physics : class11 Orbital Time Intervals : Second Law of Kepler : Gravitation MCQ Questions and Answers
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Orbital Time Intervals
MCQ questions and answers.
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MCQ Questions
1. A planet moves in an elliptical orbit with period 84 days. The area swept by the line joining the Sun to the planet during a certain interval is 5/12 of the total area of the ellipse. What is the duration of this interval?
A.
21 days
B.
24.5 days
C.
28 days
D.
35 days
Correct Answer:
24.5 days
Explanation:
According to Kepler's second law, the time interval is proportional to the area swept. Therefore, t/T = 5/12, so t = 84 × 5/12 = 24.5 days.
2. A planet sweeps out an area of 3/8 of the total orbital area in 15 days. Assuming a constant areal velocity, how long will it take to sweep an additional area equal to 5/8 of the total orbital area?
A.
20 days
B.
25 days
C.
35 days
D.
40 days
Correct Answer:
25 days
Explanation:
The first interval represents 3/8 of the orbital period, so the period is T = 15 × 8/3 = 40 days. An area of 5/8 corresponds to a time of 5T/8 = 25 days.
3. A planet passes point A after sweeping 1/4 of the total orbital area from perihelion and later passes point B after sweeping 3/4 of the total orbital area from perihelion. What fraction of the orbital period elapses between A and B?
A.
1/8
B.
1/4
C.
1/2
D.
3/4
Correct Answer:
1/2
Explanation:
The area swept from A to B is (3/4 − 1/4) = 1/2 of the total orbital area. Since time is proportional to swept area, the elapsed time is 1/2 of the orbital period.
4. During one forward revolution, a planet sweeps 17% of the total orbital area between points P and Q, and 29% between points Q and R. If the time from P to Q is 8.5 days, what is the time from Q to R?
A.
12.5 days
B.
14.5 days
C.
17 days
D.
20 days
Correct Answer:
14.5 days
Explanation:
The time ratio equals the swept-area ratio. Thus, t_QR/t_PQ = 0.29/0.17. Therefore, t_QR = 8.5 × 0.29/0.17 = 14.5 days.
5. A planet completes an elliptical orbit in 120 days. Starting from perihelion, it reaches point X after sweeping 1/6 of the total orbital area and point Y after sweeping 2/3 of the total orbital area. What is the time interval from X to Y?
A.
40 days
B.
50 days
C.
60 days
D.
80 days
Correct Answer:
60 days
Explanation:
The area swept from X to Y is 2/3 − 1/6 = 1/2 of the total area. Hence the time interval is T/2 = 120/2 = 60 days.
6. A planet sweeps an area of 2.4 × 10^20 m² in 18 days. If the total area enclosed by its orbit is 9.6 × 10^20 m², what is its orbital period?
A.
54 days
B.
72 days
C.
90 days
D.
108 days
Correct Answer:
72 days
Explanation:
The swept area fraction is (2.4 × 10^20)/(9.6 × 10^20) = 1/4. Thus, 18 days represents one-fourth of the period, giving T = 4 × 18 = 72 days.
7. Measured in the direction of motion from a fixed reference point, a planet is at area coordinate 0.85 of its orbit at time t1 and at area coordinate 0.20 at time t2 in the next forward passage. If its orbital period is T, what is t2 − t1?
A.
0.15T
B.
0.20T
C.
0.35T
D.
0.65T
Correct Answer:
0.35T
Explanation:
Because the motion is forward, the planet sweeps from area coordinate 0.85 through 1.00 and then to 0.20. The swept fraction is (1 − 0.85) + 0.20 = 0.35, so the time interval is 0.35T.
8. In an elliptical orbit, a planet takes 10 days to sweep 5% of the total orbital area. How long will it take to sweep 42% of the total orbital area?
A.
64 days
B.
72 days
C.
84 days
D.
96 days
Correct Answer:
84 days
Explanation:
The time is proportional to the swept area. Therefore, the required time is 10 × (42/5) = 84 days.
9. A planet takes 15 days to sweep 1/8 of the total orbital area and then takes an additional interval to sweep 3/8 of the total area. What is the duration of the additional interval?
A.
30 days
B.
45 days
C.
60 days
D.
75 days
Correct Answer:
45 days
Explanation:
The first interval is T/8 = 15 days, so T = 120 days. The additional interval corresponds to 3/8 of the orbit, giving 3T/8 = 45 days.
10. Two time intervals of a planet's elliptical orbit begin at different points, one near perihelion and the other near aphelion. In each interval, the radius vector sweeps exactly the same area. What can be concluded about the durations of the two intervals?
A.
The perihelion interval is always shorter.
B.
The aphelion interval is always shorter.
C.
The two intervals have equal durations.
D.
Their durations depend on the eccentricity but cannot be compared.
Correct Answer:
The two intervals have equal durations.
Explanation:
Kepler's second law states that the areal velocity is constant throughout the orbit. Therefore, equal swept areas require equal time intervals, regardless of whether the intervals occur near perihelion or aphelion.
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