Our Moon reaches apogee, (greatest distance from Earth), on Tuesday October 4th. At that time the Moon will more or less be at a distance of 31.85 Earth diameters (406,096 km or 252,336 miles) from the Earth.
Does our Moon actually go around the Earth as this graphic shows? From our perspective on the Earth the Moon appears to circle around the Earth. However, in reality, the Moon orbits the Sun together with the Earth*
Read this very informative article about the Earth-Moon system and their orbital motions, written by Joe Hanson. “Do We Orbit the Moon?”
The 5-day old waxing crescent Moon rises around mid-day local time and is over the southwestern horizon after sunset. And on this evening the Moon will be about 5o from the planet Saturn and about 9o from the reddish star Antares.