Question

Please explain all of these with steps

Thank you

1)Star A appears to move by about 0.021 arcseconds across a set of back ground stars, as measured from two extremes of the Earth's orbit. How far away, in parsecs, is Star A?

2) Star B appears to move by about 0.019 arcseconds across a set of back ground stars, as measured from two extremes of the Earth's orbit. How far away, in light years, is Star B?

3)A star is 61 light years away from Earth. How far away in parsecs is the star?

Answer 1

A way to measure the distance to an object via parallax is to make simultaneous measurements from two locations on Earth. When star moves across the sky, we measure the distance moved from two different location. The distance to the respective star can be found out by using the following equation

D = 1 / theta where theta is parallax in arcseconds

1) for star A, theta is 0.021 arcseconds,

D = 1 / 0.021 = 47.62 Parsecs

2) For star B, Theta is 0.019 arcseconds

D = 1 / 0.019 = 52.63 Parsecs. However, we want this distance in light years. Remember, In 1 parsec , there are 3.26 light years . Therefore,

D = 52.63*3.26 = 171.57 LIGHT YEARS

3) D = 61 light years

Therefore, In parsecs in will be 61/3.26 = 18.7117 parsecs