THE 1700s (The era of the telescope)
Giancomo Miraldi observes "white spots" at the poles, and discovers that the southern cap is not centered on the rotational pole.
Miraldi wonders (correctly) if the "white spots" are ice caps.
Mars is in opposition, and closer to Earth than it would be until the year 2003. The brightness in the sky causes panic.
Jonathan Swift's Gulliver's Travels described the Martian moons, although this may just be coincidence. "They have likewise discovered two lesser Stars, or Satellites, which revolve around Mars, wherof the innermost is distant from the Center of the Primary planet exactly three of his diameters, and the outermost five; the former revolves in the Space of ten Hours and the latter in Twenty-one and a Half."
Sir William Herschel (1738 - 1822), the British Astronomer Royal, studied Mars with telescopes he built himself. Herschel believed that all the planets were inhabited and that there were even intelligent beings living in a cool area under the surface of the sun.
In Herschel's paper, entitled On the remarkable appearances at the polar regions on the planet Mars, the inclination of its axis, the position of its poles, and its spheroidal figure; with a few hints relating to its real diameter and atmosphere., which declares the axial tilt to be 30 degrees. (The actual current value is 25.19 degrees.) Herschel also mistakenly assumed that the dark areas on Mars were oceans, and the lighter regions land. When two faint stars passed very close to Mars with no effect to their brightness, Herschel correctly assumed that Mars had a tenuous atmosphere. He speculated that Martian inhabitants "probably enjoy a situation similar to our own."