Chapter 8.1, Problem 60AYU

Parallax See Problem 59. 61 Cygni, sometimes called Bessel’s Star (after Friedrich Bessel, who measured the distance from Earth to the star in 1838), is a star in the constellation Cygnus.

(a) 61 Cygni is $11.14$ light-years from Earth. If 1 light-year is about $\text{5}\text{.9}$ trillion miles, how many miles is 61 Cygni from Earth?

(b) The mean distance from Earth to the Sun is 93,000,000 miles. What is the parallax of 61 Cygni?

To determine

To find:

a. 61 Cygni is $11.14$ light-years from Earth. If 1 light-year is about $5.9$ trillion miles, how many miles is 61 Cygni from Earth?

Answer to Problem 60AYU

a. Distance from earth to 61 Cygni$=6.5726\ast {10}^{13}\text{miles}$.

Explanation of Solution

Given:

61 Cygni, sometimes called Bessel’s Star (after Friedrich Bessel, who measured the distance from Earth to the star in 1838), is a star in the constellation Cygnus.

Formula Used:

$\text{sin}\theta \text{ = }\frac{\text{opposite side}}{\text{hypotenuse}}$

Calculation:

a. 61 Cygni is $11.14$ light-years from Earth

1 light-year $=5.9$ trillion miles$=5.9\ast {10}^{12}$,

Distance from earth to 61 Cygni $=11.14\ast 5.9 \text{trillion miles }=6.5726\ast {10}^{13}\text{miles}$.

To determine

To find:

b. The mean distance from Earth to the Sun is 93,000,000 miles. What is the parallax of 61 Cygni?

Answer to Problem 60AYU

b. The parallax of 61 Cygni is $0.000081°$.

Explanation of Solution

Given:

61 Cygni, sometimes called Bessel’s Star (after Friedrich Bessel, who measured the distance from Earth to the star in 1838), is a star in the constellation Cygnus.

Formula Used:

$\text{sin}\theta \text{ = }\frac{\text{opposite side}}{\text{hypotenuse}}$

Calculation:

b. Let us construct a right triangle as shown below.

$a=9.3\ast {10}^7$, $c=6.5726\ast {10}^{13}\text{miles}$

$\text{sin}\theta =\frac{a}{c}=9.3\ast {10}^7/6.5726*{10}^{13}\text{miles}$

$\text{sin}\theta =1.415\ast {10}^{-6}$

$\theta =0.000081°$

The parallax of 61 Cygni is $0.000081°$.