Transcript Orbits and Telescopes (Professor Powerpoint)

The planets’ orbits, are not very far from being circular.
The distance from P to C, or A to C = a which is also
known as the mean distance
P
Sun
a
C
a
A
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.)
e is how much the orbit departs
from a circle where e=0.
e=
e= 0.91
aphelion - perihelion
_______________________
aphelion + perihelion
a = _________________________
aphelion + perihelion
2
perihelion
e=0
circle
aphelion
Sun
Perihelion is closest , and aphelion is farthest from the Sun.
Formulas for Orbital Motion
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)
a
e
p peri  aap
2
aap  p peri
Finding the semi major axis. This is the
average distance from the Sun
How much it departs from a circle between o and 1
aap  p peri
V p peri 
Va ap 
 (1  e)
Velocity at perihelion (closest point), use
correct
p peri
 (1  e)
aap
Velocity at aphelion (farthest point), use
correct
Formulas continued:
p a
2
3
This formula is for objects orbiting the Sun.
p will be in Earth years and a is A.U.
p peri  a(1  e)
aap  a(1  e)
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
The gravitational parameter,
For the Sun,
( Note, GM   )
= 132,712,440,018
km 3
sec 2
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 ?
P  4 , p  64,
2
P
3
2
64, P  8 years
Conversions
To change from km/sec to miles/hr
Km/sec (3600 sec/hr)(0.62137 miles/km= miles/hr
To change from AU to km multiply by 150,000,000 or
1.5 X 108 km
e has no units.
** 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.
a
e
p peri  aap
2
aap  p peri
aap  p peri
2  4.5
a
 3.25au
2
4.5  2 2.5
e

 0.385
4.5  2 6.5
Find the perihelion, and aphelion distances.
p peri  a (1  e) = 3.25au (1 - 0.385) = (3.25)(.615) = 1.99 au
aap  a (1  e)
= 3.25au (1+ 0.385) = 4.43 au
Find the period.
Pperiod  a
2
3
Pperiod  3.253
2
Pperiod  5.86 years
For distance, Perihelion, and aphelion must be changer to km, since  contains
km . To change multiply au by 150,000,000 km/au , or
1.5 X 108
= 132,712,440,018
Find the velocity at perihelion
V p peri 
 (1  e)
p peri
Vpperi  2.48km / sec
Vpperi  24.8km / sec
km 3
sec 2
1.327 X 10 (1  0.385)

8
1.99(1.5 X 10 )
11
Vp peri
Vp peri
18.38 X 1010

2.99 X 108
24.8 km/sec(2236.93) = 55,475 miles/hour
Find the velocity at aphelion.
Va ap 
1.3267 x1011 (1  .385)
Va 
4.43(1.5 X 108 )
 (1  e)
aap
11
0.816 X 10
Va 
8
6, 645 X 10 )
8.16 X 1010
Va 
6.645 X 108 )
Va  3.504km / sec = 3.504(2236.93 )
= 7,838.2
miles/hour
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
•The names have to do with the optical
light.
phenomenon at work (refraction (bend) or
reflection).
•A curved primary surface ( mirror or lens) is
necessary to bring the light to focus.
Refracting Telescopes
•Refracting telescopes use two convex lenses to magnify
distance objects.
Objective Lens & eyepiece
•
Focus
Secondary Lens
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
Largest
Refracting
Telescope 40
inch
The
Refractor
Optics
focal length
The Yerkes 40” Refractor
Good & Bad of Refracting Telescopes
•They are easy to use.
•The “original” type was invented in the
•1500’s and used by Galileo.
•Lenses are heavy and expensive!
•Sharpest, brightest images.
•Prone to chromatic aberration.
•Gives an inverted (upside-down) image.
•Maximum size of telescope about 40
• inches in diameter due to weight..
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.
Cassegrains: Lens & Mirror
•Very short tube length, because the light gets
“folded” back on itself twice. This makes the
scope easy to handle & transport.
The corrector plate is a type of lens. A secondary mirror
is glued to its inside.
•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 Magnify
• Magnification is the number of times larger
an object appears through a telescope than
as seen by the naked eye
Focal Length of the Objective Lens or Mirror
Magnification 
Focal Length of the Eyepiece
M = fo / fe
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
Factors Affecting Optical Astronomy
• Weather & Earth’s Atmosphere
Seeing – turbulence in the atmosphere, causes
the twinkling of stars and images to shift. Note:
Planets do not twinkle
1908
Los Angeles
–Light Pollution
from near by
street lights or
distant city lights
1988
Light 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 atmosphere
Darker skies especially for infrared
You 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
Water vapor blocks IR at altitudes 2-10 km.
Various atoms , and molecules block x-rays , and
gamma rays.
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 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 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