(adsbygoogle = window.adsbygoogle || []).push({}); Edit: perhaps this might belong in one of the Physics help forums? Oops. Mods, please move if so!

1. The problem statement, all variables and given/known data

Show that a transit of Venus across the Sun’s disk lasts at most about 8 hours. The synodic period of Venus is 584 days and its orbital radius is 0.723 A.U. The Sun’s angular diameter is 32′. Assume that the orbits of Venus and the Earth are coplanar and circular. Do not use any other numerical data. (Hint: find the angular velocity of Venus relative to the Earth-Sun line and as seen from the Earth. The greatest duration of transit is when Venus passes through a diameter of the solar disk.)

2. Relevant equations

ω_{Venus}- ω_{Earth}= ω_{synodic}

3. The attempt at a solution

I understand the concept of synodic period, I'm just unsure how to tackle this problem. The transit must occur at inferior conjunction. I know the synodic period, which I can use to calculate the synodic angular velocity as ~ 0.02568 degrees per hour. This gives a maximum transit duration of nearly 21 hours! That's not right.

How can I convert this synodic angular velocity (which is with respect to a reference frame that is co-rotating with the Earth-Sun line) to an angular velocity seen by an observer on Earth?

Please don't be too specific with your hints as this is coursework, and I do want to figure things out for myself. I just need a nudge in the right direction :)

Thanks!

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Astrophysics: orbital dynamics - duration of a transit of Venus

**Physics Forums | Science Articles, Homework Help, Discussion**