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A spacecraft flies toward an asteroid whose trajectory threatens to impact the Earth. The spacecraft's weight on earth is 20,000 lb, and it flies with its center of gravity 160 ft from the asteroid's surface. The asteroid is a homogeneous pure iron of specific weight y = 491 lb/ft³ and has a 1290 ft diameter (assumed spherical) shape. (a) Convert all of the given physical quantities to SI units. Show your work and avoid online unit conversion calculators. (b) Determine the force of gravitational attraction (in Newtons) between the two bodies by treating the spacecraft as a particle. useful conversions: 1 lb = 4.448 N, 1 ft = 0.3048 m

A spacecraft flies toward an asteroid whose trajectory threatens to impact the Earth. The spacecraft's weight on earth is 20,000 lb, and it flies with its center of gravity 160 ft from the asteroid's surface. The asteroid is a homogeneous pure iron of specific weight y = 491 lb/ft³ and has a 1290 ft diameter (assumed spherical) shape. (a) Convert all of the given physical quantities to SI units. Show your work and avoid online unit conversion calculators. (b) Determine the force of gravitational attraction (in Newtons) between the two bodies by treating the spacecraft as a particle. useful conversions: 1 lb = 4.448 N, 1 ft = 0.3048 m

Elements Of Electromagnetics
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
Problem 1.1MA
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**Problem Statement:** A spacecraft flies toward an asteroid whose trajectory threatens to impact the Earth. The spacecraft’s weight on earth is 20,000 lb, and it flies with its center of gravity 160 ft from the asteroid’s surface. The asteroid is a homogeneous pure iron of specific weight \( \gamma = 491 \, \text{lb/ft}^3 \) and has a 1290 ft diameter (assumed spherical) shape. **Tasks:** (a) Convert all of the given physical quantities to SI units. Show your work and avoid online unit conversion calculators. (b) Determine the force of gravitational attraction (in Newtons) between the two bodies by treating the spacecraft as a particle. **Useful Conversions:** - \(1 \, \text{lb} = 4.448 \, \text{N}\) - \(1 \, \text{ft} = 0.3048 \, \text{m}\) **Diagram Explanation:** The image shows a spacecraft nearing a rocky asteroid in space. The asteroid appears large and irregularly shaped, suggesting its potentially hazardous trajectory towards Earth. The spacecraft, much smaller in comparison, is equipped with solar panels and positioned at a set distance from the asteroid, as referenced in the problem statement.
Transcribed Image Text:**Problem Statement:** A spacecraft flies toward an asteroid whose trajectory threatens to impact the Earth. The spacecraft’s weight on earth is 20,000 lb, and it flies with its center of gravity 160 ft from the asteroid’s surface. The asteroid is a homogeneous pure iron of specific weight \( \gamma = 491 \, \text{lb/ft}^3 \) and has a 1290 ft diameter (assumed spherical) shape. **Tasks:** (a) Convert all of the given physical quantities to SI units. Show your work and avoid online unit conversion calculators. (b) Determine the force of gravitational attraction (in Newtons) between the two bodies by treating the spacecraft as a particle. **Useful Conversions:** - \(1 \, \text{lb} = 4.448 \, \text{N}\) - \(1 \, \text{ft} = 0.3048 \, \text{m}\) **Diagram Explanation:** The image shows a spacecraft nearing a rocky asteroid in space. The asteroid appears large and irregularly shaped, suggesting its potentially hazardous trajectory towards Earth. The spacecraft, much smaller in comparison, is equipped with solar panels and positioned at a set distance from the asteroid, as referenced in the problem statement.
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