Estimating the distance between Earth and Mars using a telescope involves a process called parallax measurement. Parallax is the apparent shift in the position of an object when viewed from different vantage points. Here's a step-by-step explanation of how you can estimate the Earth-Mars distance:
Choose the right time: Planetary opposition is the ideal time for distance estimation. This occurs when Mars and Earth are on opposite sides of the Sun, and Mars is closest to Earth. During this time, Mars appears brightest and largest in the night sky.
Measure the angular separation: Use a telescope to observe both Earth and Mars when they are visible in the night sky. Measure the angular separation between the two planets. This can be done by aligning your telescope with a reference point (e.g., a star) and measuring the angular distance to both Earth and Mars.
Calculate the parallax angle: Wait for a few days (or weeks) and repeat the observation of Earth and Mars. Measure the new angular separation between them. The difference between the initial and subsequent angular separations will allow you to calculate the parallax angle.
Apply trigonometry: Once you have the parallax angle, you can use basic trigonometry to estimate the Earth-Mars distance. The parallax angle is the apparent shift in the position of Mars as seen from Earth due to the change in Earth's position. By knowing the distance between your observation points on Earth (e.g., the baseline) and the parallax angle, you can calculate the Earth-Mars distance.
The magnification required for this purpose depends on the size and resolution of your telescope, as well as the atmospheric conditions. However, it's important to note that estimating distances between planets through parallax is a challenging task due to the vast distances involved. The most accurate measurements are typically obtained using space probes specifically designed for interplanetary missions.