# Unique Roche limit and Saturn's rings

Hello everyone !

I am new here, so before to post my question, I'll just introduce myself shortly. I'm a French student in schools that we call CPGE - highly selective classes to prepare for national competitive entrance exams to leading French "grandes écoles", specializing in mathematics and physics.

Each year, we have to write a report about a chosen topic, and mine is the Roche limit and its application to Saturn's rings. Surfing through the web, I found several websites who answered most of my questions, but one of them remains unanswered, so I dare post it here.

In fact, many people say that most of the Saturn's rings lie within this Roche limit, but the problem is that the Roche limit depends on satellites and primary densities. So, why is it assumed that a unique Roche limit can be calculated ? And if there is a unique Roche limit for Saturn's rings (for example), why just do we take the same densities ? Indeed, why a meteorite that could be a part of the rings should be the same density as Saturn ?

I thank you all for all your answers, hoping not to have wasted your time ! :shy:

And by the way, sorry if my English isn't as perfect as yours.
Thanks again !

Damien.

## Answers and Replies

well in any binary system (in your case, the ring and saturn) can be thought of as a restricted 3 body problem. THe effective potential of a test particle moving in the field of the two masses, ALWAYS has 5 stationary points (the are called Lagrange points) where the attractive force of Saturn is equal to the attractive force of the ring. That comes out of a lot of maths.

Now the Lagrange point between the ring and the Saturn defines the Roche limit. It depends ONLY on the ratio of masses (or densities) and orbital separation.

Hi i too new for pf

Hey guys,

It's been a while and I hope you people welcome me again. Thank God my friend has brought up this topic about the Roche Limit. I have been facing problem trying to understand where the inconsistancy is coming from. I read a book by Paul A. Tipler fourth edition named "Physics for Scientists and Engineers". I saw the Roche Limit was solved and the equation came out to R=r(16 dp/ds)^1/3 but I was checking few websites and I saw the sixteen replaced by 2. Which one is correct? I need a little help. I think I tried solving and I noticed from the book, in solving for the gravitational attractive force b/w a point mass and the remaining point masses of the satellite, they took the masses to be the same but they had the calculation of the tidal force correct. Now for the website, the point mass was just another mass << than the sum of the remaining other masses and I thought that was correct. Now on the website there was a tidal force indicated but they didn't show how they got that and it had something like Ft=2Mmr/R^3 which after I calculated didn't look correct to me at all. Please help me. Maybe I got this all wrong.