SME
Grade 12 Science · Problem type
Distance from parallax
Use this for “A star’s parallax is 0.1″. How far away is it, in parsecs and light-years?”
Diagram
d
=
1
p
=
1
0.1
=
10
parsecs,
or
3.26
×
10
=
32.6
light-years.
Half a year apart, Earth has moved 2 AU, so the near star shifts by 2p against the far stars; the farther the star, the smaller the shift.
This is an example. Type your own values to start a new problem.
d (pc)
=
1
÷
p (″)
D
Distance in light-years
calculated · light-years
Formulas
d
=
1
p
10
=
1
0.1
D
=
3.26
×
d
32.6 = 3.26 × 10
Assumptions
•
Earth is on opposite sides of the Sun six months apart, 2 AU apart.
•
p is half the near star’s shift against the far stars: the angle 1 AU makes at the star.
•
1 parsec = 3.26 light-years.
Step-by-step
WE KNOW
p = 0.1 ″
FIND
distance in parsecs (d), distance in light-years (D)
Step 1 · Find distance in parsecs (d)
Use d = 1 ÷ p
A parsec is the distance at which 1 AU looks 1″ wide: the smaller the angle, the farther the star.
d
=
1
0.1
d
=
10
pc
Step 2 · Find distance in light-years (D)
Use D = 3.26 × d
Light takes 3.26 years to cross a parsec.
D
=
3.26
×
10
D
=
32.6
light-years
Check
Put the numbers back in. Both sides should match.
10
=
1
0.1
✓
32.6 = 3.26 × 10 ✓
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