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is roughly 947 1012 km This turns out to be a little less than 6 trillion miles There we go with incomprehensible numbers again! Let s think on a cosmic scale The nearest star to our Solar System is a little more than 4 light-years away The standard distance for measuring absolute magnitude is 326 light-years The Milky Way galaxy is 100,000 light-years across The Andromeda galaxy is about 22 million light-years away Using powerful telescopes, astronomers can peer out to distances of several billion light-years (where 1 billion is defined as 109 or 1,000 million) Well, the light-year helps us to comprehend the distances to stars within our galaxy, but once we get into intergalactic space, even this unit is not enough to make distances easy to imagine

14:

where Ecm is the lumped common mode errors other that the ionospheric 403 delay Ia = f1 f2 T EC, i represents the sum of the receiver noise and multipath errors, and f1 and f2 are the carrier frequencies In the analysis to follow, we will assume that 1 and 2 are independent, Gaussian random 2 variables with variance Eqns (883 884) can be manipulated to provide an ionospheric free pseudorange observable as =

2 Under Options, click the Set link The Select The Report Options screen displays showing the default values for the report:

(885)

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The actual distances to the stars remained a mystery until the advent of the telescope, with which it became possible to measure extremely small angles The angular degree represents 1/360 of a full circle Smaller units are the minute of arc, representing 1/60 of an angular degree, and the second of arc, measuring 1/60 of a minute These units were introduced in 1 To determine the distances to the stars, astronomers had to be clever Could it be done by triangulation, the way surveyors measure distances on Earth For this to work, it would be necessary to use the longest possible baseline What would that be How about the diameter of the Earth s orbit around the Sun This presented a problem for people who believed that Earth was the center of creation and that everything else revolved around it However, by the time astronomers were ready to seriously attempt to determine distances to the stars, the heliocentric theory had gained general acceptance Figure 13-1 shows how distances to the stars can be measured This scheme works only for nearby stars Most stars are too far away to produce any measurable parallax against a background of much more distant objects, even when they are observed from opposite sides of Earth s orbit (In this figure, the size of Earth s orbit is exaggerated for clarity) The star appears displaced when viewed from opposite sides of the Sun This displacement is maximum when the line connecting the star and the Sun is perpendicular to the line connecting the Sun and Earth A star thus oriented, and at just the right distance from us, will be displaced by 1 second of arc when viewed on two occasions 6 months apart in time This distance is

Part III:

(886)

3 Select the Override The Default Values checkbox The Select The Report Options screen displays with report options that can be modified:

Eqn (885) is not usually used directly, because as shown in eqn (886), 2 the noise variance (ie, e ect of 1 and 2 on ) is approximately 9 The following two paragraphs discuss alternative approaches to the construction of ionospheric free pseudorange observables An estimate of the ionospheric delay can be computed as Ia = f1 f2 2 2 ( 2 1 ) f1 f2 (887)

called a parsec (a contraction of parallax second) The word parsec is abbreviated pc and is equivalent to approximately 326 light-years Sometimes units of kiloparsecs (kpc) and megaparsecs (Mpc) are used to express great distances in the Universe; in this scheme, 1 kpc 1,000 pc 3,260 light-years, and 1 Mpc 1 million pc 326 million light-years Now, finally, intergalactic distances become credible The nearest visible object outside our Solar System is the Alpha Centauri star system, which is 14 pc away There are numerous stars within 20 to 30 pc of Earth The standard distance for measuring absolute visual magnitude is 10 pc The Milky Way is 30 kpc in diameter The Andromeda galaxy is 670 kpc away And on it goes, out to the limit of the observable Universe, somewhere around 3 billion pc, or 3,000 Mpc

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