

longitude (measured East-

West) and latitude

(measured North-South)

The choice of reference

points for latitude are

obvious: the

(geographic) poles, with

the (geographic) equator

between them.

The choice of an origin for

longitude is less clear; in

principle it could go

anywhere.

Waterloo: Latitude 43o 28’ North, Longitude 80o 31’ West



N.B.:The problem of longitude (16th - 19th c.)

Earth has poles in the North-South direction, but is symmetric in the East-West direction

Without absolute time signals, how to determine one’s location on the Earth in the East-West direction?

⇒ catalogues of celestial events (e.g. motions of the planets),

and of celestial objects (e.g nebulae)

which can then be observed from different locations, to tie together different local skies



Spherical Coordinates on the Earth

In practice, history dictates that the

reference point for longitude passes

through the Royal Greenwich

Observatory, just outside London,

England, where some of the

pioneering work was done measuring

longitude by astronomical and

technological means.



Spherical Coordinates on the Sky

Projecting and axis running

through the poles and a

plane running through the

equator out into space, we

can define a 2-D coordinate

system: the celestial sphere.

This can be thought of as an

imaginary sphere of arbitrary

size, centered on the Earth,

on which we draw the

projected coordinate system.

Reference points are the

celestial poles, the

celestial equator , and the

vernal equinox.



Spherical Coordinates on the Sky:

Right Ascension and Declination

By analogy with latitude

and longitude, we can

define spherical (2-D)

coordinates on the sky.

Declination measures

the angular distance

above or below thecelestial equator.

Right ascension

measures the angular

distance around the

sphere starting from a

fixed reference point, the

vernal equinox.

The vernal equinox is one

of the two places where

the celestial equator

intercepts the ecliptic.



The inclination (“obliquity”) of the ecliptic

The Earth’s axis of rotation is tilted by 23.5 degrees with respect to the

ecliptic. This tilt means we seen the Sun at an angle, and explains the

seasons.



The origin of seasons on the Earth

Note that seasons are not due to the eccentricity of the Earth’s

orbit; if the orbit were very eccentric it would produce cold or hotseasons simultaneously in both hemispheres.



The origin of seasons on the Earth

The Earth’s axis of rotation is tilted by 23.5 degrees with respect to

the ecliptic. This tilt means we seen the Sun at an angle, andexplains the seasons.

The maximum and minimum

altitude of the Sun over the

course of the year as defines

particular latitudes:

- between the Tropics the Sun

reaches the zenith at some

point of the year

- above/below the Arctic /

Antarctic Circle, the Sun dips

below the horizon at some

times of year



Precession of the Earth’s Axis of Rotation

Although the Earth’s axis currently points to Polaris, its position

actually changes slowly with time due to forces from the Sun andMoon on its non-spherical shape.



A second reference circle on the sky: the ecliptic

Note that the Moon and the

other planets all appear to move

roughly on the ecliptic as well,

at least to within a few degrees.

The Ecliptic seen from New Zealand - image from http://www.twanight.org



A second reference circle on the sky: the ecliptic

Note that the Moon and

the other planets allappear to move roughly

on the ecliptic as well, at

least to within a few

degrees.

the ecliptic seen from China - image from http://www.twanight.org



The ecliptic is the plane of the Solar System

Since the planets move along the same projected circle, if they are at different distances theymust define a plane. This plane is that of the Sun’s motion around the Earth, or seen from the

Sun’s point of view, the plane of the Earth’s orbit.

The major planets orbit within 7 degrees of this plane; in fact all but Mercury lie within 3.5

degrees of it.

The inner solar system, showing the ecliptic plane



Aside: Siderial versus Synodic periods

Because the Earth is both rotating and orbiting, it takes slightly longer to reach the

same position w.r.t. the Sun as it does to reach the same position w.r.t. the stars

siderial day: 23hr 56 min

solar day: 24hr

Similarly there is a siderial month (w.r.t. stars),

and a synodic month (w.r.t Sun).

There is also a siderial year

and a tropical year, shorter by 20 min

due to precession.



The Earth’s Moon: Eclipses

Because the Moon’s orbital plane it close to the ecliptic (within about 5o), as it orbits the Earth it

can block the Sun or be blocked by the Earth. These alignments are called solar and lunar

eclipses respectively.




Because the Moon’s orbital plane it close to the ecliptic (within about 5o), as it orbits the Earth it

can block the Sun or be blocked by the Earth. These alignments are called solar and lunar

eclipses respectively.




Whether we see a total or partial “annular” solar eclipse depends on the precise Earth-Moon

distance at the time.



Predicting EclipsesEclipses occur roughly twice a year, when the nodes of the Moon’s orbit are aligned along the Earth-Sun axis,and the Moon is full (lunar eclipse possible) or new (solar eclipse poss ible). (See 4 slides back for figure.)

Precession of the Moon’s orbit make the actual interval between eclipses s lightly less than six months (~5.4months). The entire cycle of eclipses repeats roughly every 18 years (the Saros cycle, discovered in ancient

times).



Summary of today’s lecture

Topics Covered

For each topic you should check the references, understand the concepts listed, know thedefinitions of the underlined terms [equivalent terms are given in b rackets], and understand

how to apply any equations or formulae. Terms in italics are optional material.

– The Local Sky concepts/definitions: Local Sky, horizon, zenith, cardinal points

(N,S,E,W), meridian, direction [ = azimuth], altitude

– Night, day and the motion of the Sunconcepts/definitions: daily motion of the Sun across the sky,

solar noon, midnight, the meridian

– Constellations and angular distances

concepts/definitions: constellation, angular distance [= angular size, angular

separation], arcsecond, arcminute, minute of time (for right ascension), second of time

(for right ascension), small angle formula

– Points on the celestial sphere

concepts/definitions: the celestial sphere, the celestial equator, the north celes tial pole,

the south celestial pole, the ecliptic, circumpolar stars, Polaris (right ascension,

declination)



Summary of today’s lecture

Topics Covered (Continued)

– Points on the terrestrial sphere

concepts/definitions: longitude, latitude, the prime meridian, equation/result: the altitude

of the pole = observer’s latitude

– The ecliptic

concepts/definitions: the obliquity of the ecliptic, the origin of seasons , the tropics and

the Arctic and Antarctic Circles, variations in insolation (light flux from the Sun), the solar year, solstices and equinoxes, precession

– Motion and Phases of the Moon

concepts/definitions: s iderial period, synodic period, months, phases, nodes, s olar and

lunar eclipses, (Saros cycle)

275 l2 observations

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