A Megaparsec is:
- The distance to the Andromeda galaxy
- The distance from which 1 AU subtends an angle of 1 microarcsecond
- The distance from which 1 AU subtends an angle of 1 arcsecond
- The size of the observable universe
The distance from which 1 AU subtends an angle of 1 microarcsecond.
That's a lot easier than your other questions!
1. Distance in parsecs (d)= 1/(parallax angle in arcseconds
2. 1 arsec = 1/60(arcminute) =4.8481368 µrad
3. 1 parsec = 206264.806 au
4. d = 1/206264.806 = 4.8481368 µrad = 1 arsec
5. d = 1/Megaparsec = 1 micro arsec
To determine the correct definition of a Megaparsec, we can break down each option and explain how to arrive at the answer.
1. The distance to the Andromeda galaxy: To verify if this is true, we can look up the distance between our Milky Way galaxy and the Andromeda galaxy. According to current scientific estimates, this distance is approximately 2.537 million light-years or about 780 kiloparsecs. Therefore, a Megaparsec cannot be defined as the distance to the Andromeda galaxy.
2. The distance from which 1 AU subtends an angle of 1 microarcsecond: To validate this option, we can start by understanding the terms involved. AU stands for Astronomical Unit, which is the average distance between the Earth and the Sun, about 93 million miles or 150 million kilometers. On the other hand, a microarcsecond is a unit of angular measurement, where one arcsecond is divided into one million equal parts. To find if this option is correct, we need to determine whether a distance exists from which the Earth-Sun distance subtends an angle of 1 microarcsecond. Calculating the angle of an object based on its distance is done through simple trigonometry, specifically the formula: Angle (in radians) = Object Size / Distance. Since the size of the Earth-Sun distance is known (1 AU), we can substitute these values into the formula and determine the distance required for the angle to be 1 microarcsecond. By performing this calculation, we find that the distance required is approximately 3.09 Gigaparsecs, which is much larger than a Megaparsec. Therefore, a Megaparsec cannot be defined as the distance from which 1 AU subtends an angle of 1 microarcsecond.
3. The distance from which 1 AU subtends an angle of 1 arcsecond: Similar to the previous option, we can determine whether a Megaparsec is the distance from which 1 AU subtends an angle of 1 arcsecond by utilizing the trigonometric formula to calculate the distance required for the angle to be 1 arcsecond. By substituting the known values into the formula, we find that the distance required is approximately 2.063 Megaparsecs. This suggests that a Megaparsec can indeed be defined as the distance from which 1 AU subtends an angle of 1 arcsecond.
4. The size of the observable universe: To determine if this option is accurate, we need to understand the size of the observable universe. The observable universe refers to the portion of the universe that we can potentially observe from Earth, given the constraints of the speed of light and the age of the universe. The current estimation of the observable universe's size is approximately 93 billion light-years or about 28,500 Megaparsecs. Therefore, a Megaparsec is not equivalent to the size of the observable universe.
In conclusion, a Megaparsec can be defined as the distance from which 1 AU subtends an angle of 1 arcsecond.