Table 79.1, in Unit 79, shows that material we see at a...

Table $79.1,$ in Unit $79,$ shows that material we see at a redshift of 1000 was emitted when the material was 45 million ly away from us. This distance determines the angular size of regions at this redshift, as given by the angular size formula in Unit 10.4 a. Show that a region that is $1^{\circ}$ across at this redshift has a diameter of approximately 800,000 ly. b. How big is that region today?

Table $79.1,$ in Unit $79,$ shows that material we see at a redshift of 1000 was emitted when the material was 45 million ly away from us. This distance determines the angular size of regions at this redshift, as given by the angular size formula in Unit 10.4
a. Show that a region that is $1^{\circ}$ across at this redshift has a diameter of approximately 800,000 ly.
b. How big is that region today?

Key Concepts

Angular Size Formula

The angular size formula relates an object's physical size to its observed angular size and its distance from the observer. In cosmological contexts, this formula is key for converting between an angular measurement, such as 1° on the sky, and the actual physical dimensions of distant objects. It helps scientists infer the size and structure of cosmic features from their apparent angular extents.

Angular Diameter Distance

Angular diameter distance is a specific measure used in cosmology that relates the physical size of an object to its observed angular size. It accounts for the effects of the expanding universe, allowing researchers to determine actual sizes of objects at significant redshifts. This distance measure is crucial when comparing observations of the early universe with current cosmic scales.

Redshift

Redshift is the phenomenon where light from distant objects in the universe is shifted to longer wavelengths due to the expansion of space. It acts as a proxy for both the distance and the age of astronomical objects, such that higher redshifts correspond to earlier times in the universe. This concept is used to understand how cosmic structures evolve over time.

Cosmic Expansion

Cosmic expansion refers to the increase in distances between galaxies over time due to the expansion of the universe. This evolving distance means that physical sizes of regions in the early universe will appear different when observed today versus when they emitted the light. It plays a vital role in understanding how measurements at high redshifts transform into the current scale of the universe.

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