(I) If a galaxy is traveling away from us at 2.2% of the speed of light, roughly how far away is it?

Verified step by step guidance

1. Identify the given velocity of the galaxy relative to the speed of light, which is 2.2% of the speed of light. Denote the speed of light as c.
2. Use Hubble's Law, which states v = H_0 \times d, where v is the velocity of the galaxy, H_0 is the Hubble constant, and d is the distance to the galaxy.
3. Substitute the given velocity into Hubble's Law. Convert the percentage to a decimal and multiply by the speed of light to find v (v = 0.022c).
4. Rearrange Hubble's Law to solve for the distance d. The formula becomes d = \frac{v}{H_0}.
5. Substitute the value of v from step 3 into the rearranged formula to find the distance d in terms of the Hubble constant and the speed of light.

Key Concepts

Hubble's Law

Hubble's Law states that the recessional velocity of a galaxy is directly proportional to its distance from us. This relationship implies that galaxies further away are moving away faster, which is a key observation supporting the expansion of the universe. The law can be expressed mathematically as v = H₀d, where v is the velocity, H₀ is the Hubble constant, and d is the distance.

Speed of Light

The speed of light in a vacuum is approximately 299,792 kilometers per second (or about 186,282 miles per second). This constant is fundamental in physics, particularly in the context of relativity and cosmology. When discussing astronomical distances, the speed of light serves as a crucial reference point for understanding how far light travels over time, which helps in calculating distances to celestial objects.

Cosmological Distance

Cosmological distance refers to the measurement of how far away an object is in the universe, taking into account the expansion of space. Unlike simple Euclidean distance, cosmological distance can be affected by the universe's expansion, which means that the observed distance to a galaxy can differ from its actual distance at the time light was emitted. This concept is essential for interpreting redshift data and understanding the scale of the universe.