There are several ways in which astronomers determine the distances from Earth to other planets. For nearby neighbors, such as Mars and Mercury, the radio signal method is used: a signal is sent toward the planet, and the time required for the signal to return after reflecting off the surface is measured.
Since waves propagate at the speed of light, which is constant (approximately 300,000 km/s), the distance can be calculated based on this time. Although the calculation is complicated in practice by the movement of the Earth and the planet in space, astronomers take these factors into account when performing calculations. This approach is known as the radar method.
A similar principle is used when studying bodies visited by space probes and spacecraft; in this case, the apparatus sends signals back to Earth.
For more distant objects, such as stars, the so-called trigonometric parallax is applied. Despite the complexity of the name, the underlying geometry is quite simple. Two observers occupy different points on Earth and look at the same star. These two points and the star form the vertices of a triangle, for which two quantities are known: the length of one side (the distance between the observers) and one of the angles (the difference in viewing direction of the star from each point). Using the rules of trigonometry, the distance between the Earth and the object is determined.
The ancient Greek astronomer Hipparchus conducted the first astronomical measurements using the parallax method back in the 2nd century BC. He is considered the father of trigonometry.