2. Saturn has a radius of about 9.0 earth radii, and a mass 95 times the Earth’s mass. Estimate the gravitational field on the surface of Saturn compared to that on the Earth.

Question

2.	Saturn has a radius of about 9.0 earth radii, and a mass 95 times the Earth’s mass. Estimate the gravitational field on the surface of Saturn compared to that on the Earth.

flexastexas · Answer

Need some guidance

dboome · Answer

$$F=G \frac{ m_1m_2 }{ r^2 }$$This is Newton's famous Law of Gravitation. It says that 2 objects of masses m1 and m2 a radius r apart will feel a force proportional to the square of that radius, times a constant G, which was determined experimentally. 

So, we're looking for the gravitational field strength. That is a basically a measure of how much *acceleration* an object will have due to the gravitational force of a present gravitational field. We know this, on Earth, as g = 9.8m/s^2. It's the same all over Earth, so long as you don't change elevation (the radius r to the center of the Earth). This acceleration is independent of your mass, which you can see by plugging in Newton's 2nd Law F =m*a, and solving for a by cancelling out the mass of the object in question. 

Do you see how we can do the same with Saturn to find the acceleration an object would feel on the surface of this heavier and larger planet?

dboome · Answer

The masses will feel a force proportional to the *inverse* square of the distance, i should have said, since its on the bottom of the fraction of the law of gravitation, but I hope you know what i mean :P

flexastexas · Answer

I am getting you some what. Can we try it?

flexastexas · Answer

So we have to substitute the G for the G on saturn?

dboome · Answer

Fields are a strange concept to wrap your head around. Capital G in the equation there is the gravitational constant, its literally constant all over the 'universe'. Whats changed is now we have saturn's mass and saturn's radius.

flexastexas · Answer

So what does our equation look like? and why?

dboome · Answer

So we basically have 2 equations we should know going into this problem, The first is the one I priginally lsited, the gravity one, and the other is Newton's 2nd Law which I'm assuming you're familiar with, F=m*a. Let me draw you a picture..

dboome · Answer

|dw:1460584993542:dw|Not sure if this helps lol