In 1772, Johann Bode published the following formula for predicting the mean distances, in astronomical units (AU), of the planets from the sun: a 1 = 0.4 , a n = 0.4 + 0.3 * 2 n − 2 Where n ≥ 2 is the number of the planet from the sun. a. Determine the first eight terms of this sequence.

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Answer 1

Question

Chapter 9.1, Problem 97AYU

To determine

To find: In 1772, Johann Bode published the following formula for predicting the mean distances, in astronomical units (AU), of the planets from the sun:

$a_{1} = 0.4$ , $a_{n} = 0.4 + 0.3 * 2^{n - 2}$

Where $n \geq 2$ is the number of the planet from the sun.

a. Determine the first eight terms of this sequence.

To determine

To find: In 1772, Johann Bode published the following formula for predicting the mean distances, in astronomical units (AU), of the planets from the sun:

$a_{1} = 0.4$ , $a_{n} = 0.4 + 0.3 * 2^{n - 2}$

Where $n \geq 2$ is the number of the planet from the sun.

b. At the time of Bode’s publication, the known planets were Mercury $(0.39 AU)$ , Venus $(0.72 AU)$ , Earth $(1 AU)$ , Mars $(1.52 AU)$ , Jupiter $(5.20 AU)$ , and Saturn $(9.54 AU)$ . How do the actual distances compare to the terms of the sequence?

To determine

To find: In 1772, Johann Bode published the following formula for predicting the mean distances, in astronomical units (AU), of the planets from the sun:

$a_{1} = 0.4$ , $a_{n} = 0.4 + 0.3 * 2^{n - 2}$

Where $n \geq 2$ is the number of the planet from the sun.

c. The planet Uranus was discovered in 1781, and the asteroid Ceres was discovered in 1801. The mean orbital distances from the sun to Uranus and Ceres are $19.2 AU$ and $2.77 AU$ , respectively. How well do these values fit within the sequence?

Ceres, Haumea, Makemake, Pluto, and Eris are referred to as dwarf planets.

To determine

To find: In 1772, Johann Bode published the following formula for predicting the mean distances, in astronomical units (AU), of the planets from the sun:

$a_{1} = 0.4$ , $a_{n} = 0.4 + 0.3 * 2^{n - 2}$

Where $n \geq 2$ is the number of the planet from the sun.

d. Determine the ninth and tenth terms of Bode’s sequence.

To determine

To find: In 1772, Johann Bode published the following formula for predicting the mean distances, in astronomical units (AU), of the planets from the sun:

$a_{1} = 0.4$ , $a_{n} = 0.4 + 0.3 * 2^{n - 2}$

Where $n \geq 2$ is the number of the planet from the sun.

e. The planets Neptune and Pluto were discovered in 1846 and 1930, respectively. Their mean orbital distances from the sun are $30.07 AU$ and $39.44 AU$ , respectively. How do these actual distances compare to the terms of the sequence?

To determine

To find: In 1772, Johann Bode published the following formula for predicting the mean distances, in astronomical units (AU), of the planets from the sun:

$a_{1} = 0.4$ , $a_{n} = 0.4 + 0.3 * 2^{n - 2}$

Where $n \geq 2$ is the number of the planet from the sun.

f. On July 29, 2005, NASA announced the discovery of a dwarf planet $(n = 11)$ , which has been named Eris. Use Bode’s Law to predict the mean orbital distance of Eris from the sun. Its actual mean distance is not yet known, but Eris is currently about 97 astronomical units from the sun.

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Answer 2

Question

Chapter 9.1, Problem 97AYU

To determine

To find: In 1772, Johann Bode published the following formula for predicting the mean distances, in astronomical units (AU), of the planets from the sun:

$a_{1} = 0.4$ , $a_{n} = 0.4 + 0.3 * 2^{n - 2}$

Where $n \geq 2$ is the number of the planet from the sun.

a. Determine the first eight terms of this sequence.

To determine

To find: In 1772, Johann Bode published the following formula for predicting the mean distances, in astronomical units (AU), of the planets from the sun:

$a_{1} = 0.4$ , $a_{n} = 0.4 + 0.3 * 2^{n - 2}$

Where $n \geq 2$ is the number of the planet from the sun.

b. At the time of Bode’s publication, the known planets were Mercury $(0.39 AU)$ , Venus $(0.72 AU)$ , Earth $(1 AU)$ , Mars $(1.52 AU)$ , Jupiter $(5.20 AU)$ , and Saturn $(9.54 AU)$ . How do the actual distances compare to the terms of the sequence?

To determine

To find: In 1772, Johann Bode published the following formula for predicting the mean distances, in astronomical units (AU), of the planets from the sun:

$a_{1} = 0.4$ , $a_{n} = 0.4 + 0.3 * 2^{n - 2}$

Where $n \geq 2$ is the number of the planet from the sun.

c. The planet Uranus was discovered in 1781, and the asteroid Ceres was discovered in 1801. The mean orbital distances from the sun to Uranus and Ceres are $19.2 AU$ and $2.77 AU$ , respectively. How well do these values fit within the sequence?

Ceres, Haumea, Makemake, Pluto, and Eris are referred to as dwarf planets.

To determine

To find: In 1772, Johann Bode published the following formula for predicting the mean distances, in astronomical units (AU), of the planets from the sun:

$a_{1} = 0.4$ , $a_{n} = 0.4 + 0.3 * 2^{n - 2}$

Where $n \geq 2$ is the number of the planet from the sun.

d. Determine the ninth and tenth terms of Bode’s sequence.

To determine

To find: In 1772, Johann Bode published the following formula for predicting the mean distances, in astronomical units (AU), of the planets from the sun:

$a_{1} = 0.4$ , $a_{n} = 0.4 + 0.3 * 2^{n - 2}$

Where $n \geq 2$ is the number of the planet from the sun.

e. The planets Neptune and Pluto were discovered in 1846 and 1930, respectively. Their mean orbital distances from the sun are $30.07 AU$ and $39.44 AU$ , respectively. How do these actual distances compare to the terms of the sequence?

To determine

To find: In 1772, Johann Bode published the following formula for predicting the mean distances, in astronomical units (AU), of the planets from the sun:

$a_{1} = 0.4$ , $a_{n} = 0.4 + 0.3 * 2^{n - 2}$

Where $n \geq 2$ is the number of the planet from the sun.

f. On July 29, 2005, NASA announced the discovery of a dwarf planet $(n = 11)$ , which has been named Eris. Use Bode’s Law to predict the mean orbital distance of Eris from the sun. Its actual mean distance is not yet known, but Eris is currently about 97 astronomical units from the sun.

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Answer 3

Question

Chapter 9.1, Problem 97AYU

To determine

To find: In 1772, Johann Bode published the following formula for predicting the mean distances, in astronomical units (AU), of the planets from the sun:

$a_{1} = 0.4$ , $a_{n} = 0.4 + 0.3 * 2^{n - 2}$

Where $n \geq 2$ is the number of the planet from the sun.

a. Determine the first eight terms of this sequence.

To determine

To find: In 1772, Johann Bode published the following formula for predicting the mean distances, in astronomical units (AU), of the planets from the sun:

$a_{1} = 0.4$ , $a_{n} = 0.4 + 0.3 * 2^{n - 2}$

Where $n \geq 2$ is the number of the planet from the sun.

b. At the time of Bode’s publication, the known planets were Mercury $(0.39 AU)$ , Venus $(0.72 AU)$ , Earth $(1 AU)$ , Mars $(1.52 AU)$ , Jupiter $(5.20 AU)$ , and Saturn $(9.54 AU)$ . How do the actual distances compare to the terms of the sequence?

To determine

To find: In 1772, Johann Bode published the following formula for predicting the mean distances, in astronomical units (AU), of the planets from the sun:

$a_{1} = 0.4$ , $a_{n} = 0.4 + 0.3 * 2^{n - 2}$

Where $n \geq 2$ is the number of the planet from the sun.

c. The planet Uranus was discovered in 1781, and the asteroid Ceres was discovered in 1801. The mean orbital distances from the sun to Uranus and Ceres are $19.2 AU$ and $2.77 AU$ , respectively. How well do these values fit within the sequence?

Ceres, Haumea, Makemake, Pluto, and Eris are referred to as dwarf planets.

To determine

To find: In 1772, Johann Bode published the following formula for predicting the mean distances, in astronomical units (AU), of the planets from the sun:

$a_{1} = 0.4$ , $a_{n} = 0.4 + 0.3 * 2^{n - 2}$

Where $n \geq 2$ is the number of the planet from the sun.

d. Determine the ninth and tenth terms of Bode’s sequence.

To determine

To find: In 1772, Johann Bode published the following formula for predicting the mean distances, in astronomical units (AU), of the planets from the sun:

$a_{1} = 0.4$ , $a_{n} = 0.4 + 0.3 * 2^{n - 2}$

Where $n \geq 2$ is the number of the planet from the sun.

e. The planets Neptune and Pluto were discovered in 1846 and 1930, respectively. Their mean orbital distances from the sun are $30.07 AU$ and $39.44 AU$ , respectively. How do these actual distances compare to the terms of the sequence?

To determine

To find: In 1772, Johann Bode published the following formula for predicting the mean distances, in astronomical units (AU), of the planets from the sun:

$a_{1} = 0.4$ , $a_{n} = 0.4 + 0.3 * 2^{n - 2}$

Where $n \geq 2$ is the number of the planet from the sun.

f. On July 29, 2005, NASA announced the discovery of a dwarf planet $(n = 11)$ , which has been named Eris. Use Bode’s Law to predict the mean orbital distance of Eris from the sun. Its actual mean distance is not yet known, but Eris is currently about 97 astronomical units from the sun.

Expert Solution & Answer

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Answer 4

Question

Chapter 9.1, Problem 97AYU

To determine

To find: In 1772, Johann Bode published the following formula for predicting the mean distances, in astronomical units (AU), of the planets from the sun:

$a_{1} = 0.4$ , $a_{n} = 0.4 + 0.3 * 2^{n - 2}$

Where $n \geq 2$ is the number of the planet from the sun.

a. Determine the first eight terms of this sequence.

To determine

To find: In 1772, Johann Bode published the following formula for predicting the mean distances, in astronomical units (AU), of the planets from the sun:

$a_{1} = 0.4$ , $a_{n} = 0.4 + 0.3 * 2^{n - 2}$

Where $n \geq 2$ is the number of the planet from the sun.

b. At the time of Bode’s publication, the known planets were Mercury $(0.39 AU)$ , Venus $(0.72 AU)$ , Earth $(1 AU)$ , Mars $(1.52 AU)$ , Jupiter $(5.20 AU)$ , and Saturn $(9.54 AU)$ . How do the actual distances compare to the terms of the sequence?

To determine

To find: In 1772, Johann Bode published the following formula for predicting the mean distances, in astronomical units (AU), of the planets from the sun:

$a_{1} = 0.4$ , $a_{n} = 0.4 + 0.3 * 2^{n - 2}$

Where $n \geq 2$ is the number of the planet from the sun.

c. The planet Uranus was discovered in 1781, and the asteroid Ceres was discovered in 1801. The mean orbital distances from the sun to Uranus and Ceres are $19.2 AU$ and $2.77 AU$ , respectively. How well do these values fit within the sequence?

Ceres, Haumea, Makemake, Pluto, and Eris are referred to as dwarf planets.

To determine

To find: In 1772, Johann Bode published the following formula for predicting the mean distances, in astronomical units (AU), of the planets from the sun:

$a_{1} = 0.4$ , $a_{n} = 0.4 + 0.3 * 2^{n - 2}$

Where $n \geq 2$ is the number of the planet from the sun.

d. Determine the ninth and tenth terms of Bode’s sequence.

To determine

To find: In 1772, Johann Bode published the following formula for predicting the mean distances, in astronomical units (AU), of the planets from the sun:

$a_{1} = 0.4$ , $a_{n} = 0.4 + 0.3 * 2^{n - 2}$

Where $n \geq 2$ is the number of the planet from the sun.

e. The planets Neptune and Pluto were discovered in 1846 and 1930, respectively. Their mean orbital distances from the sun are $30.07 AU$ and $39.44 AU$ , respectively. How do these actual distances compare to the terms of the sequence?

To determine

To find: In 1772, Johann Bode published the following formula for predicting the mean distances, in astronomical units (AU), of the planets from the sun:

$a_{1} = 0.4$ , $a_{n} = 0.4 + 0.3 * 2^{n - 2}$

Where $n \geq 2$ is the number of the planet from the sun.

f. On July 29, 2005, NASA announced the discovery of a dwarf planet $(n = 11)$ , which has been named Eris. Use Bode’s Law to predict the mean orbital distance of Eris from the sun. Its actual mean distance is not yet known, but Eris is currently about 97 astronomical units from the sun.

Expert Solution & Answer

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Check out a sample textbook solution

See solution

Answer 5

Chapter 9.1, Problem 97AYU

To determine

To find: In 1772, Johann Bode published the following formula for predicting the mean distances, in astronomical units (AU), of the planets from the sun:

$a_{1} = 0.4$ , $a_{n} = 0.4 + 0.3 * 2^{n - 2}$

Where $n \geq 2$ is the number of the planet from the sun.

a. Determine the first eight terms of this sequence.

To determine

To find: In 1772, Johann Bode published the following formula for predicting the mean distances, in astronomical units (AU), of the planets from the sun:

$a_{1} = 0.4$ , $a_{n} = 0.4 + 0.3 * 2^{n - 2}$

Where $n \geq 2$ is the number of the planet from the sun.

b. At the time of Bode’s publication, the known planets were Mercury $(0.39 AU)$ , Venus $(0.72 AU)$ , Earth $(1 AU)$ , Mars $(1.52 AU)$ , Jupiter $(5.20 AU)$ , and Saturn $(9.54 AU)$ . How do the actual distances compare to the terms of the sequence?

To determine

To find: In 1772, Johann Bode published the following formula for predicting the mean distances, in astronomical units (AU), of the planets from the sun:

$a_{1} = 0.4$ , $a_{n} = 0.4 + 0.3 * 2^{n - 2}$

Where $n \geq 2$ is the number of the planet from the sun.

c. The planet Uranus was discovered in 1781, and the asteroid Ceres was discovered in 1801. The mean orbital distances from the sun to Uranus and Ceres are $19.2 AU$ and $2.77 AU$ , respectively. How well do these values fit within the sequence?

Ceres, Haumea, Makemake, Pluto, and Eris are referred to as dwarf planets.

To determine

To find: In 1772, Johann Bode published the following formula for predicting the mean distances, in astronomical units (AU), of the planets from the sun:

$a_{1} = 0.4$ , $a_{n} = 0.4 + 0.3 * 2^{n - 2}$

Where $n \geq 2$ is the number of the planet from the sun.

d. Determine the ninth and tenth terms of Bode’s sequence.

To determine

To find: In 1772, Johann Bode published the following formula for predicting the mean distances, in astronomical units (AU), of the planets from the sun:

$a_{1} = 0.4$ , $a_{n} = 0.4 + 0.3 * 2^{n - 2}$

Where $n \geq 2$ is the number of the planet from the sun.

e. The planets Neptune and Pluto were discovered in 1846 and 1930, respectively. Their mean orbital distances from the sun are $30.07 AU$ and $39.44 AU$ , respectively. How do these actual distances compare to the terms of the sequence?

To determine

To find: In 1772, Johann Bode published the following formula for predicting the mean distances, in astronomical units (AU), of the planets from the sun:

$a_{1} = 0.4$ , $a_{n} = 0.4 + 0.3 * 2^{n - 2}$

Where $n \geq 2$ is the number of the planet from the sun.

f. On July 29, 2005, NASA announced the discovery of a dwarf planet $(n = 11)$ , which has been named Eris. Use Bode’s Law to predict the mean orbital distance of Eris from the sun. Its actual mean distance is not yet known, but Eris is currently about 97 astronomical units from the sun.

Answer 6

Chapter 9.1, Problem 97AYU

To determine

To find: In 1772, Johann Bode published the following formula for predicting the mean distances, in astronomical units (AU), of the planets from the sun:

$a_{1} = 0.4$ , $a_{n} = 0.4 + 0.3 * 2^{n - 2}$

Where $n \geq 2$ is the number of the planet from the sun.

a. Determine the first eight terms of this sequence.

Answer 7

Chapter 9.1, Problem 97AYU

To determine

To find: In 1772, Johann Bode published the following formula for predicting the mean distances, in astronomical units (AU), of the planets from the sun:

$a_{1} = 0.4$ , $a_{n} = 0.4 + 0.3 * 2^{n - 2}$

Where $n \geq 2$ is the number of the planet from the sun.

a. Determine the first eight terms of this sequence.

Answer 8

To determine

To find: In 1772, Johann Bode published the following formula for predicting the mean distances, in astronomical units (AU), of the planets from the sun:

$a_{1} = 0.4$ , $a_{n} = 0.4 + 0.3 * 2^{n - 2}$

Where $n \geq 2$ is the number of the planet from the sun.

b. At the time of Bode’s publication, the known planets were Mercury $(0.39 AU)$ , Venus $(0.72 AU)$ , Earth $(1 AU)$ , Mars $(1.52 AU)$ , Jupiter $(5.20 AU)$ , and Saturn $(9.54 AU)$ . How do the actual distances compare to the terms of the sequence?

Answer 9

To determine

To find: In 1772, Johann Bode published the following formula for predicting the mean distances, in astronomical units (AU), of the planets from the sun:

$a_{1} = 0.4$ , $a_{n} = 0.4 + 0.3 * 2^{n - 2}$

Where $n \geq 2$ is the number of the planet from the sun.

b. At the time of Bode’s publication, the known planets were Mercury $(0.39 AU)$ , Venus $(0.72 AU)$ , Earth $(1 AU)$ , Mars $(1.52 AU)$ , Jupiter $(5.20 AU)$ , and Saturn $(9.54 AU)$ . How do the actual distances compare to the terms of the sequence?

Answer 10

To determine

To find: In 1772, Johann Bode published the following formula for predicting the mean distances, in astronomical units (AU), of the planets from the sun:

$a_{1} = 0.4$ , $a_{n} = 0.4 + 0.3 * 2^{n - 2}$

Where $n \geq 2$ is the number of the planet from the sun.

c. The planet Uranus was discovered in 1781, and the asteroid Ceres was discovered in 1801. The mean orbital distances from the sun to Uranus and Ceres are $19.2 AU$ and $2.77 AU$ , respectively. How well do these values fit within the sequence?

Ceres, Haumea, Makemake, Pluto, and Eris are referred to as dwarf planets.

Answer 11

To determine

To find: In 1772, Johann Bode published the following formula for predicting the mean distances, in astronomical units (AU), of the planets from the sun:

$a_{1} = 0.4$ , $a_{n} = 0.4 + 0.3 * 2^{n - 2}$

Where $n \geq 2$ is the number of the planet from the sun.

c. The planet Uranus was discovered in 1781, and the asteroid Ceres was discovered in 1801. The mean orbital distances from the sun to Uranus and Ceres are $19.2 AU$ and $2.77 AU$ , respectively. How well do these values fit within the sequence?

Ceres, Haumea, Makemake, Pluto, and Eris are referred to as dwarf planets.

Answer 12

To determine

To find: In 1772, Johann Bode published the following formula for predicting the mean distances, in astronomical units (AU), of the planets from the sun:

$a_{1} = 0.4$ , $a_{n} = 0.4 + 0.3 * 2^{n - 2}$

Where $n \geq 2$ is the number of the planet from the sun.

d. Determine the ninth and tenth terms of Bode’s sequence.

Answer 13

To determine

To find: In 1772, Johann Bode published the following formula for predicting the mean distances, in astronomical units (AU), of the planets from the sun:

$a_{1} = 0.4$ , $a_{n} = 0.4 + 0.3 * 2^{n - 2}$

Where $n \geq 2$ is the number of the planet from the sun.

d. Determine the ninth and tenth terms of Bode’s sequence.

Answer 14

To determine

To find: In 1772, Johann Bode published the following formula for predicting the mean distances, in astronomical units (AU), of the planets from the sun:

$a_{1} = 0.4$ , $a_{n} = 0.4 + 0.3 * 2^{n - 2}$

Where $n \geq 2$ is the number of the planet from the sun.

e. The planets Neptune and Pluto were discovered in 1846 and 1930, respectively. Their mean orbital distances from the sun are $30.07 AU$ and $39.44 AU$ , respectively. How do these actual distances compare to the terms of the sequence?

Answer 15

To determine

To find: In 1772, Johann Bode published the following formula for predicting the mean distances, in astronomical units (AU), of the planets from the sun:

$a_{1} = 0.4$ , $a_{n} = 0.4 + 0.3 * 2^{n - 2}$

Where $n \geq 2$ is the number of the planet from the sun.

e. The planets Neptune and Pluto were discovered in 1846 and 1930, respectively. Their mean orbital distances from the sun are $30.07 AU$ and $39.44 AU$ , respectively. How do these actual distances compare to the terms of the sequence?

Answer 16

To determine

To find: In 1772, Johann Bode published the following formula for predicting the mean distances, in astronomical units (AU), of the planets from the sun:

$a_{1} = 0.4$ , $a_{n} = 0.4 + 0.3 * 2^{n - 2}$

Where $n \geq 2$ is the number of the planet from the sun.

f. On July 29, 2005, NASA announced the discovery of a dwarf planet $(n = 11)$ , which has been named Eris. Use Bode’s Law to predict the mean orbital distance of Eris from the sun. Its actual mean distance is not yet known, but Eris is currently about 97 astronomical units from the sun.

Answer 17

To determine

To find: In 1772, Johann Bode published the following formula for predicting the mean distances, in astronomical units (AU), of the planets from the sun:

$a_{1} = 0.4$ , $a_{n} = 0.4 + 0.3 * 2^{n - 2}$

Where $n \geq 2$ is the number of the planet from the sun.

f. On July 29, 2005, NASA announced the discovery of a dwarf planet $(n = 11)$ , which has been named Eris. Use Bode’s Law to predict the mean orbital distance of Eris from the sun. Its actual mean distance is not yet known, but Eris is currently about 97 astronomical units from the sun.

Answer 18

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Answer 19

Expert Solution & Answer

Answer 20

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Answer 21

Ch. 9.1 - For the function , find and . Ch. 9.1 - Prob. 2AYU Ch. 9.1 - Prob. 3AYU Ch. 9.1 - Prob. 4AYU Ch. 9.1 - Prob. 5AYU Ch. 9.1 - Prob. 6AYU Ch. 9.1 - Prob. 7AYU Ch. 9.1 - Prob. 8AYU Ch. 9.1 - Prob. 9AYU Ch. 9.1 - Prob. 10AYU

In 1772, Johann Bode published the following formula for predicting the mean distances, in astronomical units (AU), of the planets from the sun: a 1 = 0.4 , a n = 0.4 + 0.3 * 2 n − 2 Where n ≥ 2 is the number of the planet from the sun. a. Determine the first eight terms of this sequence.

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