I am not sure the given numbers you have for the sputnik example (example 3) make sense.  Sputnik's distance from the center of the earth is not significantly different than the surface of the earth from the center so the orbital g cannot be much less than g on the surface.  600 N does not make sense though it is correctly calculated??.

Jacob, please let me know what problem set/presentation you're referring to - I can't find it. Thanks, John

In the Centripetal Force section of the presentation slides

Example 3: Centripetal Force
The first artificial satellite to orbit Earth, Sputnik, had a mass of 84 kg
and orbited Earth every 5900 s at a distance from Earth's center of
6.4 x 106 m.
What was the magnitude of the gravitational force acting on Sputnik?

Jacob, thanks, now I see it. The problem is flawed. The Sputnik moved at different heights during its orbit, so the orbital time kept changing. And, the wrong radius was used - the question actually had Sputnik deep within the Earth. The only way to fix it was to use the gravitational force formula for distance from the center of the Earth, but that is not taught until the next unit. So, we are deleting the problem. Thank you for your correction. As you said, the force should be much closer to the satellite's weight on Earth. John