7. Isaac Newton was the first person to correctly explain the twice-daily occurence of high and low tides. This happens because gravity is a force that depends on distance. Thus, the part of the Earth closest to the Moon (position 1 in Fig. 1) feels a stronger pull than the diametrically opposite part (position 2) which is the farthest from the Moon. The magnitude of the gravitational force between any two masses is given by where a is a constant that contains the two masses and d is the distance between the object feeling the force and the centre of the object exerting the force. Let R be distance from the centre of the Moon to the centre of the Earth and Rg be the radius of the Earth (see Fig. 1). Compute the tidal force using Fide 0 2. where 1,2 are the positions described above (red dots in the figure). To do this, let ar represent RE/R which is much smaller than 1 since R << R. Then using the Maclaurin series for d2 and d₂2 in Eq. (1) obtain the first non-zero term for the Fride as a series in a multiplied by constants. Finally, substitute x = RE/R into your expression to find that the tidal force depends on the inverse of the cube of R. RE 1 F1-F20 • (-a) R Figure 1: The Earth-Moon system (not to scale). Rg is the radius of the Earth and R is the Earth-Moon distance measured from the centres.
7. Isaac Newton was the first person to correctly explain the twice-daily occurence of high and low tides. This happens because gravity is a force that depends on distance. Thus, the part of the Earth closest to the Moon (position 1 in Fig. 1) feels a stronger pull than the diametrically opposite part (position 2) which is the farthest from the Moon. The magnitude of the gravitational force between any two masses is given by where a is a constant that contains the two masses and d is the distance between the object feeling the force and the centre of the object exerting the force. Let R be distance from the centre of the Moon to the centre of the Earth and Rg be the radius of the Earth (see Fig. 1). Compute the tidal force using Fide 0 2. where 1,2 are the positions described above (red dots in the figure). To do this, let ar represent RE/R which is much smaller than 1 since R << R. Then using the Maclaurin series for d2 and d₂2 in Eq. (1) obtain the first non-zero term for the Fride as a series in a multiplied by constants. Finally, substitute x = RE/R into your expression to find that the tidal force depends on the inverse of the cube of R. RE 1 F1-F20 • (-a) R Figure 1: The Earth-Moon system (not to scale). Rg is the radius of the Earth and R is the Earth-Moon distance measured from the centres.
College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
Section: Chapter Questions
Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
Related questions
Topic Video
Question
Transcribed Image Text:7. Isaac Newton was the first person to correctly explain the twice-daily occurence
of high and low tides. This happens because gravity is a force that depends on
distance. Thus, the part of the Earth closest to the Moon (position 1 in Fig. 1)
feels a stronger pull than the diametrically opposite part (position 2) which is the
farthest from the Moon. The magnitude of the gravitational force between any
two masses is given by
where a is a constant that contains the two masses and d is the distance between
the object feeling the force and the centre of the object exerting the force. Let R
be distance from the centre of the Moon to the centre of the Earth and RE be
the radius of the Earth (see Fig. 1). Compute the tidal force using
α
d²
2.
RE
Ftide=Fg,1Fg,2 = a
where 1,2 are the positions described above (red dots in the figure). To do this,
let a represent RE/R which is much smaller than 1 since RE < R. Then using
the Maclaurin series for d2 and d₂2 in Eq. (1) obtain the first non-zero term for
the Ftide as a series in a multiplied by constants. Finally, substitute x =
RE/R
into your expression to find that the tidal force depends on the inverse of the cube
of R.
1
1
(-2)
R
Figure 1: The Earth-Moon system (not to scale). RE is the radius of the Earth and R
is the Earth-Moon distance measured from the centres.
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 3 steps
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, physics and related others by exploring similar questions and additional content below.Recommended textbooks for you
College Physics
Physics
ISBN:
9781305952300
Author:
Raymond A. Serway, Chris Vuille
Publisher:
Cengage Learning
University Physics (14th Edition)
Physics
ISBN:
9780133969290
Author:
Hugh D. Young, Roger A. Freedman
Publisher:
PEARSON
Introduction To Quantum Mechanics
Physics
ISBN:
9781107189638
Author:
Griffiths, David J., Schroeter, Darrell F.
Publisher:
Cambridge University Press
College Physics
Physics
ISBN:
9781305952300
Author:
Raymond A. Serway, Chris Vuille
Publisher:
Cengage Learning
University Physics (14th Edition)
Physics
ISBN:
9780133969290
Author:
Hugh D. Young, Roger A. Freedman
Publisher:
PEARSON
Introduction To Quantum Mechanics
Physics
ISBN:
9781107189638
Author:
Griffiths, David J., Schroeter, Darrell F.
Publisher:
Cambridge University Press
Physics for Scientists and Engineers
Physics
ISBN:
9781337553278
Author:
Raymond A. Serway, John W. Jewett
Publisher:
Cengage Learning
Lecture- Tutorials for Introductory Astronomy
Physics
ISBN:
9780321820464
Author:
Edward E. Prather, Tim P. Slater, Jeff P. Adams, Gina Brissenden
Publisher:
Addison-Wesley
College Physics: A Strategic Approach (4th Editio…
Physics
ISBN:
9780134609034
Author:
Randall D. Knight (Professor Emeritus), Brian Jones, Stuart Field
Publisher:
PEARSON