Question 4
Source header: International Mathematics and Science Olympiad for Primary Schools (IMSO) 2004 · Science Contest in Taiwan. Fields: Name, School, Grade, ID number. No round or duration is printed. This combined four-experiment package uses one shared 120-minute fallback, not a historical time claim.
## Experiment IV: Our neightbour MARS [source spelling]
The source states: “On August 27th,2003, Mars was in the opposition (the closest position to the Earth).” This event is shown in the following original figure:
The next opposition can be estimated using
$$\frac1{P_{\mathrm{opp}}}=\frac1E-\frac1M.$$
$P_{\mathrm{opp}}$ is the period between oppositions of Mars; Earth's revolution period is $E=365$ days; Mars's is $M=687$ days.
1\. Find the period of opposition of Mars. **5 points.**
2 a\. How many revolutions should Mars make around the Sun to reach the next opposition? **3 points.**
2 b\. How many revolutions should Earth make around the Sun to reach the next opposition with Mars? **4 points.**
3\. Predict approximately when the next opposition will occur: date, month and year. **8 points.**
4\. Draw the diagram of the next opposition. **6 points.**
Original figure labels: Sun; Earth; “Mar” (truncated Mars). Source wording and starting date are retained for the calculation; their astronomical limitations are explained in the solution. Total 26 printed points.
## Experiment IV: Our neightbour MARS [source spelling]
The source states: “On August 27th,2003, Mars was in the opposition (the closest position to the Earth).” This event is shown in the following original figure:
The next opposition can be estimated using
$$\frac1{P_{\mathrm{opp}}}=\frac1E-\frac1M.$$
$P_{\mathrm{opp}}$ is the period between oppositions of Mars; Earth's revolution period is $E=365$ days; Mars's is $M=687$ days.
1\. Find the period of opposition of Mars. **5 points.**
2 a\. How many revolutions should Mars make around the Sun to reach the next opposition? **3 points.**
2 b\. How many revolutions should Earth make around the Sun to reach the next opposition with Mars? **4 points.**
3\. Predict approximately when the next opposition will occur: date, month and year. **8 points.**
4\. Draw the diagram of the next opposition. **6 points.**
Original figure labels: Sun; Earth; “Mar” (truncated Mars). Source wording and starting date are retained for the calculation; their astronomical limitations are explained in the solution. Total 26 printed points.