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.
So I was doing this and I got stuck here;
gs = G*Ms/Rs² = G*(95Me)/(9²Re²) = ge*(95/9²) = 1.173*ge ....
Am I even doing this right?
Yes, you are on the right track! To estimate the gravitational field on the surface of Saturn compared to that on Earth, you need to use the formula for gravitational field strength, which is given by:
gs = G * Ms / Rs²
where gs is the gravitational field strength on Saturn's surface, G is the gravitational constant, Ms is Saturn's mass, and Rs is Saturn's radius.
By substituting in the values given in the question, you have:
gs = G * (95 * Me) / (9² * Re²)
Now, let's break it down step by step:
1. gs = G * (95 * Me) / (9² * Re²): This part is correct.
2. Now, you can simplify the expression further by using the fact that ge, the gravitational field on Earth's surface, is approximately equal to 9.8 m/s².
So, ge = G * Me / Re²
3. Substitute this value into the equation:
gs = G * (95 * Me) / (9² * Re²) = (G * Me / Re²) * (95 / 9²)
You can see that the expression in the parentheses is ge, so:
gs = ge * (95 / 9²)
4. Calculate the numerical value:
gs = 9.8 m/s² * (95 / 9²) ≈ 1.17 * 9.8 m/s²
Therefore, the gravitational field strength on the surface of Saturn is estimated to be around 1.17 times the gravitational field strength on Earth's surface.
I hope this clarifies your doubts and helps you proceed with your calculations!