Life magazine graphic, 1950s†, from the Faulkner at Virginia archive:
THE ORBIT WEAVES A WEB AS WHOLE WORLD WATCHES. PATTERN OF ORBITS traced by Sputnik in typical 24-hour period is demonstrated by red bulb going around globe built by Robert H. Farquhar. Earth rotates from west to east (left to right) and position of orbits (red lines) shifts west each time satellite goes around earth. At noon, orbit passes just east of Florida, going northwest to southeast. It appears 96 minutes later over western U.S. After midnight when earth has turned around so U.S. is on reverse side of globe in picture, orbit goes from southwest to northeast, passing through Midwest and, 96 minutes later, through California.
† The original site claims it’s from the 1 October, 1956, issue, but it seems more likely that it’s actually from 1957, since that’s the year Sputnik was launched.