Review of the Principles of Stellar Parallax and Practice Problems

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Presentation transcript:

Review of the Principles of Stellar Parallax and Practice Problems Review Chapter 11.1.1 Distances – Trignometric Parallax in AstronomyNotes for a more complete discussion of the details of stellar Parallax.

The Geometry of Stellar Parallax The Sun, ʘ, is at point a and the planet/location of the observer is at point b. The distance to the star is indicated by D and is expressed in parsecs (1 parsec = 3.26 lyr) The baseline distance between the Sun and the point of observation is denoted as ab and must be expressed in astronomical units (AU). a b Distance, D ʘ p The measured parallax angle is indicated as p and must be expressed in arcseconds (3,600 arcseconds = 1 degree). The stellar parallax relation is

The stellar parallax relation is Practice Problem 1: As seen from Earth, the measured parallax of a star is 0.35 arcseconds. How far away is the star in parsecs, ly and AUs? Solution: Determine the baseline distance. Since the parallax measurement is made from Earth then the baseline distance from the Sun to the Earth is simply 1 AU, So ab =1 in the stellar parallax relation. Solve the stellar parallax relation Convert parsecs to lys 4. Convert lys to AU Answer in a sentence: The star is 2.86 parsecs from Earth, equivalent to 9.31 ly and 589,000 astronomical units.

The stellar parallax relation is Practice Problem 2: As seen from Earth, the measured parallax of a star is 0.051 arcseconds. How far away is the star in parsecs, ly and AUs? Answer in a sentence: The star is 19.6 parsecs from Earth, equivalent to 63.9 ly and 4.04 million astronomical units.

The stellar parallax relation is Practice Problem 3: As seen from Mars, the measured parallax of a star is 0.405 arcseconds. How far away is the star in parsecs, ly and AUs? Note: The semimajor axis of the orbit of Mars is 1.52 AU. Answer in a sentence: The star is 3.75 parsecs from Earth, equivalent to 12.2 ly and 774,000 astronmical units.

The stellar parallax relation is Practice Problem 4: As seen from Earth, the measured parallax of a star is 0.25 arcseconds. What would be the measured parallax of this star as observed from Saturn? Note: The semimajor axis of the orbit of Saturn is 9.5 AU. Hint: First find the distance to the Star using the Earth observation and then change to baseline distance to that appropriate for the Saturn observation and solve the stellar parallax relation for the parallax angle using the distance to the star you found from the Earth observation. Answer in a sentence: The measured parallax of this star as observed from Saturn would be 2.37″.

The stellar parallax relation is Practice Problem 5: You wish to measure the stellar parallax of a star at the galactic center 28,000 ly away. However, your best technology can measure parallax angles only as small as 0.005″. How far from the Sun must your instrument be placed in orbit to measure the parallax of this star at the galactic center? Hint: First convert 28,000 ly into parsecs, then using the minimum parallax angle measureable solve the stellar parallax relation for the baseline distance ab. Answer in a sentence: The instrument must orbit the Sun at a distance of 42.9 AU to measure a parallax angle of 0.005″ for a star 28,000 ly distant.