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Elliptical Orbits

Elliptical Orbits. 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. a. a. Sun. A. P. C.

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Elliptical Orbits

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  1. Elliptical Orbits

  2. 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 a a Sun A P C 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.)

  3. e= 0.91 e is how much the orbit departs from a circle where e=0. aphelion - perihelion e = _______________________ aphelion + perihelion e=0 a = aphelion + perihelion circle _________________________ 2 perihelion aphelion Sun Perihelion is closest , and aphelion is farthest from the Sun.

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

  5. Formulas continued: This formula is for objects orbiting the Sun. p will be in Earth years and a is A.U. 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, ( Note, ) For the Sun, = 132,712,440,018

  6. Using the Kepler’sThird Law P2µ 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 ?

  7. 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 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.

  8. 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. Find the perihelion, and aphelion distances. = 3.25au (1 - 0.385) = (3.25)(.615) = 1.99 au = 3.25au (1+ 0.385) = 4.43 au

  9. Find the period. For distance, Perihelion, and aphelion must be changer to km, since contains km . To change multiply au by 150,000,000 km/au , or = 132,712,440,018 Find the velocity at perihelion 24.8 km/sec(2236.93) = 55,475 miles/hour

  10. Find the velocity at aphelion. = 3.504(2236.93 ) = 7,838.2 miles/hour

  11. Telescopes Why use a telescope? • To Brighten • To Magnify • To Resolve

  12. 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.

  13. Refracting Telescopes Focus • Refracting telescopes use two convex lenses to magnify distance objects. Objective Lens & eyepiece Secondary Lens (Eyepiece) Objective Lens Focal Length of a lens

  14. 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

  15. Largest Refracting Telescope 40 inch The Refractor Optics focal length The Yerkes 40” Refractor

  16. 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..

  17. Newtonian Telescopes • curved concave mirror • flat mirror (Diagonal Mirror) • eyepiece • a.k.a. Reflecting Telescopes

  18. 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.

  19. 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.

  20. 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.

  21. Alt-azimuth mounting – Telescope axis points toward the zenith. • Requires movement along both axes to track an object.

  22. 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

  23. 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.

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

  25. Telescopes Magnify • Magnification is the number of times larger an object appears through a telescope than as seen by the naked eye 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

  26. 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

  27. 1908 Los Angeles • Light Pollution from near by street lights or distant city lights 1988

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

  29. Light Pollution Nighttime around the Earth

  30. 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.

  31. 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.

  32. 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.

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

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

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

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

  37. 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)

  38. SPITZER SPACE TELESCOPE • Infrared telescope • 85 cm diameter (33.5 inches) • Wavelength Coverage: 3 - 180 microns • 2.5 years (minimum); 5+ years (goal)

  39. 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.

  40. X-RAY ASTRONOMY • Must be done from space • Extremely high energy radiation (black hole accretion disks). • Requires special grazing incidence telescopes

  41. CHANDRA X-RAY OBSERVATORY

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