Oh okay... So gravitational intensity is gravitational force per unit mass... otherwise stated as F/m.
We know gravitational force is GmM/r^2, so therefore gravitational intensity is GM/r^2. Which is... ta dah! The same thing we had before!
Yeah, I'm not sure what digits were used in the...
What is this gravitational intensity you keep bringing up?
PS... I edited my post in the time you replied. I had made a calc error. I got a = 2.79 m/s^2, which is pretty close to 2.60m/s^2. I'm wondering if your book has different, perhaps rounded values for Saturn's mass and radius.
What's the book's answer? I was anticipating the reasoning you said you followed.
Below I pulled Saturn's mass and radius from Google, thought if it's a book problem, I'm sure your text has similar values printed inside.
mv^2/r = GmM/r^2
v^2/r = GM/r^2
where M = mass of saturn = 568.3 x...
Ohh... yeah, that's a totally correct assumption. I misread the scenario!
I got the same answer, 9.77... but not sure where you have the Ma term as haruspex mentioned. If you consider the mass is falling with F = ma, how much tension remains on the line? This is a downwards force on the...
Well, you have two masses to consider, the satellite's mass and Saturn's mass. After you make some cancellations in your equations, you may not need both values, though.
Anyway, if this satellite is in orbit, it's experiencing a centripetal force. The real question: what force IS PROVIDING...