Answer to Question #89339 in Astronomy | Astrophysics for Peace Adejumobi

Question

Problem A.3 :
The stellar parallax of the star Arcturus in the constellation Boötes was measures with 0.0900
.
(a) Calculate the distance (in parsec) between Arcturus and the Earth.
(b) How long does it take to send a light message from Earth to Arcturus?

For a special mission to Mars you need to know the smallest distance between Earth and Mars.
However, you have lost your astronomy book and you could only find these values:
Distance Earth to Sun: 149.6 million km
Orbital period Earth: 1.00 years
Orbital period Mars: 1.88 years
By using these values and assuming that Mars and Earth move an circular orbits, calculate the
smallest possible distance between Earth and Mars.

Answer 1

(a) Calculate the distance (in parsec) between Arcturus and the Earth.

The relationship between a star's distance and its parallax angle:

$$d=\frac {1} {p} (1)$$

Using (1) we get:

d=11.11 parsecs

Answer:

11.11 parsecs

(b) How long does it take to send a light message from Earth to Arcturus?

1 light-year=0.3 parsecs

11.11 parsecs=37 light-year

Answer:

37 light-year