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CONTENTS
 

Introduction

Fermi's Piano Tuner Problem

How Old is Old?

If the Terrestrial Poles were to Melt...

Sunlight Exerts Pressure

Falling Eastward

What if an Asteroid Hit the Earth

Using a Jeep to Estimate the Energy in Gasoline

How do Police Radars really work?

How "Fast" is the Speed of Light?

How Long is a Light Year?

How Big is a Trillion?

"Seeing" the Earth, Moon, and Sun to Scale

Of Stars and Drops of Water

If I Were to Build a Model of the Cosmos...

A Number Trick

Designing a High Altitude Balloon

Pressure in the Vicinity of a Lunar Astronaut Space Suit due to Outgassing of Coolant Water

Calendar Calculations

Telling Time by the Stars - Sidereal Time

Fields, an Heuristic Approach

The Irrationality of

The Irrationality of

The Number (i)i

Estimating the Temperature of a Flat Plate in Low Earth Orbit

Proving that (p)1/n is Irrational when p is a Prime and n>1

The Transcendentality of

Ideal Gases under Constant Volume, Constant Pressure, Constant Temperature and Adiabatic Conditions

Maxwell's Equations: The Vector and Scalar Potentials

A Possible Scalar Term Describing Energy Density in the Gravitational Field

A Proposed Relativistic, Thermodynamic Four-Vector

Motivational Argument for the Expression-eix=cosx+isinx

Another Motivational Argument for the Expression-eix=cosx+isinx
Calculating the Energy from Sunlight over a 12 hour period
Calculating the Energy from Sunlight over actual full day
Perfect Numbers-A Case Study
Gravitation Inside a Uniform Hollow Sphere
Further note on Gravitation Inside a Uniform Hollow Sphere
Pythagorean Triples
Black Holes and Point Set Topology
Additional Notes on Black Holes and Point Set Topology
Field Equations and Equations of Motion (General Relativity)
The observer in modern physics
A Note on the Centrifugal and Coriolis Accelerations as Pseudo Accelerations - PDF File
On Expansion of the Universe - PDF File
 

Falling Eastward

This page is under review.

Problem:
Let a test object be at an initial height h, small enough that the variation in the value of g (= 9.807 m/sec2) may be ignored. Calculate the eastward deflection due to the Coriolis effect if the object is allowed to free-fall from an initial state of rest to the earth's surface.

Solution:
Let omega = earth's angular velocity due to rotation. Then, omega(cos l) is the component of the angular velocity tangent to the earth's surface at latitude l, and is the component of concern to this problem since it is perpendicular to the plane of the test object's motion6. The Coriolis acceleration due to this component of angular velocity is

2 vomega (cos l)
1.

and is directed eastward. The term v is the velocity of the falling test object as a function of time. If the eastward deflection is assumed sufficiently small compared to h, we may approximate v and h as

v = gt
2.
and
h = (1/2) gt2
3.

Substituting 2. into 1. gives for the Coriolis acceleration

2 gt omega(cos l)
4.

Integrating once give the eastward velocity as a function of time

vE = gt2 omega (cos l)
5.

Integrating a second time gives the required deflection

xE = (1/3) gt3 omega (cos l)
6.

Using 3., t3 = (2h/g)3/2, so that for the entire fall from height h,

xE = (2h)3/2 g-1/2 omega (cos l)
7.

Let us now assume that the initial height h = 100 m, and l = 42 deg. With omega = 7.27 x 10-7 /sec, we find that at the moment of impact,

t = 4.52 sec
v = 44.3 m/sec
vE = 1.08 x 10-4 m/sec
xE = 1.63 x 10-4 m = .16 mm

Comparing vE and v, we also see that the deviation of the velocity from the vertical is

arctan (1.08 x 10-4/44.3) = 1.4 x 10-4 deg.

With h = 1000 m, l = 42 deg, we find

t = 14.3 sec
v = 140 m/sec
vE = 1.08 x 10-3 m/sec
xE = 5.16 x 10-3 m = 5.16 mm
with arctan (1.08 x 10-3/140) = 4.4 x 10-4 deg.

 


6. The deviation of the test object's velocity vector from the vertical is assumed small enough to be ignored; hence, its cross product with the vertical component of the earth's angular velocity is also small enough to be ignored.

Please send suggestions/corrections to:
Web Related: David.Mazza@grc.nasa.gov
Technology Related: Joseph.C.Kolecki@grc.nasa.gov
Responsible NASA Official: Theresa.M.Scott (Acting)