1. What is the Parallax Method?

The parallax method is a technique used to measure distances to nearby objects in astronomy and other fields by observing the apparent shift in position when viewed from different vantage points.

2. How Does the Calculator Work?

The calculator uses the parallax formula:

Where:

• \( d \) — Distance to object (meters)
• \( b \) — Baseline distance between observation points (meters)
• \( \theta \) — Parallax angle (radians)

Explanation: The exact formula uses the tangent function, while the approximation (valid for small angles) simply divides baseline by angle in radians.

3. Importance of Parallax Measurement

Details: Parallax is fundamental in astronomy for measuring stellar distances. It's also used in photogrammetry, 3D imaging, and various surveying applications.

4. Using the Calculator

Tips: Enter baseline in meters and parallax angle in radians. For small angles (less than about 10°), the approximation will be very close to the exact value.

5. Frequently Asked Questions (FAQ)

Q1: What's the typical baseline in astronomy?
A: For stellar parallax, astronomers use Earth's orbital diameter (2 AU ≈ 300 million km) as baseline.

Q2: How accurate is the small angle approximation?
A: For θ < 0.1 radians (≈5.7°), error is less than 0.5%. At 0.2 rad (≈11.5°), error is about 2%.

Q3: What's a parsec?
A: A parsec (3.26 light-years) is defined as the distance at which 1 AU subtends 1 arcsecond (1/206265 rad).

Q4: What are common sources of error?
A: Atmospheric refraction, instrument precision, and proper motion of the observed object can affect measurements.

Q5: Can this be used for terrestrial measurements?
A: Yes, parallax is commonly used in surveying and photogrammetry with appropriate baselines.