Question

Define one astronomical unit.

Answer 1

Hint: Recall the different units used in astronomy. Also recall the basics about the unit usually used in astronomy, which is the astronomical unit.

Complete step by step answer:
One astronomical unit is the average or mean distance between the Earth and the sun.
One astronomical unit is equal to \[150\,{\text{million km}}\] or \[93\,{\text{million miles}}\].

Additional Information:
One astronomical unit is the average or mean distance between the Earth and the sun and not the exact distance between the Earth and the sun.
This is because though we say that the orbit of the Earth around the sun is circular in shape but it is not exactly circular. It is elliptical.
Hence, the distance between the Earth and sun changes with the position of the Earth on its orbit.
The astronomical unit is denoted by the symbol AU.
The distance between other astronomical objects is also measured in astronomical units. This helps one to compare the distance between the astronomical distance between the objects as compared to the distance between the Earth and the sun.
For example, the distance between the sun and Saturn is 9.5 AU. This shows that the distance between Saturn and the sun is 9.5 times the distance between the Earth and the sun.
The value of one astronomical unit \[A\] in the SI system of units i.e. meter can be determined using the following formula:
\[{A^3} = \dfrac{{GM{D^2}}}{{{k^2}}}\]
Here, \[G\] is the universal gravitational constant, \[M\] is the mass of the Earth, \[D\] is the time for the one day and \[k\] is the numerical value of the Gaussian gravitational constant.
One astronomical unit is equal to \[149595870700\,{\text{m}}\].
\[1\,{\text{AU}} = 149595870700\,{\text{m}}\]

Note:
The value of one astronomical unit is maximum for aphelion (when distance between the sun and the Earth is maximum) and minimum for perihelion (when distance between the sun and the Earth is minimum).