Astronomical Units and Scales

Step 1 — Read the observation: A planetary distance is expressed in astronomical units. Step 2 — Recall the relevant idea: An astronomical unit is a standardized length approximately Earth's mean distance from the Sun. Step 3 — Connect the observation to the idea: The scenario is an illustration of astronomical unit. Step 4 — Check the limit: This short scenario illustrates the concept; it does not establish every detail or exclude every other influence in a real situation.

Step 1 — Read the observation: A star's separation is stated as a length in light-years. Step 2 — Recall the relevant idea: A light-year is the distance light travels in vacuum in one Julian year. Step 3 — Connect the observation to the idea: The scenario is an illustration of light-year. Step 4 — Check the limit: This short scenario illustrates the concept; it does not establish every detail or exclude every other influence in a real situation.

Step 1 — Read the observation: A nearby stellar distance is expressed in parsecs. Step 2 — Recall the relevant idea: A parsec is a distance unit tied to one arcsecond of annual parallax in the standard definition. Step 3 — Connect the observation to the idea: The scenario is an illustration of parsec. Step 4 — Check the limit: This short scenario illustrates the concept; it does not establish every detail or exclude every other influence in a real situation.

Step 1 — Read the observation: A distant object covers a small angle despite large physical size. Step 2 — Recall the relevant idea: Angular size is the angle an object's apparent extent subtends. Step 3 — Connect the observation to the idea: The scenario is an illustration of angular size. Step 4 — Check the limit: This short scenario illustrates the concept; it does not establish every detail or exclude every other influence in a real situation.

Step 1 — Read the observation: A distant object is seen in its past state. Step 2 — Recall the relevant idea: Look-back time is the interval since received light was emitted, with cosmological interpretation requiring care. Step 3 — Connect the observation to the idea: The scenario is an illustration of look-back time. Step 4 — Check the limit: This short scenario illustrates the concept; it does not establish every detail or exclude every other influence in a real situation.

Step 1 — Read the observation: A comparison does not treat a galaxy as the size of a planetary system. Step 2 — Recall the relevant idea: A scale hierarchy distinguishes planetary, stellar, galactic, and larger distances. Step 3 — Connect the observation to the idea: The scenario is an illustration of scale hierarchy. Step 4 — Check the limit: This short scenario illustrates the concept; it does not establish every detail or exclude every other influence in a real situation.

Step 1 — Identify the quantities and assumptions in the prompt. Step 2 — Select the relationship: Light-travel time in this simple model = distance / light speed. Step 3 — Calculate: 5 light-years / 1 light-year per year = 5. Step 4 — Report with units: 5 years. This result applies to the stated example, under the assumptions specified in the question.