Sun

The distance from P to C, or A to C = a which is also known as the mean distance

For the Earth, this distance is known as the mean distance 93,000,000 miles or 150,000,000 km and it is also known as one Astronomical Unit (A.U.)

PC

A

The planets’ orbits, are not very far from being circular.

a a

aphelionperihelion

a = aphelion + perihelion_________________________

2

e = _______________________aphelion - perihelionaphelion + perihelion e=0

e= 0.91e is how much the orbit departs from a circle where e=0.

circle

Sun

Perihelion is closest , and aphelion is farthest from the Sun.

Formulas for Orbital Motion

Finding the semi major axis. This is the average distance from the Sun

Aphelion, perihelion refer to farthest distance, and closest to the Sun. Apogee, perigee refer to farthest distance and closest to the Earth. (peri is the closest)

How much it departs from a circle between o and 1

Velocity at perihelion (closest point), use correct

Velocity at aphelion (farthest point), use correct

2

(1 )

(1 )

peri

ap

peri ap

ap peri

ap peri

pperi

aap

p aa

a pe

a p

eV

p

eV

a

Closet distance the orbiting object comes to the object being orbited in an elliptical orbit

Farthest distance the orbiting object comes to the object being orbited in an elliptical orbit

This formula is for objects orbiting the Sun. p will be in Earth years and a is A.U.

(1 )

(1 )

peri

ap

p a e

a a e

2 3p a

Formulas continued:

The gravitational parameter,

For the Sun, = 132,712,440,018 3

2sec

km

GM ( Note, )

Using the Kepler’sThird Law

P2 a3

P2 a3 if :

P measured in earth years, and a in AU.

A planet’s avg distance from the sun is 4 au,

what is the period of the planet ?2 3 24 , 64,

64, 8

P p

P P years

ConversionsTo change from km/sec to miles/hr

Km/sec (3600 sec/hr)(0.62137 miles/km= miles/hr

e has no units.

To change from AU to km multiply by 150,000,000 or

km81.5 10X

** Be sure you use the of the body that is being orbited ***

Answers may vary slightly depending upon how you round off the decimals, and that’s ok.

This problem covers a lot of formulas. An asteroid’s closest approach to the sun is 2 au, and its farthest distance from the Sun is 4.5 au. Find a, the eccentricity, distance at perihelion, distance at aphelion, period, velocity at perihelion, and aphelion.

ap peri

ap peri

a pe

a p

2 4.53.25

2a au

4.5 2 2.50.385

4.5 2 6.5e

Find the perihelion, and aphelion distances.

(1 )perip a e = 3.25au (1 - 0.385) = (3.25)(.615) = 1.99 au

(1 )apa a e = 3.25au (1+ 0.385) = 4.43 au

2peri app a

a

Find the period. 2 3

periodP a 2 33.25periodP 5.86periodP years

(1 )perip

peri

eV

p

For distance, Perihelion, and aphelion must be changer to km, since contains km . To change multiply au by 150,000,000 km/au , or

81.5 10X

11

8

1.327 10 (1 0.385)

1.99(1.5 10 )perip

XV

X

2.48 / secperipV km 10

8

18.38 10

2.99 10perip

XV

X

24.8 km/sec(2236.93) = 55,475 miles/hour

24.8 / secperipV km

Find the velocity at perihelion= 132,712,440,018

3

2sec

km

(1 )apa

ap

eV

a

11

8

1.3267 10 (1 .385)

4.43(1.5 10 )a

xV

X

11

8

0.816 10

6,645 10 )a

XV

X

10

8

8.16 10

6.645 10 )a

XV

X

3.504 / secaV km = 3.504(2236.93 )

Find the velocity at aphelion.

= 7,838.2 miles/hour

Why use a telescope?Why use a telescope?

•To Brighten

•To Magnify

•To Resolve

Optical Telescope Design• Two basic designs

• Refractor– uses a lens to collect light.

• Reflector- uses a mirror to collect light.•The names have to do with the optical

phenomenon at work (refraction (bend) or reflection).

•A curved primary surface ( mirror or lens) is necessary to bring the light to focus.

Objective Lens

Secondary Lens

(Eyepiece)

Focus

Refracting TelescopesRefracting Telescopes•Refracting telescopes use two convex lenses to magnify distance objects. Objective Lens & eyepiece

•

Focal Length of a lens

•Chromatic Aberration

•This means that different colors are bent different angles and thus do not come to a common focus in a double convex lens.

Solution: A second lens is added to help with color separation. Expensive

The RefractorOptics

focal length

The Yerkes 40” Refractor

Largest Refracting Telescope 40 inch

•They are easy to use.•The “original” type was invented in the •1500’s and used by Galileo.

•Sharpest, brightest images. •Lenses are heavy and expensive!

•Prone to chromatic aberration. •Gives an inverted (upside-down) image. •Maximum size of telescope about 40 • inches in diameter due to weight..

Good & Bad of Refracting Telescopes

Newtonian Telescopes – curved concave mirror– flat mirror (Diagonal Mirror)

– eyepiece– a.k.a. Reflecting Telescopes

Reflectors

• Usually a concave, parabolic mirror is used as the primary optical element to bring the light into focus.

• A secondary optical element is often used to divert light to a conveniently located focus. Its position and nature defines the kind of reflector it is.

Reflecting Telescopes - Advantages• Mirrors are much cheaper to make than

lenses, and are very light-weight, easy to carry. Mirrors can be VERY large. Multiple mirrors can be combined . No chromatic aberration.

• Disadvantages •Mirror coatings will oxidize over time.

Not as sharp or bright an image as the same size refractor. Large scopes get currents of different temperature air inside their tubes, and this can make images blurry.

The corrector plate is a type of lens. A secondary mirror is glued to its inside.

Cassegrains: Lens & Mirror•Very short tube length, because the light gets “folded” back on itself twice. This makes the scope easy to handle & transport.

•Alt-azimuth mounting – Telescope axis points toward the zenith.

Requires movement along both axes to track an object.

Telescope Mounts

• Equatorial mounting - Telescope axis points toward the NCP.

Allows the telescope to track an object in the sky by movement along one axis only.

German Equatorial Mount

• The larger the diameter of the light collecting element (mirror or lens) of a telescope, the more light it collects.

•The larger the diameter of the telescope, the better its resolution.

As a rule of thumbs, about 50 X per inch of telescope is the maximum useful power for a telescope on a good seeing night.

Telescopes MagnifyTelescopes Magnify• Magnification is the number of times larger

an object appears through a telescope than as seen by the naked eye

M = fo / fe

Focal Length of the Objective Lens or MirrorMagnification

Focal Length of the Eyepiece

To calculate the magnification of the telescope,

M = fl. telescope/ fl. of eyepiece

For a 1500 mm fl scope and a 30mm eyepiece,

the magnification is M = 1500 mm/30mm , M = 50 X

Seeing – turbulence in the atmosphere, causes the twinkling of stars and images to shift. Note: Planets do not twinkle

Factors Affecting Optical Astronomy• Weather & Earth’s Atmosphere

Los Angeles1908

1988

–Light Pollution from near by street lights or distant city lights

Light PollutionLight Pollution• Light Pollution makes it difficult to see stars in the city.

Light Pollution

Nighttime around the Earth

Why Put Telescopes In Space?No distortion, blurring from atmosphereDarker skies especially for infraredYou can see ultraviolet(UV), x-rays, gamma rays, and infrared (IR) rays.

Why can’t we see this radiation from earth ?Ozone, O3, blocks UV at altitude 20-40 km

Various atoms , and molecules block x-rays , and gamma rays.

Water vapor blocks IR at altitudes 2-10 km.

So how do we see objects in all these radiations ?

IR can be seen from mountain tops, balloons, and airplanes.

X-rays,gamma rays can be seen from balloons, rockets, and orbiting satellites.

UV, optical are the focus of the HST orbiting telescope.

Spitzer Space Telescope is used to obtain IR data.Chandra is used to observe x-rays.

Things that Detect LightThings that Detect Light• Human Eye and Photographic Film

• Photometers - an electronic device that measures the brightness of stars.

• CCD’s (charge-couple device) - an electronic imaging device that records the intensity of light falling on it.

CCD Camera and Color FiltersCCD Camera and Color Filters

All large telescopes these days are reflectors, usually placed on high mountaintops away from cities.

Telescopes on Mauna Kea, Hawaii (14,000 ft)

Mirrors can be hollow honeycombed in the back, light and, easy to mount. The Largest telescopes are often now built using multi-mirrors.

Mirrors can be hollow honeycombed in the back, light and, easy to mount. The Largest telescopes are often now built using multi-mirrors.

RADIO ASTRONOMY

• Can be done from the Earth's surface

• Radio waves pass through interstellar dust and even clouds on Earth

• Cool neutral hydrogen radiates at radio wavelengths (spiral arms of Galaxy)

SPITZER SPACE TELESCOPE

• Infrared telescope• 85 cm diameter (33.5

inches)• Wavelength

Coverage: 3 - 180 microns

• 2.5 years (minimum); 5+ years (goal)

ULTRAVIOLET ASTRONOMY

• Must be done from space (ozone absorbs UV)

• Some critical information is only available at UV wavelengths

• Hot, energetic stars and stellar chromospheres radiate strongly in UV.

X-RAY ASTRONOMY

• Must be done from space

• Extremely high energy radiation (black hole accretion disks).

• Requires special grazing incidence telescopes

CHANDRA X-RAY OBSERVATORY

                                                                                                                                   

                    

GAMMA RAY ASTRONOMY

• Must be done from space

• Gamma rays can not be focused, so only detectors are used

• The most energetic photons in the Universe.

The Hubble Space Telescope

I Hope I was able to shed a little light on this topic