Our Moon reaches apogee, (furthest from Earth), for this orbit, on Sunday July 12th. At that time the last quarter Moon will be at a distance of 31.68 Earth diameters, 251,158 miles (404,200 km) from the Earth.
On the date of the apogee Moon the Moon will be about 4-5o to the east (left) from the planet Mars.
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*
*Click here to read my 2006 Scope on the Sky column “The Real Shape of the Moon’s Orbit”. (PDF)