Kepler's 3rd Law relates the period of a planet to its distance from the Sun. The orbital period (P) is the length of time it takes to complete one orbit around the Sun. The distance from the Sun (a) is the semi-major axis of a planet's elliptical orbit. Using years for time units and AU for distance units, Kepler's third law becomes, "The period of a planet (in years), squared, equals the semi-major axis of the planet (in AU), cubed," or P² = a³ 1. Algebraically solve Kepler's third law for the period of a planet, in the space below, expressing the answer as a raised to an exponent, without the square root sign V:
Kepler's 3rd Law relates the period of a planet to its distance from the Sun. The orbital period (P) is the length of time it takes to complete one orbit around the Sun. The distance from the Sun (a) is the semi-major axis of a planet's elliptical orbit. Using years for time units and AU for distance units, Kepler's third law becomes, "The period of a planet (in years), squared, equals the semi-major axis of the planet (in AU), cubed," or P² = a³ 1. Algebraically solve Kepler's third law for the period of a planet, in the space below, expressing the answer as a raised to an exponent, without the square root sign V:
Applications and Investigations in Earth Science (9th Edition)
9th Edition
ISBN:9780134746241
Author:Edward J. Tarbuck, Frederick K. Lutgens, Dennis G. Tasa
Publisher:Edward J. Tarbuck, Frederick K. Lutgens, Dennis G. Tasa
Chapter1: The Study Of Minerals
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![**Kepler’s 3rd Law** relates the period of a planet to its distance from the Sun.
The orbital period (P) is the length of time it takes to complete one orbit around the Sun.
The distance from the Sun (a) is the semi-major axis of a planet’s elliptical orbit.
Using years for time units and AU for distance units, Kepler’s third law becomes, “The period of a planet (in years), squared, equals the semi-major axis of the planet (in AU), cubed,” or
\[ P^2 = a^3 \]
1. Algebraically solve Kepler’s third law for the period of a planet, in the space below, expressing the answer as a raised to an exponent, without the square root sign √:
2. In the third column of the table below, the actual, measured orbital periods of the eight known planets, and the dwarf planets Ceres and Pluto, are already written down.
3. Use your equation (derived above) to calculate the period of each planet or minor planet from its semi-major axis. Write your answers in the table below, in the fourth column.
Only go to the same decimal place in writing each answer in column 4 as the number in the actual period in column 3.
Calculate the discrepancy, the difference between the actual and the calculated orbital periods, and write the discrepancies in the last column. Leave off any negative signs.
| Planet or Minor Planet | Semi-major Axis (AU) | Actual Period (yr) | Calculated Period (yr) | Discrepancy | Discrepancy % |
|------------------------|---------------------|-------------------|-----------------------|-------------|---------------|
| Mercury | 0.3871 | 0.2408 | | | |
| Venus | 0.7233 | 0.61515 | | | |
| Earth | 1.0000 | 1.0000 | | | |
| Mars | 1.5237 | 1.8808 | | | |
| Ceres | 2.767 | 4.5998 | | | |
| Jupiter | 5.2028 | 11.86461 | | | |
| Saturn | 9.5388](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F94589190-d7d8-41be-9c6e-d2d51b756765%2Fbe76555a-20b8-440f-bdb1-2cc65bb6f8de%2Fzhffgmh_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Kepler’s 3rd Law** relates the period of a planet to its distance from the Sun.
The orbital period (P) is the length of time it takes to complete one orbit around the Sun.
The distance from the Sun (a) is the semi-major axis of a planet’s elliptical orbit.
Using years for time units and AU for distance units, Kepler’s third law becomes, “The period of a planet (in years), squared, equals the semi-major axis of the planet (in AU), cubed,” or
\[ P^2 = a^3 \]
1. Algebraically solve Kepler’s third law for the period of a planet, in the space below, expressing the answer as a raised to an exponent, without the square root sign √:
2. In the third column of the table below, the actual, measured orbital periods of the eight known planets, and the dwarf planets Ceres and Pluto, are already written down.
3. Use your equation (derived above) to calculate the period of each planet or minor planet from its semi-major axis. Write your answers in the table below, in the fourth column.
Only go to the same decimal place in writing each answer in column 4 as the number in the actual period in column 3.
Calculate the discrepancy, the difference between the actual and the calculated orbital periods, and write the discrepancies in the last column. Leave off any negative signs.
| Planet or Minor Planet | Semi-major Axis (AU) | Actual Period (yr) | Calculated Period (yr) | Discrepancy | Discrepancy % |
|------------------------|---------------------|-------------------|-----------------------|-------------|---------------|
| Mercury | 0.3871 | 0.2408 | | | |
| Venus | 0.7233 | 0.61515 | | | |
| Earth | 1.0000 | 1.0000 | | | |
| Mars | 1.5237 | 1.8808 | | | |
| Ceres | 2.767 | 4.5998 | | | |
| Jupiter | 5.2028 | 11.86461 | | | |
| Saturn | 9.5388
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