You are at a weekly meeting of your Astronomy Club. The club members are excited because access is now available to real-time data on light intensity from the star at the center of another planetary system. The plane of the system is parallel to the direction from the system toward the Earth, so it is possible to detect transits: a planet passes between the Earth and the star of the system, so that the light from the star dims slightly. The planets of this system are very close to their parent star and revolve very rapidly. Planet X in this system has a period of 4.00 Earth days! As you graph the incoming data from the star as it appears on a computer, you see the dip in light intensity. You make a printout of the graph of light intensity versus time and compare it to the graph from 4.00 days ago. The latest graph shows a difference. The time interval from the beginning of the dimming of the light from the star to the return to full brightness took much longer than it did during the observation 4.00 days ago, and the light became significantly dimmer than the observation 4.00 days ago. As you continue to watch the data over several days, the light data every 4.00 days is similar to that in the first graph. Then, 16.0 days after you noticed the unusual behavior, you see it again! You realize that the unusual behavior must be due to a double occultation: two planets are lined up between you and the other star: Planet X and Planet Y! You inform your club members about the data and they excitedly ask you to find out the percentage by which the semimajor axis of the Planet Y is larger that of Planet X.

You are at a weekly meeting of your Astronomy Club. The club members are excited because access is now available to real-time data on light intensity from the star at the center of another planetary system. The plane of the system is parallel to the direction from the system toward the Earth, so it is possible to detect transits: a planet passes between the Earth and the star of the system, so that the light from the star dims slightly. The planets of this system are very close to their parent star and revolve very rapidly. Planet X in this system has a period of 4.00 Earth days! As you graph the incoming data from the star as it appears on a computer, you see the dip in light intensity. You make a printout of the graph of light intensity versus time and compare it to the graph from 4.00 days ago. The latest graph shows a difference. The time interval from the beginning of the dimming of the light from the star to the return to full brightness took much longer than it did during the observation 4.00 days ago, and the light became significantly dimmer than the observation 4.00 days ago. As you continue to watch the data over several days, the light data every 4.00 days is similar to that in the first graph. Then, 16.0 days after you noticed the unusual behavior, you see it again! You realize that the unusual behavior must be due to a double occultation: two planets are lined up between you and the other star: Planet X and Planet Y! You inform your club members about the data and they excitedly ask you to find out the percentage by which the semimajor axis of the Planet Y is larger that of Planet X.