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 determine k. If t 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= 6.255-10 x d²r dr² = k R² X satellite of mass m surface
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 determine k. If t 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= 6.255-10 x d²r dr² = k R² X satellite of mass m surface
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Transcribed Image Text: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 = 6.255.107
d²r
dt²
k
R²
X
satellite of
mass m
surface
R
Earth of mass M
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