Distance from earth to sun = 1.50 * 1011m
Earth's orbital period = 3.16 * 107 s
Distance from venus to sun = 1.08 * 1011m
Venus's orbital period = 1.94 * 107 s
Both orbits around the sun are coplanar, and the transit of venus about the sun is observed by a telescope on earth.
QN: To calculate the smallest perpendicular velocity to its orbit, required by venus so that the next expected transit does not occur.
Since venus and earth are orbiting at different angular velocities, (with venus moving faster)
Relative period = 5.02 * 107 s
Therefore, time interval between successful transists = 5.02 * 107 s
The Attempt at a Solution
The angle theta was found to be 0.00928 rad.
In order for the next transit not to occur (say originally both earth venus are along the left line that connects to left extreme end of sun), in the 5.02 * 107 s that venus spends travelling relative to earth, it must be displaced by an angle of 0.00928 rad for venus to 'escape' being caught in the camera's frame that is pointing to the sun.
But the answer says that " If during the interval between transits venus has a velocity vs perpendicular to its orbit and as a result, is displaced by (1/2)(0.00928) rad as observed from earth (half aug. diameter of of sun at earth) , venus will not pass in front of the sun"
My question is - why only half the angle?!
The original question can be found here at Qn 8:
Qn paper: http://www.physics.ox.ac.uk/olympiad/Downloads/PastPapers/BPhO_Paper2_2005_QP.pdf
Really appreciate any help offered!
11.7 KB Views: 328
Last edited by a moderator: