Who first calculated the distance between our sun and the earth?
Aristarchus made the first calculation of the Earth-Sun distance in about 300BC. He did it by measuring the angular separation of the Sun and Moon. His results however were incorrect by a factor of about 20.
When Johannes Kepler produced his three laws of planetary orbits it was possible to calculate the relative difference of the positions of the planets by measuring their orbital period. It was known for example that Mars is about 1.5 times further from the Sun than the Earth.
In 1672 Cassini and another astronomer made simultaneous measurement of the position of Mars from different places when it was at its closest point to the Earth. Using parallax, Cassini was able to calculate the distance between Earth and Mars quite accurately. From this distance and the relative distances of Earth and Mars it is simple geometry to calculate the Earth-Sun distance.
Since the 1960s it has been possible to bounce a radio signal off Venus. By timing how long it takes for the signal to return and given that radio waves travel at the speed of light it is possible to calculate the distance from Earth to Venus with great accuracy. Given the relative distances of Earth and Venus from the Sun, the distance from Earth to Sun can be calculated accurately.