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 after 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 of the observable universe, beyond which light has not had time to reach us since the beginning 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.
3. The cosmic horizon is much smaller than the universe itself because the universe may be infinite in size, while the observable universe is limited by the time it has taken light to reach us since the Big Bang.
4. (a) The three components that make up the universe are ordinary matter (baryonic matter), dark matter, and dark energy. (b) Visible matter (ordinary matter that we can detect directly) 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. Proxima Centauri's distance is a very small percentage, about 0.0000424% of the lower - bound diameter estimate. (c) The nearest major galaxy to the Milky Way is the Andromeda Galaxy, which is about 2.5 million light - years away.
6. (a) In a flat universe, two parallel light beams would continue to travel parallel to each other indefinitely. (b) In a positively curved universe, two parallel light beams would eventually converge.
7. We know dark matter and dark energy exist through their gravitational and cosmic expansion effects. Dark matter's gravitational influence is seen in the rotation curves of galaxies and the behavior of galaxy clusters. Dark energy is inferred from the accelerating expansion of the universe.

Answer:

1. The boundary of the observable universe beyond which light has not had time to reach us since the beginning of the universe.
2. Approximately 46.5 billion light - years in radius.
3. Because the universe may be infinite while the observable universe is limited by the time it has taken light to reach us since the Big Bang.
4. (a) Ordinary matter, dark matter, dark energy. (b) About 5%.
5. (a) About 4.24 light - years. (b) About 0.0000424% of the lower - bound diameter estimate of the Milky Way. (c) About 2.5 million light - years.
6. (a) They would continue to travel parallel indefinitely. (b) They would eventually converge.
7. Through their gravitational and cosmic expansion effects such as galaxy rotation curves and the accelerating expansion of the universe.