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# Connect with Maths ~Maths in Action~ Pulsars in the Classroom

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Pulsars in the Classroom: Presenter Stephen Broderick
"Let's do real world mathematics" The "Pulsar" project is designed to engage students in scientific projects that will give them a positive attitude towards science and mathematics, and appreciation of how maths is applied in the real world.
PULSE@Parkes allows students to directly control Parkes radio telescope over the Internet and use it to do real science. It is the only program of its kind in the world.

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### Connect with Maths ~Maths in Action~ Pulsars in the Classroom

1. 1. Australian Telescope National Facility Marsfield, Sydney
3. 3. International SKA (Square Kilometre Array)
4. 4. How high would a stack of 15 million ipods be? What area would all of the ipods cover when laid flat?
5. 5. How high would a stack of 15 million ipods be? 15 000 000 x 0.5 cm ÷ 100 000 = 75 km What area would all of the ipods cover when laid flat? Area = 15 000 000 x 11 x 6 ÷ 1002 = 99 000 m2 (9.9 ha)
6. 6. Australian Curriculum Measurement and geometry Solve problems involving surface area and volume of right pyramids, right cones, spheres and related composite solids (ACMMG271)
7. 7. Statistics and probability Use scatter plots to investigate and comment on relationships between two continuous variables (ACMSP251)
8. 8. Number and algebra Solve problems involving direct proportion. Explore the relationship between the graphs and equations corresponding to simple rate problems (ACMNA208)
9. 9. Number and algebra Use the definition of a logarithm to establish and apply the laws of logarithms (ACMNA265)
10. 10. SKA Will generate approximately 7 000 000 000 000 000 000 bytes of data in the first week. (7 x 1018 bytes = 7 exobytes) ≈ All the words ever spoken by humanity
11. 11. Average number of words ever spoken by all of humanity (per day) 100 billion people (100 x 109) throughout the ages. Average number of words spoken per person in one life time 7 × 1018 = 100 × 109 = 7 x 107 7 × 107 75 × 365 ≈ 2600 words per day Average per day =
12. 12. Facts about Parkes, Pulsars and Pulse@Parkes
13. 13. Fact # 1 Since December 2007, over 1000 students from interstate schools and overseas institutions have used the Parkes Radio Telescope to collect data on pulsars for analysis. Students have controlled the telescope via the internet to observe several pulsars. Frequently Asked Questions answered at: http://outreach.atnf.csiro.au/education/pulseatparkes/teachers/teachers.html
14. 14. Fact # 2 A pulsar is a rapidly rotating neutron star. Jets of electromagnetic radiation stream from the pulsar and are observed as pulses of radio waves because of this rotation. The Parkes Radio telescope has been instrumental in discovering nearly two-thirds of all known pulsars.
15. 15. Fact # 3 What is a Pulsar? • In 1934 Walter Baade and Fritz Zwicky proposed the existence of a new type of star -neutron star • In 1967 Jocelyn Bell discovered a pulsar(media reported the discovery as little green men)
16. 16. Fact # 4 Properties • density of 1017 Kg/m-3 • thimbleful has a mass of 109 tonnes • rotates once to several hundred times per second • acceleration due to gravity at surface of pulsar is ~ 1012 m.s-2 (10 m.s-2 at Earth) • escape velocity ~ 50% of the speed of light.
17. 17. Fact # 5 Typical pulsar diameters are approximately 20 to 25 kilometres with a mass roughly 1.4 times the mass of the Sun. The mean density is approximately 6.7 x 1014 grams/cm3 which is equivalent to a single sugar cube weighing as much as all of humanity (approximately the weight of 7 billion people).
18. 18. Fact # 6 PSR J1023+0038, is the fastest known millisecond pulsar. It lies 4,000 light years away in the constellation Sextants and spins at a rate of 592 times a second. After discovery in 2007 , the Parkes radio telescope was used to get the first full orbit observations. Astronomers have long thought that millisecond pulsars are ordinary pulsars “spun up” with the help of an orbiting companion star. The companion dumps matter onto the pulsar, causing it to spin far faster.
19. 19. Fact # 6 continued Speed = 푑푖푠푡푎푛푐푒 푡푚푒 = 휋 푑 푡푖푚푒 = 휋 25 1 592 diameter = 25 km = 46,496 km/sec (15% speed of light)
20. 20. Fact # 5 The 64 metre Parkes radio telescope was built in 1961 and has operated continuously for over 50 years. It is a world class instrument at the forefront of radio astronomy due to continual upgrades. It is now 10,000 times more sensitive than when it was first built.
21. 21. Fact # 6 A pulsar map was included on the Pioneer 10 and 11 probes launched in 1972 and 1973 respectively. They show the position of the Sun, relative to 14 pulsars, so that our position in space can be calculated by extra-terrestrials that encounter the probes.
22. 22. Fact # 7 The pulsar catalogue has over 1,900 pulsars and can be accessed electronically at the link below. Some pulsars have two different designations (B and J). The designation B indicates 1950 coordinates which were used prior to 1993, whereas the J designation is now used in 2000 coordinates . The J designation also uses a more accurate declination. The example below includes both designations for the same pulsar. Before 1993 PSR B 1919+21 Pulsating source of radio After 1993 PSR J 1919+2153 Location of the pulsar (right ascension , declination) The complete pulsar catalogue can be found at: http://www.atnf.csiro.au/research/pulsar/psrcat/
23. 23. Fact # 8 The line graph indicates the number of known pulsars from 1967 to 2011. Discovery of the first pulsar PSR B 1919+21 in July 1967 by Jocelyn Bell.
24. 24. Fact # 9 The nearest millisecond pulsar (MSP)discovered in 1992 during the Parkes 70 cm survey is approximately 510 light years away. It is known as PSR J0437-4715 and it has a period of 5.757451831072007  0.000000000000008 milliseconds It is the most stable natural clock in the whole universe.
25. 25. Fact # 10 The Parkes radio telescope is so sensitive that a mobile phone call from Pluto would be considered a really strong signal.
26. 26. Australian and U.S. astronomers used CSIRO's Parkes radio telescope to measure the distortion of space-time around the pulsar J0437-4715 and its companion white dwarf. In this pulsar system, the pulsar's radio waves travel through the curved space-time around its white dwarf companion, and arrive on Earth a little later than if they had travelled through undistorted space-time. The effect, called the Shapiro delay, was first proposed in 1964 by Irwin I. Shapiro. The data clearly showed the predicted delay, making this the first test of general relativity in which the geometry of the system has been used to predict a relativistic effect. This provided another confirmation of Einstein's general theory of relativity. Fact # 11
27. 27. Fact # 12 75% of all known pulsars have a period of less than a second. In 1999, Astronomers using the Parkes radio telescope found the pulsar J 2144-3933. This pulsar, which spins only once every eight seconds, defied existing theories on the upper limit for pulsar periods.
28. 28. Fact # 13 Astronomers using the Parkes radio telescope in conjunction with the 76-metre Lovell Telescope in England have discovered a possible diamond planet orbiting a newly detected pulsar, PSR J1719-1438 located 4,000 light years away.
29. 29. Fact # 14 The first confirmed exoplanets discovered several years before the first detections of exoplanets around “normal” solar-like stars, were found in orbit around a millisecond pulsar, PSR B1257+12. These planets remained for many years the only Earth-mass objects known outside our solar system. And one of them comparable to that of our Moon in mass, is still today the smallest-mass object known beyond the solar system.
30. 30. Fact # 17 The magnetic axis of a pulsar aligned with the radio beam is usually not aligned with the rotation axis.
31. 31. Fact # 18 The hard disk drive of a computer rotates at high speed, commonly 7,200 revolutions per minute or 120 revolutions per second. The time to complete one revolution is 8.33 milliseconds. This is similar to the pulsar J1518+0204 which has a period of 7.9 milliseconds and hence rotates slightly quicker at 127 revolutions per second. period = 8.33 milliseconds period = 7.9 milliseconds
32. 32. Fact # 19 Millisecond pulsars (MSPs) have rotational periods in the range from 1 to 30 milliseconds. They have been detected in radio, x-ray and gamma ray portions of the electromagnetic spectrum. One theory about their formation is that they begin life as longer period pulsars but are spun up or "recycled" through accretion of a companion star. The transfer of angular momentum from the accretion of the companion can theoretically increase the rotation rate of the pulsar to hundreds of times a second, as is observed in millisecond pulsars.
33. 33. Fact # 20 Two main types of pulsars Normal pulsars • Are quite young, ˂ 107 years • Periods from 0.03 – 10 seconds • Mostly single (non-binary) • Formed in supernova • Magnetic field strength approximately 1012 gauss Millisecond pulsars • Are very old, ˃ 109 years • Periods from 1 – 30 milliseconds • Mostly binary • Accretion from companion “spins up” the neutron star to a millisecond pulsar • Magnetic field strength between 108 -109 gauss
34. 34. Fact # 21 The first binary pulsar was discovered by the Parkes radio telescope in 2003. One of the pulsars has a period of 22 milliseconds and the other pulsar has a period of 2.7 seconds. The orbital period for the binary pulsar system is 2.4 hours. This is a highly relativistic binary system which is a laboratory for testing Einstein’s general theory of relativity.