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What is the ratio of the sun's gravitational force on you to the earth's gravitational force on you?
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Ch 13: Newton's Theory of Gravity
Knight Calc5th EditionPhysics for Scientists and EngineersISBN: 9780137344796
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TOC.tableOfContents
- Ch 01: Concepts of Motion35
- Ch 02: Kinematics in One Dimension75
- Ch 03: Vectors and Coordinate Systems58
- Ch 04: Kinematics in Two Dimensions60
- Ch 05: Force and Motion23
- Ch 06: Dynamics I: Motion Along a Line53
- Ch 07: Newton's Third Law27
- Ch 08: Dynamics II: Motion in a Plane52
- Ch 09: Work and Kinetic Energy56
- Ch 10: Interactions and Potential Energy50
- Ch 11: Impulse and Momentum56
- Ch 12: Rotation of a Rigid Body71
- Ch 13: Newton's Theory of Gravity52
- Ch 14: Fluids and Elasticity44
- Ch 15: Oscillations55
- Ch 16: Traveling Waves37
- Ch 17: Superposition39
- Ch 18: A Macroscopic Description of Matter53
- Ch 19: Work, Heat, and the First Law of Thermodynamics60
- Ch 20: The Micro/Macro Connection53
- Ch 21: Heat Engines and Refrigerators34
- Ch 22: Electric Charges and Forces40
- Ch 23: The Electric Field39
- Ch 24: Gauss' Law32
- Ch 25: The Electric Potential63
- Ch 26: Potential and Field57
- Ch 27: Current and Resistance42
- Ch 28: Fundamentals of Circuits39
- Ch 29: The Magnetic Field47
- Ch 30: Electromagnetic Induction60
- Ch 31: Electromagnetic Fields and Waves32
- Ch 32: AC Circuits63
- Ch 33: Wave Optics32
- Ch 34: Ray Optics57
- Ch 35: Optical Instruments30
- Ch 36: Special Relativity38
- Ch 37: The Foundations of Modern Physics25
- Ch 38: Quantization49
- Ch 39: Wave Functions and Uncertainty31
- Ch 40: One-Dimensional Quantum Mechanics35
- Ch 41: Atomic Physics18
- Ch 42: Nuclear Physics27
Knight Calc5th EditionPhysics for Scientists and EngineersISBN: 9780137344796Non è quello che usi tu?Cambia libro di testo
Capitolo 13, Problema 4
The International Space Station orbits 300 km above the surface of the earth. What is the gravitational force on a 1.0 kg sphere inside the International Space Station?
Guida verificata passo dopo passo1
Step 1: Understand the problem. The gravitational force on the sphere is determined by Newton's law of universal gravitation, which states that the force between two masses is proportional to the product of their masses and inversely proportional to the square of the distance between their centers.
Step 2: Write down the formula for gravitational force: , where is the gravitational constant (), is the mass of the Earth, is the mass of the sphere, and is the distance between the center of the Earth and the sphere.
Step 3: Determine the values for the variables. The mass of the Earth is approximately . The radius of the Earth is approximately , and the sphere is located above the Earth's surface. Therefore, the total distance is , which must be converted to meters: .
Step 4: Substitute the values into the formula. Replace , , , and with their respective values: .
Step 5: Simplify the expression to calculate the gravitational force. Perform the arithmetic operations step by step, ensuring proper handling of exponents and units. The result will give the gravitational force in newtons (N).
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Gravitational Force
Gravitational force is the attractive force between two masses, described by Newton's law of universal gravitation. It states that the force is directly proportional to the product of the two masses and inversely proportional to the square of the distance between their centers. This force is what keeps objects in orbit, including the International Space Station (ISS) around the Earth.
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05:41
Gravitational Forces in 2D
Weightlessness in Orbit
Weightlessness, or microgravity, occurs when an object is in free fall, such as when the ISS orbits the Earth. Although gravity is still present, the ISS and everything inside it, including a 1.0 kg sphere, are falling towards Earth at the same rate, creating the sensation of weightlessness. This condition affects how gravitational force is perceived by objects inside the ISS.
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04:45Geosynchronous Orbits
Altitude and Gravitational Acceleration
Gravitational acceleration decreases with altitude, but it does not become zero. At 300 km above Earth's surface, the gravitational acceleration is approximately 9.1 m/s², compared to 9.81 m/s² at sea level. This reduction is important for calculating the gravitational force acting on objects in the ISS, as it directly influences the force experienced by the 1.0 kg sphere.
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07:32Weight Force & Gravitational Acceleration
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