How is the distance between earth and the sun measured?
The distance from the Earth to the Sun can be determined by trigonometry and another planet.
To give an example Venus will be used and it will be assumed that the orbits of Earth and Venus are concentric perfect circles. The orbits are not perfect circles but it simplifies the calculations and is not too inaccurate.
First we need to know the distance
Whee c is the speed of light and t is the time it takes for the radar signal to get to Venus and back.
The average value is
If the distance from the Earth to the Sun is
The other piece of information required is Venus' greatest elongation
With some trigonometry we can determine that:
Plugging the numbers in gives
The actual distance can now be calculated to great accuracy using the NASA DE430 data which is calculated using numerical integration techniques based on observational data from satellites.