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Chapter 6: Problem 797

The orbital speed of jupiter is (A) greater than the orbital speed of earth (B) less than the orbital speed of earth (C) equal to the orbital speed of earth (D) zero

Short Answer

Expert verified
The orbital speed of Jupiter (\(13,100 \, m/s\)) is less than the orbital speed of Earth (\(29,500 \, m/s\)). Therefore, the correct answer is (B) less than the orbital speed of Earth.

Step by step solution

01

Understand orbital speed

Orbital speed is the speed at which an object, in this case, a planet, moves in its orbit around another object, usually the Sun. The orbital speed depends on the mass of the object being orbited and the distance between the two objects.
02

Calculate Earth's orbital speed

The Earth's orbital speed can be found using the formula for the orbital speed of an object around another object, given by: \[v_{Earth} = \sqrt{\frac{G * M_{Sun}}{r_{Earth}}}\] Where: - \(v_{Earth}\) is the orbital speed of Earth - \(G\) is the gravitational constant (\(6.674 \times 10^{-11} \, N \cdot m^2/kg^2\)) - \(M_{Sun}\) is the mass of the Sun (\(1.989 \times 10^{30} \, kg\)) - \(r_{Earth}\) is the average distance from Earth to the Sun (about \(1.496 \times 10^{11}\, m\)) Plugging in the values and calculating Earth's orbital speed: \[v_{Earth} = \sqrt{\frac{6.674 \times 10^{-11} * 1.989 \times 10^{30}}{1.496 \times 10^{11}}} \approx 29,500 \, m/s\]
03

Calculate Jupiter's orbital speed

Similarly, we can find Jupiter's orbital speed using the same formula: \[v_{Jupiter} = \sqrt{\frac{G * M_{Sun}}{r_{Jupiter}}}\] Where: - \(v_{Jupiter}\) is the orbital speed of Jupiter - \(r_{Jupiter}\) is the average distance from Jupiter to the Sun (about \(7.785 \times 10^{11}\, m\)) Plugging in the values and calculating Jupiter's orbital speed: \[v_{Jupiter} = \sqrt{\frac{6.674 \times 10^{-11} * 1.989 \times 10^{30}}{7.785 \times 10^{11}}} \approx 13,100 \, m/s\]
04

Compare the orbital speeds of Earth and Jupiter

Now that we have calculated the orbital speeds of both Earth and Jupiter, we can compare them: - Earth's orbital speed: \(29,500 \, m/s\) - Jupiter's orbital speed: \(13,100 \, m/s\) As we can see, Jupiter's orbital speed is lower than Earth's. So, our answer is: (B) less than the orbital speed of earth

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