Notes on Constellations, Andromeda, and Light Travel Time

Great Square of Pegasus and nearby constellations

Four bright stars form the Great Square of Pegasus.
If you follow the top two stars to the left, you reach a few bright stars in the constellation Andromeda.
The right side of the W-shaped Cassiopeia points to the Andromeda stars.
These stars help locate the faint fuzzy light of the Andromeda Galaxy (M31).
This sequence provides a practical star-hopping method to find M31 in the night sky.

The Andromeda Galaxy is located at a distance of about d_{M31} \,\approx\, 2.5 \times 10^{6} \ \text{ly} (2.5 million light years).
Light entering our eyes from M31 left its origin about t_{M31} \,\approx\, 2.5 \times 10^{6} \ \text{yr} ago. In other words, we see Andromeda as it was 2.5 million years in the past.
Through a telescope, the Andromeda Galaxy is revealed as a vast spiral-shaped collection of more than N_{\star} \,\approx\, 1.0 \times 10^{11} stars (i.e., about 100,000,000,000 stars).
The term for the “look-back” effect is that we are seeing an object as it appeared in the past due to the finite speed of light.

The disk of the Milky Way galaxy has a diameter of about D_{MW} \,\approx\, 1.0 \times 10^{5} \ \text{ly} (100,000 light years).
The far side of the Milky Way is located roughly \Delta D \,=\, 1.0 \times 10^{5} \ \text{ly} farther away from us than the near side.
Question: How does the light travel time from the far side compare to the near side?
- Answer: The travel time from the far side is greater.
- Reason: Since the far side is \Delta D = 1.0 \times 10^{5} \ \text{ly} farther away, the light from the far side that reaches us today must have left about \Delta t \,=\, 1.0 \× 10^{5} \ \text{yr} before the light that currently reaches us from the near side.
Consequence: The photo of our galaxy not only contains light that has traveled for about t_{MW} \,=\, 2.5 \times 10^{6} \ \text{yr} (in the sense of the Milky Way’s distance scale to us for the Andromeda image) but also includes light that left at different times over a period of roughly \Delta t \,=\, 1.0 \times 10^{5} \ \text{yr} due to depth along the line of sight within the disk.

This example demonstrates that when we study the universe, space and time become intertwined.
Key idea: look-back time connects spatial distances with temporal history because light takes time to travel across space.
For distant objects, we are effectively looking back in time: we see the universe as it was when the light began its journey.

Look-back time is directly related to distance in light-years: for any object at distance D, the light-travel time is approximately t \approx D years (in years and light-years units).
Observing nearby extended structures (like the Milky Way’s disk) reveals a spread of arrival times corresponding to internal depth, not just the time offset to Earth.
For distant galaxies, the look-back time becomes a tool to study the history of the universe, star formation rates, galaxy evolution, and cosmology.
Practical implication: when interpreting images, astronomers must account for the fact that different parts of an object can reflect light emitted at different times, effectively showing a time-lrupted snapshot.

Andromeda Galaxy distance: d_{M31} \approx 2.5 \times 10^{6} \ \text{ly}
Andromeda look-back time: t_{M31} \approx 2.5 \times 10^{6} \ \text{yr}
Andromeda star count: N_{\star} \approx 1.0 \times 10^{11}
Milky Way disk diameter: D_{MW} \approx 1.0 \times 10^{5} \ \text{ly}
Far side distance offset: \Delta D = 1.0 \times 10^{5} \ \text{ly}
Far side light-travel time difference: \Delta t = 1.0 \times 10^{5} \ \text{yr}
Milky Way look-back region span in a single image: \Delta t \,\approx\, 1.0 \times 10^{5} \ \text{yr}
Conceptual statement: space and time become intertwined when studying the universe.