Loose Leaf For Explorations:  Introduction To Astronomy
Loose Leaf For Explorations: Introduction To Astronomy
9th Edition
ISBN: 9781260432145
Author: Thomas T Arny, Stephen E Schneider Professor
Publisher: McGraw-Hill Education
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Chapter 3, Problem 3TY
To determine

The contribution of Newton’s work in Kepler’s laws.

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Newton's Law of Gravitation 2. The magnitude of the acceleration of an object under the pull of Earth's gravity is given by Newton's Universal Law of Gravitation МЕ a = G R? where G is the universal gravitational constant, ME is the mass of Earth, and R is the distance of the object from the center of Earth. Let x be the distance above Earth's surface. We can rewrite the formula for the acceleration as a function of x by noting that R = Rp + x, where Rp is the radius of Earth. Therefore, МЕ a(x) = G- (RE + x)2 d. (a) Show that dx 1 1 (1 – x)* - x. (b) Use the above fact, along with the power series of 1 to determine a power 1- x 1 series for (1+x)²* (c) What is the radius of convergence for the series in part (b)? (Hint: You do not need to calculate anything. What is the radius of convergence for the power series of 1 does not change the radius of convergence.) -? This series has the same radius of convergence since taking a derivative
Describe three propositions, now known as Kepler’s laws of planetary motion?
Gravitational Forces (A) Gravitational, Electrical, Magnetic, and Nuclear Forces Math Connections Gm The surface gravity, g, on a planet can be calculated using the formula: g = , where • G = Gravity = 6.673×10-11 N • m² kg • m = mass in kg • r= radius in m Characteristics of the Planets Planet Mass (kg) Radius (m) Surface Gravity (m/s?) Mercury 3.30 х 1023 2,440,000 3.70 Venus 4.87 x 1024 6,051,000 Earth 5.97 х 1024 9.79 Mars 6.42 x 1023 3,397,000 Jupiter 1.90 x 1027 71,492,000 Saturn 5.69 x 1026 10.45 Uranus 8.66 x 1025 25,559,000 8.84 Neptune 1.03 х 1026 24,764,000 Use the table above to answer the following questions. Insert your answers into the spaces in the table. 9. Calculate the surface gravity on the following planets: (6.673x10-")(4.87×10²4)_ a) Venus g= 6,051, 000 (6.673×10"")(1.90 ×10") 71, 492, 000 b) Jupiter g= %3D c) Neptune (6.673×10-")(1.03×10%) g= 24, 764, 000 (6.673×10 ")(6.42 ×10") g= d) Mars 3, 397,000 Gm 10. Calculate the radius of each of the following planets…
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