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Given that SgrA* lies at a distance of 26,000 ly away from Earth, find the distance subtended by star S2 when our telescopes detect that S2 moves 1 arcsec. Remember to convert angles into radians, and express your answer in ld (light days). This ratio of 1 arcsec...

a) Distance Subtended = π(26,000 ly)

b) Distance Subtended = 26,000 ld

c) Distance Subtended = 26,000 π ld

d) Distance Subtended = 1 ld / 26,000

User HeikoG
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Final answer:

The distance subtended by star S2 when it moves 1 arcsecond is found by converting the angle to radians and then using the formula for the subtended distance, which is not matched by any of the answer options given in the question.

Step-by-step explanation:

The question is asking for the distance subtended by star S2 when it moves 1 arcsec as seen from our telescopes on Earth, with the known distance to SgrA* at 26,000 light-years (ly). To solve this, we need to convert the angular measurement from arcseconds to radians because the formula for finding the subtended distance (s) is s = θ × D, where θ is the angle in radians and D is the distance to the object. One arcsecond is 1/206,265 of a degree (since 1 degree = 3600 arcseconds and 1 parsec = 206,265 AU), and to convert degrees to radians we multiply by π/180. Therefore, we convert the 1 arcsec to radians as follows: 1 arcsec × (π/180 degrees) × (1 degree/206,265 arcsec) = π/(180 × 206,265).

Now, we multiply this angle in radians by the distance to SgrA* in light-years to find the distance subtended by S2 in light-years. Since we want the answer in light-days (ld), we use the fact that 1 ly = 365.25 ld. Therefore, the distance subtended by S2 moving 1 arcsec is π/(180 × 206,265) × 26,000 ly × 365.25 ld/ly. Simplifying this gives us the answer, which is none of the options provided in the question. It's important to realize that the distance has to be calculated rather than simply picked from the options a) through d).

User ZeroStack
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