Parallax Method for Measuring Stellar Distances

Parallax and Distance Measurement

• The fundamental principle relies on measuring the angle to an object from two different positions.
• Knowing the distance between the observation points allows the calculation of the object's distance using trigonometry.

Parallax in Space

• Analogy: The distance between our eyes provides a baseline for judging the distance to nearby objects.
• To measure distances in space, we use the Earth's orbit around the Sun as the baseline.
  • Observations are taken six months apart, when the Earth is on opposite sides of its orbit.

Standardizing the Angle: The Parsec

• The goal is to standardize the angle measurement to correspond to a specific distance.
• Arc Second: A very small unit of angular measurement.
  • 1 degree = 3600 arc seconds ( 1^{\circ} = 3600'').
  • Therefore, 1 arc second = \frac{1}{3600} of a degree.

Definition of a Parsec

• If the angle measured (parallax angle) is exactly 1 arc second, the object's distance is defined as 1 parsec.
• 1 parsec (pc) = 3.26 light-years (ly).

Light-Year

• A unit of astronomical distance.
• 1 light-year ≈ 9.46 \times 10^{15} meters (as found in data booklets).

Parsec vs. Light-Year

• A parsec is significantly larger than a light-year.
• 1 \text{ parsec} = 3.26 \text{ light-years}

Why Use Light-Years or Parsecs?

• Meters are too small and impractical for measuring interstellar distances.
• Light-years and parsecs provide more manageable units for these vast distances.

Limitations of Parallax

• Measuring parallax angles is challenging.
  • Requires waiting six months between observations.
  • The angles are incredibly small (often less than 1 arc second).

Atmospheric Effects

• Ground-Based Telescopes: Observations are affected by the Earth's atmosphere.
  • Atmospheric turbulence and distortion reduce the accuracy of measurements.

Distance Limitations with Ground-Based Telescopes

• Ground-based telescopes are limited in the distances they can accurately measure using parallax.
• Approximate limit: 100 parsecs.
• Beyond this distance, the atmospheric fuzziness makes it difficult to measure the tiny angular shifts.

Example: 100 Parsecs

• At 100 parsecs, the angular shift becomes extremely small.
• The blurring effect of the atmosphere makes accurate measurement nearly impossible.

Space-Based Telescopes

• Placing telescopes in space eliminates atmospheric distortion.
• This allows for more accurate measurements and extends the range of parallax measurements.

Formula Application

• It's essential to be able to calculate distances using the parallax formula.
• Consult the data booklet (specifically section E5) for relevant information and formulas related to parallax and distance calculations.