Question

Паралакс Сіріуса дорівнює 0".37, а паралакс Веги 0". 12. Виміряйте відстань до цих зір в парсеках, у світлових роках, в астрономічних одиницях та в кілометрах.​

Answer 1

Ответ:   Расстояние до Сириуса =  2,(702) пк. = 557472,9 а.е. =  8,3398*10^10 км.

Расстояние до Веги = 8,(3) пк. =  1718875 а.е. =

2,57144 *10^14 км

Объяснение:  Расстояние в парсеках определяется выражением Sпк = 1/p",  здесь p" - параллакс.

Для Сириуса Sпк = 1/0,37" = 2,(702) пк.

В одном парсеке 206265 астрономических единиц. Значит, расстояние до Сириуса в а.е.

Sа.е. = 2,(702)*206265 ≈ 557472,9 а.е.

В одной астрономической единице 149600000 км, значит расстояние до Сириуса в километрах

Sкм = 557472,9*149600000 = 83397956756,(756) км ≈

≈ 8,3398*10^10 км.

Для Веги          Sпк = 1/0,12" = 8,(3) пк.

          Sа.е = 8,(3)*206265 = 1718875 а.е.

          Sкм = 1718875 * 149600000 = 257143700000000 км ≈

≈ 2,57144 *10^14 км

Answer 2

Parallax of Sirius and Vega

The parallax of a star is a measurement used to determine its distance from Earth. It is based on the apparent shift in the position of the star as observed from different points in Earth's orbit around the Sun. The parallax angle is usually measured in arcseconds (") and is inversely proportional to the distance of the star.

According to the provided information, the parallax of Sirius is 0".37, while the parallax of Vega is 0".12. We can use these values to calculate the distances to these stars in parsecs, light-years, astronomical units, and kilometers.

Calculating the Distances

To calculate the distances to Sirius and Vega, we can use the formula:

Distance (in parsecs) = 1 / Parallax (in arcseconds)

1. Distance in Parsecs: - For Sirius: Distance = 1 / 0".37 = 2.7027 parsecs - For Vega: Distance = 1 / 0".12 = 8.3333 parsecs

2. Distance in Light-Years: - To convert parsecs to light-years, we can use the conversion factor: 1 parsec = 3.2616 light-years. - For Sirius: Distance = 2.7027 parsecs * 3.2616 light-years/parsec = 8.7896 light-years - For Vega: Distance = 8.3333 parsecs * 3.2616 light-years/parsec = 27.1833 light-years

3. Distance in Astronomical Units: - To convert parsecs to astronomical units, we can use the conversion factor: 1 parsec = 206,265 astronomical units. - For Sirius: Distance = 2.7027 parsecs * 206,265 astronomical units/parsec = 557,335.6 astronomical units - For Vega: Distance = 8.3333 parsecs * 206,265 astronomical units/parsec = 1,719,997.4 astronomical units

4. Distance in Kilometers: - To convert parsecs to kilometers, we can use the conversion factor: 1 parsec = 3.086e+13 kilometers. - For Sirius: Distance = 2.7027 parsecs * 3.086e+13 kilometers/parsec = 8.34e+13 kilometers - For Vega: Distance = 8.3333 parsecs * 3.086e+13 kilometers/parsec = 2.57e+14 kilometers

Therefore, the distances to Sirius and Vega are as follows: - Sirius: - Distance in parsecs: 2.7027 parsecs - Distance in light-years: 8.7896 light-years - Distance in astronomical units: 557,335.6 astronomical units - Distance in kilometers: 8.34e+13 kilometers

- Vega: - Distance in parsecs: 8.3333 parsecs - Distance in light-years: 27.1833 light-years - Distance in astronomical units: 1,719,997.4 astronomical units - Distance in kilometers: 2.57e+14 kilometers

Please note that these calculations are based on the provided parallax values and the conversion factors mentioned above.