A graphing calculator is recommended. The table shows the mean (average) distances d of the planets from the sun (taking the unit of measurement to be the distance from the earth to the sun) and their periods T (time of revolution in years). Planet T(d) = Mercury Venus Earth Mars Jupiter Saturn Uranus d 0.387 0.723 1.000 1.523 5.203 19.190 T Neptune 30.086 0.241 0.615 1.000 1.881 9.541 29.457 11.861 84.008 164.784 (a) Fit a power model to the data. Use n = 2. (Round your values to one decimal place.) (b) Kepler's Third Law of Planetary Motion states that "The square of the period of revolution of a planet is proportional to the cube of its mean distance from the sun." Does your model corroborate Kepler's Third Law? O Yes O No
A graphing calculator is recommended. The table shows the mean (average) distances d of the planets from the sun (taking the unit of measurement to be the distance from the earth to the sun) and their periods T (time of revolution in years). Planet T(d) = Mercury Venus Earth Mars Jupiter Saturn Uranus d 0.387 0.723 1.000 1.523 5.203 19.190 T Neptune 30.086 0.241 0.615 1.000 1.881 9.541 29.457 11.861 84.008 164.784 (a) Fit a power model to the data. Use n = 2. (Round your values to one decimal place.) (b) Kepler's Third Law of Planetary Motion states that "The square of the period of revolution of a planet is proportional to the cube of its mean distance from the sun." Does your model corroborate Kepler's Third Law? O Yes O No
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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![### Mean Distances and Periods of Planets from the Sun
A graphing calculator is recommended.
The table below shows the mean (average) distances \( d \) of the planets from the sun (taking the unit of measurement to be the distance from the earth to the sun) and their periods \( T \) (time of revolution in years).
| Planet | \( d \) | \( T \) |
|---------|-----------|-------------|
| Mercury | 0.387 | 0.241 |
| Venus | 0.723 | 0.615 |
| Earth | 1.000 | 1.000 |
| Mars | 1.523 | 1.881 |
| Jupiter | 5.203 | 11.861 |
| Saturn | 9.541 | 29.457 |
| Uranus | 19.190 | 84.008 |
| Neptune | 30.086 | 164.784 |
#### Exercise
**(a)** Fit a power model to the data. Use \( n = \frac{3}{2} \) (Round your values to one decimal place).
\[ T(d) = \_\_\_\_\_ \]
**(b)** Kepler's Third Law of Planetary Motion states that "The square of the period of revolution of a planet is proportional to the cube of its mean distance from the sun."
Does your model corroborate Kepler's Third Law?
- Yes
- No](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F4e135d5c-f867-4afd-9f0d-b505f4f19664%2F094414ab-7fc5-49e6-a3ca-84f24e36ae2a%2Fxejn569_processed.png&w=3840&q=75)
Transcribed Image Text:### Mean Distances and Periods of Planets from the Sun
A graphing calculator is recommended.
The table below shows the mean (average) distances \( d \) of the planets from the sun (taking the unit of measurement to be the distance from the earth to the sun) and their periods \( T \) (time of revolution in years).
| Planet | \( d \) | \( T \) |
|---------|-----------|-------------|
| Mercury | 0.387 | 0.241 |
| Venus | 0.723 | 0.615 |
| Earth | 1.000 | 1.000 |
| Mars | 1.523 | 1.881 |
| Jupiter | 5.203 | 11.861 |
| Saturn | 9.541 | 29.457 |
| Uranus | 19.190 | 84.008 |
| Neptune | 30.086 | 164.784 |
#### Exercise
**(a)** Fit a power model to the data. Use \( n = \frac{3}{2} \) (Round your values to one decimal place).
\[ T(d) = \_\_\_\_\_ \]
**(b)** Kepler's Third Law of Planetary Motion states that "The square of the period of revolution of a planet is proportional to the cube of its mean distance from the sun."
Does your model corroborate Kepler's Third Law?
- Yes
- No
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