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Science · Drill 35

Science practice 35

10 questions ~9 min recommended
⏱ 00:00
Score
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Central Planet Central Planet Mass (earth masses) Moon Name Radius of Moon's Orbit (millions of m) Period of Moon (days) Orbital Speed of Moon (km/s) Gravitational Acceleration of Moon in Orbit (m/s/s)
Earth 1 Moon 385 27.30 1.0 0.00273
Jupiter 318 Andrastea1 129 0.30 31.5 7.67
Jupiter 318 Amalthea 181 0.50 26.5 3.87
Saturn 95 Atlas 138 0.60 16.6 2.01
Saturn 95 Epimetheus 151 0.69 15.8 1.66
Saturn 95 Mimas 186 0.94 14.3 1.11
Saturn 95 Enceladus 238 1.37 12.6 0.671
Saturn 95 Telesto 295 1.88 11.4 0.441
Saturn 95 Helene 378 2.74 10.0 0.267
Saturn 95 Rhea 527 4.52 8.4 0.137
Saturn 95 Hyperion 1,480 21.30 5.1 0.0173
Saturn 95 Iapetus 3,560 79.30 3.2 0.00299
Saturn 95 Phoebe 13,000 550.00 1.7 0.000226
Uranus 15 Miranda 129 1.40 6.7 0.343
Uranus 15 Ariel 191 2.52 5.5 0.159

Gravitational Acceleration of Moon vs. Inverse Radius Squared

8 7 6 5 4 3 2 1 0 Inverse radius squared (10⁷/m²) • Moons of Jupiter ▲ Moons of Saturn

Astronomers have identified more than 170 moons in the solar system. For centuries, many of these scientists have used telescopic observations to measure the time it takes each moon to complete each orbit (the period). Using proportions and geometry, the radius of each orbit has also been determined. With these data in place, the speed of each moon in its orbit may be found by taking the circumference of each orbit (2 × π × radius, assuming a circular orbit, with π, or pi, approximately equal to 3.14159) divided by the period. The acceleration of each moon in its respective orbit is equivalent to its centripetal acceleration, which is found by dividing the square of its speed by the radius of its orbit. Table 10.4 provides data for various moons in our solar system.

TABLE 10.4

In an attempt to find the relationships in the data, the gravitational acceleration versus the inverse of the orbital radius squared was graphed in Figure 10.3.

Figure 10.3

1. Which moon has a period closest in value to the period of Earth's moon?

2. Given just the data in the table, which two moons are most appropriate for studying the effect of central planet mass on gravitational acceleration?

3. What is the best description of the relationship between radius of orbit and the period of the moon?

4. Figure 10.3 indicates that the gravitational acceleration of moons is:

5. A particular moon orbits a planet that is 318 times more massive than Earth. If that moon has a radius of orbit of 422 million meters, what is a possible value for the moon's speed?

6. Using Figure 10.3, along with information in Table 10.4, what conclusion can be made about the effect of a planet's mass on the acceleration of its moons?

7. According to the passage, which columns were calculated from data gathered by scientists?

8. About how many times does the moon orbit the earth while Phoebe completes one orbit of Saturn?

9. How far does Helene travel in 15 seconds?

10. If the moons of Mars (a planet with a mass 0.107 times that of Earth) were placed on the graph in Figure 10.3, where would they most likely appear?

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