question: Astronomers say there are more stars in the universe than there are grains of sand on all the beaches on earth. How do they know how many grains of sand there are in the whole world?
comment: We can estimate both the volume and mass of the Earth. Take a bucket of sand, weigh it, measure its volume, then count the number of grains of sand in it. You now have an estimate of the number of grains per kg or per litre of sand. You can use that to estimate the maximum number of grains. We could assume the whole world were nothing but sand, take the mass of the Earth and multiple it by the number of grains of sand in a kilogram, and you’d have the maximum possible number of grains. Obviously the whole Earth isn’t made of sand, so we could be a little more careful. We could assume the top km of the Earths crust was made of sand, and multiple that volume by the number of grains of sand in a litre. This would be closer. Keep repeating this process and you’d get a ballpark figure of the number of grains of sand on Earth. Not an exact number, but a reasonable maximum.
passages: In God reminded Isaac that God had promised Abraham that God would make his heirs as numerous as the stars. In God promised that Abraham's descendants would as numerous as the stars of heaven. In God promised that the Abraham's descendants would as numerous as the stars of heaven and the sands on the seashore. The astronomer Carl Sagan reported that there are more stars in the universe than sands on all the beaches on the Earth.
   Anna Katherina Vivas (1972) is a Venezuelan astrophysicist recognized for her investigations of and finding up to 100 new and very distant RR Lyrae stars. They are between 13,000 and 220,000 light years from the Sun, and are considered some of the oldest in the Milky Way. Her research has enabled some of the first studies of the structure and properties of the whole halo of the Milky Way and not only its innermost parts. The observation was made possible by combining a telescope with a large format camera, allowing astronomers to cover large portions of the sky in a short amount of time.
   Section::::In modern interpretation.:Genesis chapter 15.
  
  In God promised that Abraham’s descendants would be as numerous as the stars of heaven. In God promised that Abraham’s descendants would be as numerous as the stars of heaven and the sands on the seashore. The astronomer Carl Sagan reported that there are more stars in the universe than sands on all the beaches on the Earth.
   In 2004, a team of astronomers focused on the cluster to estimate the age of the Milky Way Galaxy. The team consisted of Luca Pasquini, Piercarlo Bonifacio, Sofia Randich, Daniele Galli, and Raffaele G. Gratton. They used the UV-Visual Echelle Spectrograph of the Very Large Telescope at Cerro Paranal to measure the beryllium content of two stars in the cluster. This allowed them to deduce the time elapsed between the rise of the first generation of stars in the entire Galaxy and the first generation of stars in the cluster. This, added to the estimated age of the stars in the cluster, gives an estimate for the age for the Galaxy: about 13.6 billion years, which is nearly as old as the universe itself.
   After working on the WMAP mission Verde turned her attention to developing rigorous statistical tools to analyze surveys of the universe and thus connect theoretical models to the observations.
   Section::::In modern interpretation.:Deuteronomy chapter 10.
  
  In Moses reported that God had made the Israelites as numerous as the stars, echoing in which God promised that Abraham's descendants would be as numerous as the stars of heaven, and in which God promised that Abraham's descendants would be as numerous as the stars of heaven and the sands on the seashore. The astronomer Carl Sagan reported that there are more stars in the universe than sands on all the beaches on the Earth.
  
  Section::::In modern interpretation.:Deuteronomy chapter 11.
   Finding no star bigger than 200 solar masses, Oey and her colleagues at the University of Michigan at Ann Arbor have found evidence for a size limit in a survey of other clusters within our galaxy and in the nearby satellite galaxy, Magellanic clouds. "It is not clear whether the size is limited by the physics of star formation or by the size of the parent gas cloud. Larger stars, perhaps of up to 500 solar masses, may have existed in the early universe" Oey says.
  
  Section::::External links.
  
  BULLET::::- Curriculum Vitae
  
  BULLET::::- Faculty website
   Clusters are also a crucial step in determining the distance scale of the universe. A few of the nearest clusters are close enough for their distances to be measured using parallax. A Hertzsprung–Russell diagram can be plotted for these clusters which has absolute values known on the luminosity axis. Then, when similar diagram is plotted for a cluster whose distance is not known, the position of the main sequence can be compared to that of the first cluster and the distance estimated. This process is known as main-sequence fitting. Reddening and stellar populations must be accounted for when using this method.
   The closest open clusters can have their distance measured directly by one of two methods. First, the parallax (the small change in apparent position over the course of a year caused by the Earth moving from one side of its orbit around the Sun to the other) of stars in close open clusters can be measured, like other individual stars. Clusters such as the Pleiades, Hyades and a few others within about 500 light years are close enough for this method to be viable, and results from the Hipparcos position-measuring satellite yielded accurate distances for several clusters.
   BULLET::::- 2007 Astronomical Journal, 134, P.1089 Sowell, J. R.; Trippe, M.; Caballero-Nieves, S. M.; Houk, N. H-R Diagrams Based on the HD Stars in the Michigan Spectral Catalogue and the Hipparcos Catalog
  
  BULLET::::- 2007 Astronomical Journal, Volume134, P.1072 Caballero-Nieves, S. M.; Sowell, J. R.; Houk, N. Galactic Distributions and Statistics of the HD Stars in the Michigan Spectral Catalogue
   Based on their distances (measured with Hipparcos) and apparent magnitude, the absolute magnitude can be used to estimate the age of the stars. The stars in the moving group appear to have a common age of about 500 million years.
  
  Section::::Group members.:Core stars.
  
  The core of the moving group consists of 14 stars, of which 13 are in the Ursa Major constellation and the other is in the neighboring constellation of Canes Venatici.
  
  The following are members of the moving group closest to its center. These stars are all in Ursa Major except where indicated.
  
  Section::::Group members.:Stream stars.
   Yaël Nazé
  
  Yaël Nazé is a Belgian astrophysicist who works at the University of Liège. She specializes in massive stars and their interactions with their surroundings.
  
  Section::::Biography.
   At the conclusion of that fellowship in November 2013, Bauer took up the role of Research Astronomer at the AAO. Her area of research investigates the processes by which galaxies form, and particularly why they eventually stop creating new stars. In order to explore how galaxies build into the diverse structures we see today, she analyzes systematic surveys of hundreds of thousands of galaxies, looking for clues that indicate what physical processes regulate the rates at which new stars are formed in galaxies which are subjected to different conditions.
   BULLET::::- Determine the positions of stars at a magnitude of V = 10 down to a precision of 7 μas—this is equivalent to measuring the position to within the diameter of a hair from 1000 km away—between 12 and 25 μas down to V = 15, and between 100 and 300 μas to V = 20, depending on the colour of the star.
   Expansion parallaxes in particular can give fundamental distance estimates for objects that are very far, because supernova ejecta have large expansion velocities and large sizes (compared to stars). Further, they can be observed with radio interferometers which can measure very small angular motions. These combine to provide fundamental distance estimates to supernovae in other galaxies. Though valuable, such cases are quite rare, so they serve as important consistency checks on the distance ladder rather than workhorse steps by themselves.
  
  Section::::Standard candles.
   BULLET::::- 7C — Seventh Cambridge Survey
  
  BULLET::::- 8C — Eighth Cambridge Survey
  
  BULLET::::- 8pc — 8 parsec listing, "all stars within 8 parsec"
  
  BULLET::::- 9C — Ninth Cambridge survey at 15GHz
  
  Section::::A.
  
  BULLET::::- A - Antalova (open star clusters)
  
  BULLET::::- AB - Azzopardi / Breysacher (Wolf-Rayet stars in the Small Magellanic Cloud, SMC)
  
  BULLET::::- Abel (globular star clusters)
  
  BULLET::::- Abell — Abell catalogue
  
  BULLET::::- Abetti - Giorgio Abetti (double stars)
  
  BULLET::::- Abt - (for example: open star cluster Abt 1 = Biurakan 4 = Markarian 6)
  
  BULLET::::- AC — Astrographic Catalogue
  
  BULLET::::- A.C. - Alvan Clark (double stars)
   In 1983, based on radiation in the infrared portion of the electromagnetic spectrum, the InfraRed Astronomical Satellite was used to identify dust orbiting this star. This debris disk is constrained to a diameter of 12.2 AU.
  
  By 2001, the "Long Wavelength Spectrometer" at the Keck Observatory on Mauna Kea, Hawaii, was used more accurately to constrain the radius of the dust. It was found to lie within a 5.4 AU radius. The temperature of the dust was estimated as about 340 K. Based on heating from the star, this could place the grains as close as 2.5 AU from Zeta Leporis.
   Using Type Ia supernovae is one of the most accurate methods, particularly since supernova explosions can be visible at great distances (their luminosities rival that of the galaxy in which they are situated), much farther than Cepheid Variables (500 times farther). Much time has been devoted to the refining of this method. The current uncertainty approaches a mere 5%, corresponding to an uncertainty of just 0.1 magnitudes.
  
  Section::::Extragalactic distance scale.:Supernovae.:Novae in distance determinations.
   Delta Cancri also marks the famous open star cluster Praesepe (or the Beehive Cluster, also known as Messier 44). In ancient times M44 was used as a weather gauge as the following Greek rhyme from Aratos' "Prognostica" reveals:
   BULLET::::- Sh - Sher (open star clusters) (for example: Sher 1 at 11:01:04 / -60:14:00)
  
  BULLET::::- S, h - James South / John Herschel (joint 1824 catalogue of double stars)
  
  BULLET::::- Shk - Romela Karapet Shakhbazian (compact groups of galaxies) (for example: Shakhbazian 1 (the 'Russian Cluster') in Ursa Major, at 10:54.8 / +40°28')
  
  BULLET::::- Shorlin - (for example: open star cluster Shorlin 1 at 11:05:46 / -61:13:48)
  
  BULLET::::- Simeis - (for example: supernova remnant Simeis 147 / Sh2-240 in Taurus, also known as the 'Spaghetti Nebula')
  
  BULLET::::- SIMP — Sondage Infrarouge de Mouvement Propre
   A number of teams have put together fireball observatories based on the same principles, e.g. the Prairie Network (US) and the Canadian Meteorite Observation and Recovery Network, which were led primarily by observational astronomers, and yet collectively have only determined orbits for four meteorites.
   BULLET::::- Nordgren, T. E., "Stars Above, Earth Below: A Guide to Astronomy in the National Parks", 2010 (Springer).
  
  BULLET::::- Nordgren, T. E., Lane, B. F., Hindsley, R. B., and Kervella, P., "Calibration of the Barnes–Evans Relation Using Interferometric Observations of Cepheids", The Astronomical Journal, 123, 3380, 2002.
  
  BULLET::::- Nordgren, T. E., Sudol, J. J., and Mozurkewich, D., "Comparison of Stellar Angular Diameters from the NPOI, the Mark III Optical Interferometer, and the Infrared Flux Method", The Astronomical Journal, 122, 2707, 2001.
   Section::::Methods for discovery.:Nearest-neighbor test.
  
  Using a nearest neighbor statistics, a similar test to the 2D K-S test, 21 consecutive probabilities in group 4 reach the 2σ limit and 9
  
  consecutive comparisons reach the 3σ limit. One can calculate binomial probabilities. For example, 14 out of the 31 GRBs in this redshift band are concentrated in approximately 1/8 of the sky. The binomial probability of finding this deviation is p=0.0000055.
  
  Section::::Methods for discovery.:Bootstrap point-radius.
   In addition, knowing the age of one member of a star system can help determine the age of that system. In a star system, stars almost always form at the same time as each other, and given the age of one star, the age of all of the others can be known.
   Anna Watts
  
  Anna Louise Watts is an Associate Professor of Astrophysics at the University of Amsterdam. She studies neutron stars and their thermonuclear explosions.
  
  Section::::Education.
  
  Watts was educated at Bradford Girls' Grammar School. She studied Physics at Merton College, Oxford, and graduated with a first class degree from the University of Oxford in 1995. She entered the science stream at the Ministry of Defence on a graduate scheme, where she worked for five years. Watts completed her PhD in physics supervised by in the general relativity group researching neutron stars.
  
  Section::::Career and research.
  