I captured an anomalous light with my telescope pointed at the Big Dipper near the star Merak.

The thing about doing analysis here is that you need pretty precise data to identify a satellite. Your precise coordinates, precise coordinates in the sky, precise time... and you'll probably still get a list of possibilities.

Try this page:

I've set that link to my city to show the satellites visible between the time of posting and sunrise, but you can reset it for your location and a given date. This site only returns naked eye visible objects and even with Starlink specifically excluded there's dozens of them. And even a modest telescope will turn up more, good ones can see a great many, a handful of photographers have managed to resolve individual astronauts on spacewalks.

Many of those are in high inclinations such as polar and sun synchronous orbits. Several, including Lacrosse 5's upper stage, a Thor Agena that's been lingering in orbit since 1964, several Cosmos upper stages, Envisat, and Helios 1A cross through or near Ursa Major (and I didn't check more than a quarter of the page).

And notice how many are upper rocket stages and tanks rather than satellites. These upper stages separate from their payloads but are often much brighter than the satellite itself, making up a disproportionate number of naked eye visible objects. Most people who looked up to see Sputnik in the sky were actually seeing the much larger and brighter R-7 core trailing it in orbit.

Every one of those rockets released at least one payload into orbit. Upper stages, being large and doing nothing to maintain altitude, usually decay out of orbit faster than their payloads, and it's more common practice in modern rockets to intentionally demise the upper stage after release.

Because there are currently 41,322 tracked objects in Earth orbit there's not really a great way to search for what you're seeing in a telescope because on average a given constellation will contain literally hundreds of them at any given time. There are sources that will let you search down to dimmer magnitudes, some guides are in this thread:
And this will quickly illustrate the volume problem.
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