List the fundamental hypotheses of the Newtonian theory of universal gravitation and the experimental consequences. Which of the hypotheses is not directly confirmable by experiment
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List the fundamental hypotheses of the Newtonian theory of universal gravitation and the experimental consequences. Which of the hypotheses is not directly confirmable by experiment (although its consequences are)?
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- In the law of universal gravitation, Newton assumed that the force was proportional to the product of the two masses (m1m2) . While all scientific conjectures must be experimentally verified, can you provided arguments as to why this must be? (You may wish to consider simple examples in which any other form would lead to contradictory results.)You may have an image of Sir Isaac Newton sitting under a tree and after being hit on the head by an apple he suddenly "discovered" the Law of Universal Gravitation. In fact, the theory was a result of years’ worth of research, which in turn was based on centuries of accumulated knowledge. He is credited with determining that the following relationship is universal. The gravitational attraction between two objects varies jointly with their masses (m1 and m2) and inversely with the square of the distance (d) between them. By what percent does the force of gravitational attraction change if one mass is increased by 20%, the other mass decreased by 20%, and the separation is reduced by 25%?Which of the following statements is INCORRECT about the Law of Universal Gravitation? The gravitational force exerted by Earth on any object increases with the square of the object's distance from Earth's center. Henry Cavendish was the first to measure the value of universal gravitational constant, G. The magnitude of the due to gravity must be proportional to the masses of the two objects. Any object in the universe that has mass can exert a gravitational force on another object.
- In the law of universal gravitation, Newton assumed that the force was proportional to the product of the two masses (~m1m2). While all scientific inferences must be experimentally verified, can you provide arguments as to why this must be correct?Newton’s law of universal gravitation states that every object exerts a gravitational force on every other object in the universe. (a) Estimate magnitude of the gravitational force that the person sitting next to you in class exerts on your body, in units of Newtons. (b) Given your previous answer, what is the gravitational force that you exert on the person sitting next to you? (c) Compare your previous answers to your weight (the force of gravity the Earth exerts on you).You are a scientist exploring a mysterious planet. You have performed measurements and know the following things: The planet has radius d. It is orbiting his star in a circular orbit of radius b. it takes time T to complete one orbit around the star. the free-fall acceleration on the surface of the planet is a. Derive an expression for the mass and of the star in terms of b,T, and G the universal gravitational constant.
- Question: Albeit a simulation, this experiment has provided an opportunity for you to empirically determine the value of the Universal Gravitational constant G = 6.67 x 10-11 N kg2/m² on the Earth. How does the value of G vary in distant parts of the solar system, galaxy, even outside the Milky Way Galaxy? You might make a quick study of "Newton's law of universal gravitation" to answer this question.You are to solve this problem using only the tools of dimensional analysis. You are not expected to know anything about gravitation. Do not use any equations about gravity! They won't help you, anyway. Use only dimensional analysis. This problem involves estimation, but do not guess. Neatly work out your solution using dimensional analysis. You will be asked to upload your work in the next problem. Newton's Law of Gravitation tells us that any two objects attract each other by pulling each other with a gravitational force. In principle, any two objects far out in space (far from other objects) should attract each other and come together using only their gravitational attraction, but how long would this take? Newton's gravitational constant is G = 6.67 x 10-11 (m2)/(s2 kg) That says G = 6.67 x 1011 (m2)/(s² kg) (Notice that the denominator is "seconds squared" times "kg") Imagine two astronauts far out in space, very far from other objects (the picture above shows the Earth in the…a met icle an he $ 4 R ▼ 888 F4 Part A Consider a uniform gravitational field (a fair approximation near the surface of a planet). Find U(y)-U(yo)= Fg. ds. where F₁ = -mg j and ds = dy j. Express your answer in terms of m, g, yo, and yf. View Available Hint(s) IVD ΑΣΦ ? U(yf) - U (yo) = Submit Part B Consider the force exerted by a spring that obeys Hooke's law. Find II(₂) II(-). APR tv 28 % 5 F5 T 6 F6 Y & 7 F7 U * 8 ²² de DII F8 ( 9 A DD F9 0 ) O 3 of 26 Review | Constants F10 P I
- By Newton's universal law of gravitation the free-fall acceleration a of a body, such as the satellite shown in the figure, falling a great distance to the surface is not the constant g. Rather, the acceleration a is inversely proportional to the square of the distance from the center of the Earth, a = k/r2, where k is the constant of proportionality. Use the fact that at the surface of the Earth r = R and a = g to determine k. If the positive direction is upward, use Newton's second law and his universal law of gravitation to find a differential equation for the distance r. k = d?r dt2 satellite of mass m surface Earth of mass MYou are a scientist exploring a mysterious planet. You have performed measurements and know the following things: The planet has radius d. It is orbiting his star in a circular orbit of radius b. it takes time T to complete one orbit around the star. the free-fall acceleration on the surface of the planet is a. Derive an expression for the mass Mp of the planet in terms of a,d, G the universal gravitational constant. Assume that the gravitational effect of the star at the planet's surface is negligible.The mass of Mars is M = 6,42 · 1023 kg, and its radius is R = 3396 km.a) Determine the gravitational acceleration on the surface of Mars.b) How high can an astronaut jump on Mars and how high on Earth if in both caseshe leaves the ground with a starting speed v0 = 1 m/s?The value of the gravitational constant is G = 6,67 · 10−11 m3 kg−1s−2.