Understanding Right Angle Triangles in Astronomy

Understanding Star Movement

• Stars are not stationary; they actually move through space.
• Measuring this movement requires a specific observational setup.
• To measure the distance of stars, astronomers use parallax over a six-month interval, observing them from two different positions of Earth's orbit.

Geometry of Star Movement

• The star's movement can be described using simple geometry, particularly right-angle triangles.
  • Transverse Velocity: The component of the star's velocity that is along the line of sight from Earth.
  • Radial Velocity: The component that is perpendicular to the line of sight.

Example: Barnard's Star

• Images of Barnard's Star taken 22 years apart show actual movement of the star against a fixed backdrop.
  • Observation Setup: The observations needed to be taken with Earth in the same position for an accurate measurement of movement.
• The calculated movement of Barnard's Star is approximately 1.8 parsecs, translating to a distance of about 3 billion kilometers per year or 88 kilometers per second.
  • Comparison: The escape speed for Earth is 11 kilometers per second, meaning Barnard’s Star moves about 8 times faster than required to escape Earth's gravity.

Calculating Star Distances

• To calculate the distances and speeds, astronomers apply basic geometry, particularly the Pythagorean theorem.
  • Pythagorean Theorem Formula: a^2 + b^2 = c^2
  • Where (a) and (b) are the lengths of the legs of the triangle and (c) is the hypotenuse.
• This method allows astronomers to determine the distances to stars and their respective velocities by combining transverse and radial velocities.