(455) Distance to stars [IB Physics SL/HL]

Measuring Distances in Astronomy

• Units of Measurement:

  • Standard units like meters can be cumbersome due to large numbers.

  • Light Year (ly):

    • The distance light travels in one year.

    • 1 ly = 9.46 × 10^15 meters.

• Parsec (pc):

  • Featured in popular culture (e.g., Star Wars), but is a unit of distance, not time.

  • 1 pc = 3.26 light years.

  • Based on a parallax angle of one arc second.

• Astronomical Unit (AU):

  • The average distance from Earth to the Sun.

  • 1 AU = 1.5 × 10^11 meters.

Methods to Measure Distances to Stars

• Parallax Method:

  • Visual depth perception technique, similar to how human eyes work.

  • Utilizes the apparent movement of nearby stars against distant background stars when viewed from different positions in Earth's orbit.

  • Requires measuring angle (theta) which is very small due to vast distances, measured in arc seconds.

• Angle Measurement:

  • 360 degrees in a circle; further divided into minutes and seconds (1 arc second = 1/3,600 of a degree).

  • Parallax distances are expressed in parsecs, where P is the parallax angle.

• Calculating Distance:

  • Distance (D) is calculated as D = 1/P (P in arc seconds).

  • Example: For a star with a parallax angle of 0.08 arc seconds, D = 1/0.08 = 12.5 parsecs.

Practical Example: Trappist-1

• Distance to Trappist-1:

  • Parallax angle of 0.08 arc seconds.

  • Distance = 12.5 parsecs, which equals approximately 40.75 light years (12.5 pc x 3.26 ly/pc).

  • Communication with a hypothetical alien civilization on a planet in Trappist-1 would take 41 years for a radio signal to reach them, as signal travels at the speed of light.