What are the distances of the planets from the sun

Asked by admin @ 28/10/2021 in Mathematics viewed by 267 People

Part A:

Planet Distance from sun (in km) Distance in scientific notation
Mercury 57,909,000 5.7909 × 10^7
Venus 67,240,000 6.724 × 10^7
Earth 92,960,000 9.296 × 10^7
Mars 141,600,000 1.416 × 10^8
Jupiter 483,800,000 4.838 × 10^8
Saturn 890,700,000 8.907 × 10^8
Uranus 1,784,000,000 1.784 × 10^9
Neptune 2,793,000,000 2.793 × 10^9
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Part B
1.If a spacecraft was parked on Venus and needed to make a flight to Jupiter, how far would it need to travel? (Assume both planets are aligned with the sun and are on the same side of the sun.) Show your work and provide your answer in scientific notation.
2.Mercury, Venus, and Earth are the three planets closest to the sun. Would their combined distance from the sun be greater or less than the distance from the sun to Neptune? Show your work and justify your answer.
3.If Earth was 10 times farther away from the sun than it is now, which planet would it be closest to? (Assume all the planets are aligned with the sun and are on the same side of the sun.) Compare Earth's new distance to that planet. How far apart would they be in standard notation? How far apart in scientific notation? Show your work.
4.The space shuttle travels at about 28,000 km per hour. Using that information, estimate how many hours it will take the shuttle to reach Saturn from Earth. (Assume both planets are aligned with the sun and are on the same side of the sun.) Show your work. Convert your answer into scientific notation if necessary.
(I already did Part A, it is just a guide to help. Just answer all the questions from Part B and SHOW YOUR WORK!! please!! Thank you so much, if you help you will be getting 34 points.)

Answered by admin @ 28/10/2021

Part B - Question 1

Distance for the spacecraft to travel from Venus to Jupiter = Distance of Jupiter from Sun - Distance of Venus from Sun

⇒ Distance for the spacecraft to travel from Venus to Jupiter = 4.838 × 10⁸ - 6.724 × 10⁷

⇒ Distance for the spacecraft to travel from Venus to Jupiter = 483,800,000 - 67,240,000

⇒ Distance for the spacecraft to travel from Venus to Jupiter = 416,560,000

⇒ Distance for the spacecraft to travel from Venus to Jupiter = 4.1656 × 10⁸

Part B - Question 2

Combined distance of Mercury, Venus, and Earth from the Sun = Distance of Mercury from Sun + Distance of Venus from Sun + Distance of Earth from Sun

⇒ Combined distance of Mercury, Venus, and Earth from the Sun = 5.7909 × 10⁷ + 6.724 × 10⁷ + 9.296 × 10⁷

⇒ Combined distance of Mercury, Venus, and Earth from the Sun = 21.8109 × 10⁷

⇒ Combined distance of Mercury, Venus, and Earth from the Sun = 2.18109 × 10⁸

Distance of Neptune from the Sun = 2.793 × 10⁹

Hence, we can see that the combined distance of Mercury, Venus and Earth from the Sun is less than that of Neptune from the Sun.

Part B - Question 3

If Earth was 10 times farther away from the sun, then the new distance between the Sun and the Earth = 10 × 9.296 × 10⁷

⇒ New distance between the Sun and the Earth = 9.296 × 10⁸

Now, the Earth will be closest to Saturn, which is 8.907 × 10⁸ away from the Sun

New Distance between Earth and Saturn = Distance of Earth from Sun - Distance of Saturn from Sun

⇒ New Distance between Earth and Saturn = 9.296 × 10⁸ - 8.907 × 10⁸

⇒ New Distance between Earth and Saturn = 0.389 × 10⁸

⇒ New Distance between Earth and Saturn = 3.89 × 10⁷ (in scientific notation)

⇒ New Distance between Earth and Saturn = 38,900,000 (in standard notation)

Part B - Question 4

Speed of space shuttle = 28,000 km per hour

Time spent to travel from Saturn to Earth = $\frac{\text{Distance between Saturn and Earth}}{\text{Speed of space shuttle} }$

⇒Time spent to travel from Saturn to Earth = $\frac{\text{Distance of Saturn from Sun - Distance of Earth from Sun}}{\text{Speed of space shuttle} }$

⇒Time spent to travel from Saturn to Earth = $\frac{8.907 * 10^8 - 9.296 * 10^7}{28,000}$

⇒Time spent to travel from Saturn to Earth = $\frac{797,740,000 }{28,000}$

⇒Time spent to travel from Saturn to Earth = 28,490.7 hours

⇒Time spent to travel from Saturn to Earth = 28,491 hours

Hence, it will take 28,491 hours or 2.8491 x 10⁵ hours for the space shuttle to travel from Saturn to Earth.

What are the distances of the planets from the sun

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