Jupiter and Saturn

Date: 09/10/2001 at 21:30:02
From: Jean James
Subject: Jupiter and Saturn

Jupiter revolves around the Sun about once every 12 earth years.  
Saturn revolves around the Sun about once every 30 earth years. In 
1982, Jupiter and Saturn appeared very close to each other. About when 
will Jupiter and Saturn appear together again?

Date: 09/12/2001 at 10:04:07
From: Doctor Rick
Subject: Re: Jupiter and Saturn

Hi, Jean. This is a very nice problem!

Picture a race. One race car goes 100 miles an hour and another goes 
102 miles an hour. After one hour the faster car is 102-100 = 2 miles 
farther along than the slower car. Thus we can say that the distance 
between them increases at a rate of 2 miles/hour, or that their 
"relative speed" is 2 miles/hour.

Let's say the cars are on a 4-mile track. Then in two hours the faster 
car is 4 miles ahead of the other, which means he has "lapped" him - 
he has caught up with him again, one lap ahead.

That's what Jupiter does to Saturn. In one year, Jupiter moves 1/12 of 
the way around its orbit, and Saturn moves 1/30 of the way around its 
orbit. After a year, what fraction of an orbit separates them? Can you 
complete the analogy by figuring out when Jupiter "laps" Saturn?

Write back if these hints aren't enough. Show me whatever work you are 
able to do, so I can see what kind of help to give you.

- Doctor Rick, The Math Forum
  http://mathforum.org/dr.math/