Question

the shape of the universe
if you draw a triangle on a flat piece of paper the internal angles of the triangle add up to 180°. but what happens if you draw a triangle on the surface of a ball? the internal angles add up to more than 180°. and what about the internal surface of a bowl? the internal angles of a triangle add up to less that 180°. now imagine drawing a huge triangle on the \surface\ of the universe. what would the internal angles of the triangle be? the answer depends on whether or not the universe is curved or flat. the answer has important consequences for the shape and fate of the universe.
if the internal angles of your triangle add to be greater than 180°, then the universe is positively curved like a sphere. in this case, the universe is finite but has no edge. it will eventually slow its expansion and collapse back on itself.
if the triangles internal angles add to be equal to 180° then the universe is flat. in this case it will continue to expand forever; perhaps at a slower rate over an infinite amount of time. current evidence suggests the universe is flat.
if your triangle has internal angles that add to less than 180° then the universe is negatively curved, like the shape of a saddle. it is infinite and will expand forever at an ever - increasing rate.

1. what is the cosmic horizon?
2. how big is the observable universe?
3. explain why the cosmic horizon is much smaller than the universe itself.
4. (a) what are the three components that make up the universe?

(b) what percentage of the universe comprises visible matter?

1. (a) what is the distance to the suns nearest star?

(b) what percentage of the diameter of the milky way galaxy is this?
(c) what is the distance to the nearest major galaxy?

1. (a) describe the path of two parallel light beams in a flat universe.

(b) describe the path of two parallel light beams in a positively curved universe.

1. how do we know dark matter and dark energy exist when they cannot be observed directly?

Explanation:

1. The cosmic horizon is the boundary beyond which light has not had time to reach us since the beginning of the universe due to the finite speed of light and the finite age of the universe.
2. The observable universe has a radius of about 46.5 billion light - years. This is based on the age of the universe and the expansion of space since the Big Bang.
3. The cosmic horizon is much smaller than the universe itself because the universe may be infinite or at least much larger than the region from which light has had time to reach us in the 13.8 billion years since the Big Bang.
4. (a) The three components that make up the universe are ordinary (baryonic) matter, dark matter, and dark energy. (b) Visible matter makes up about 5% of the universe.
5. (a) The distance to the Sun's nearest star, Proxima Centauri, is about 4.24 light - years. (b) The diameter of the Milky Way Galaxy is about 100,000 - 120,000 light - years, so Proxima Centauri is a tiny fraction, about 0.0000424% of the diameter. (c) The nearest major galaxy to the Milky Way is the Andromeda Galaxy, and the distance is about 2.5 million light - years.
6. (a) In a flat universe, two parallel light beams would remain parallel forever. (b) In a positively curved universe, two parallel light beams would eventually converge.
7. We know dark matter and dark energy exist because of their gravitational effects on visible matter and the expansion of the universe. For example, the rotation curves of galaxies suggest the presence of dark matter, and the accelerating expansion of the universe implies the existence of dark energy.

Answer:

1. The boundary beyond which light has not had time to reach us since the start of the universe due to light's finite speed and the universe's finite age.
2. Approximately 46.5 billion light - years in radius.
3. Because the universe may be infinite or much larger than the region from which light has had time to reach us since the Big Bang.
4. (a) Ordinary (baryonic) matter, dark matter, dark energy. (b) About 5%.
5. (a) About 4.24 light - years. (b) About 0.0000424% of the diameter of the Milky Way Galaxy. (c) About 2.5 million light - years.
6. (a) Remain parallel forever. (b) Eventually converge.
7. Due to their gravitational effects on visible matter and the expansion of the universe (e.g., galaxy rotation curves for dark matter and accelerating universe expansion for dark energy).