# Sidereal & Synodic periods

1. Sep 20, 2010

### University

Is there any formula to calculate Synodic period using for example the Moon's Sidereal period

Lets say moon sidereal period is 29 days what would be its synodic period?

2. Sep 20, 2010

### Janus

Staff Emeritus
You need to use the period of the Earth's sidereal year and the equation:

$$\frac{1}{synodic_{moon}} = \frac{1}{sidereal_{moon}}- \frac{1}{sidereal_{Earth}}$$

3. Sep 20, 2010

### University

Does 33.3 days sound right?

4. Sep 20, 2010

### Janus

Staff Emeritus
No.

First, it is not the answer you would get if you use 29 days for the Moon's sidereal period, and secondly 29 days is not the Moon's sidereal period (neither is the value you apparently used, if you did the equation right).

5. Sep 20, 2010

### University

Thanks for all the hints and help but the exact problem in the text states:

If the sidereal period of the moon is 29.0 days(instead of the correct 27.32 days) what would be its synodic period?

HINT: consider how far around the sun the Earth & Moon would have travelled in 29.0 days

6. Sep 20, 2010

### Janus

Staff Emeritus
Like I said in my last post, 33.3 days is still not correct if you use a value of 29 days for the sidereal period. How did you arrive at that value?

7. Sep 20, 2010

### University

I use the equation u posted

1/Synodic period = 1/Moon sidereal Period - 1/earth's sidereal period
= 1/29 -1/365

8. Sep 20, 2010

### Janus

Staff Emeritus
33.3 days is not the answer I get when using those numbers in the equation.

9. Sep 21, 2010

### University

E = Earth sidereal year
P = Other planet sidereal year
Then sp = 1/(1/E-1/P)

using this eq I get 36.7 days. Is this correct?

Last edited: Sep 21, 2010
10. Sep 21, 2010

### Janus

Staff Emeritus
No. I don't understand how you are coming up with these answers with the numbers you are using and the equation given.

11. Sep 21, 2010

### University

I got 0.032 days but this does not seem to be a reasonable value. Besides the equation is 1/synodic period, so I was assuming 1/0.032 =31.25 days