Our Moon reaches perigee, (closest distance to Earth), for this orbit, on Saturday October 26rd. At that time the Moon will be at a distance of 28.75 Earth diameters, 224,511 miles (361,316 km) from the Earth.
On the day of the perigee Moon the 27.5-day old very thin waning crescent Moon will be over the eastern horizon rising within about 5-6o from the planet Mars. Both will be rising about 1 hour before the Sun so it may be difficult to see them.
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)