Coco12 said:Homework Statement
What is the centripetal acceleration of a satellite orbiting Saturn at the location exactly one Saturn radius above the surface of Saturn
Homework Equations
Ac=v^2/r
In the previous question found out that the fg at that location is 1/4 of 36.0 N
The Attempt at a Solution
I read somewhere that they made centripetal acceleration equal to Gm/4pi ^2
rude man said:I would not lend much credulity to what you read. The dimensions of Gm/4pi^2 are not the dimensions of acceleration.
Equate gravitational acceleration to centripetal acceleration.
Coco12 said:The answer is the same as the gravitational intensity which is 2.60N . How does that work??
zahbaz said: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 this centripetal force? What's the equation for this force that rude man is getting at? Equate this to your centripetal.
Coco12 said:Mv^2/r=gm1m2/r^2?
Oh no, the m in the first equation is the same as m1 in the equation after the equal sign.rude man said:How come three different masses?
Coco12 said:Oh no, the m in the first equation is the same as m1 in the equation after the equal sign.
So when canceled would be: v^2/r=Gm/ r^2?
Coco12 said:Mass would be the mass of Saturn and r would be the radius of Saturn *2?
The thing is , all of this info is not given in the problem, so how are we supposed to know it?
zahbaz said: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 10^24 kg
r = two saturn radii = 2(58,232,000 m)
a = GM/r^2
a = 27.9 m/s^2
zahbaz said: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.
zahbaz said: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 prior calculation that got you 2.60m/s^2, but the theory is identical in both approaches. If it was a two stage problem, I'd stick with the 2.6.
Centripetal acceleration is the acceleration that a body experiences as it moves in a circular path. It is directed towards the center of the circle and its magnitude depends on the velocity and radius of the circular path.
In satellite orbits, the centripetal acceleration is responsible for keeping the satellite in its circular orbit around a central body, such as Saturn. This acceleration is generated by the gravitational force between the satellite and the central body.
The centripetal acceleration of a satellite orbiting Saturn is affected by the mass of the satellite, the mass of Saturn, and the distance between the satellite and Saturn. The greater the mass of the satellite and Saturn, and the smaller the distance between them, the higher the centripetal acceleration will be.
The centripetal acceleration of a satellite orbiting Saturn can be calculated using the formula a = v^2/r, where a is the centripetal acceleration, v is the velocity of the satellite, and r is the radius of the orbit. This formula applies to circular orbits, but for elliptical orbits, a = (v^2)/r(1-e^2), where e is the eccentricity of the orbit.
As a satellite orbits Saturn, the centripetal acceleration remains constant in magnitude but changes in direction. This is because the velocity of the satellite is constantly changing due to the gravitational force from Saturn, but the radius of the orbit remains constant. Therefore, the direction of the centripetal acceleration must also change to keep the satellite in its circular orbit.