Exploring God's Universe|
Newton's Laws and Gravitational Astronomy
Isaac Newton did much work to help us understand the starry sky and how to explore it mathematically. One of the foundational laws he formulated was that of Inertia, the force (momentum) it takes for an object to come up to speed. He said, that in the absence of any outside influence an object at rest tends to remain at rest, and an object in motion tends to remain in motion, in a straight line, and at a constant speed. This property of a heavenly body that resists a change in motion is called inertia.
Newton said, that his first law of inertia is true for bodies. if they are in outer space or on earth itself. This helps us realize that, once God has made a good working creation, he uses its principles for as many creations as He wants to.
First we want to measure the motion of an object like the moon or a planet, we measure its momentum which is the product of the mass and velocity of the object. The mathematical formula for that is:
momentum = mass x velocity
This same formula can also be expressed as
p = mv (p = momentum; m = mass; v = velocity)
We may realize right away that mass and velocity have themselves to be explained for us to use those parts of that formula. So let us explain mass and velocity now.
Speaking of the "mass" of an object we almost always think of its weight. However, there is an important distinction between weight and mass.
The weight of an object is the force of attraction between that object and the earth - or if we lived on the moon, the force between that object and the moon. So, we recognize that strictly speaking, the weight of an object depends on where it is located.
So, what is different with mass? Mass is defined as the particular property of a body that characterizes the actual amount of material of that body. That property, its total content of matter, depends in no way where it is located.
Example of the difference between weight and mass.
If a 150 lb man travels to the moon, he may weigh there only 25 lb, but he has not changed his mass. His bones and muscles are still just as compact and together on either place. Mass, therefore, is a measure of the total number of atomic particles that compose that body. If we change its shape, vaporize or freeze it, it will not change its mass. Scientists decided to define the mass of a body to be numerically equal to its weight at sea level on earth. For this reason a 10 lb lead weight weighs 10 lbs at sea level and nothing in space. but it has a mass of 10 lbs everywhere.
There is, however, a problem with what we just said. That problem is that we actually do not know the number of atomic particles composing that body. For this reason we use Newtons definition which says, that the mass of a body is that property of a body which gives it inertia, that means, the property that resists acceleration. - It is much harder to push a 300 lb man than it is to push a 150 lb man.
What we said so far leads us to explain another property of things all around us. We want to explain what density is for it is very important not to confuse the difference between mass, volume, and density.
Volume is simply a numerical figure of the physical space a body occupies. We use for that terms like cubic inch, cubic feet, gallon, liter, etc. - In short, volume is the size of an object. It has nothing to do with its mass.
Density is a numerical figure which tells us how much mass is contained in a given volume. The formula is set up as follows:
density = mass / volumeor like this
D = m / VThe units which express density are like the following:
pounds per cubic inch ................. lb / in3It can happen sometimes that density is given in relationship to the density of water which is 62 lb / ft3 or 1 gm / cm3. That is called the specific gravity of water. Iron has a specific gravity of 7.9 or a density of 7.9 gm / cm3.
So let us see if we have now all definitions available to calculate the momentum of a body.
Let us take a 100 kg weight that travels at 10 kilometers per hour. We use decimal categories for easier calculation in this example.
m= mass x velocity . . . . . Plugging in the numbers we get . . . . . m= 100 kg x 10 km / hourWow, what does that mean? It means that a 100 kg object traveling at 10 km/hour increases its effective weight up to 10 times its actual weight - which can cause much damage if it hits an object you need to remain intact.
Let us now calculate density.
D= mass x volumeLet us assume 1000 gms travel at 100 cm3
D= 1000 / 100 D= 10 gms/cm3Result: The density calculates out to be 10 grams per one cubic centimeter.
In this section we talk about what happens when the momentum of an object changes. When the momentum changes in the same direction that the object travels in, the calculation is easier. Factors which can change the momentum of an object include: a) the pull of the earth, b) air friction, c) ground friction, d) impact (like a bat in a baseball game), d) air pressure changes and e) the thrust of a rocket engine.
We can determine three ways which are able to change the momentum of a traveling object or body. Its velocity can change, or its mass, or both. Most the time the change takes place because of a change in velocity. Our mathematical formula then looks like this:
force = mass x accelerationWow, now we need to determine what acceleration is. It is a experimentally determined value which is described as the rate of change of velocity, its acceleration, is 32 ft/sec/sec.
Let us try a calculation using the `force' formula. Let us assume the mass is 1 lbs of something, and the acceleration is 32 ft.sec/sec.
force = 1 lbs x 32 ft/sec/sec
The answer is: 32 lb-ft/sec/sec. That is 32 poundals.
Of course we know in order to apply such a calculation to heavenly bodies, we must factor in more than what we considered so far because most heavenly bodies do not travel in a straight line, but in a sort of circle or close to a circle.
To make things easier, we say that to calculate force under these conditions requires the following formula:
centripetal force = (mass x velocity2)/radius
Let us use 1000 miles for the radius. Plugging in the numbers we get ...
centripetal force = 1 lb x (32 ft/sec/sec x 32 ft/sec/sec) / 1000 miles
Ok, we could go on and on and do a lot of calculations. However, we don't want to go that direction. We want to simply help us understand the great God we have come to believe in and how He holds everything together and gives us enough evidence that He does exist. We want to once more confirm the reasons for our faith as good as we can by simple means.
In order to do that we use mostly His Word to us and a little what we humans have learned over the ages that might help us along.
Calculating the volume of a sphere
This type of calculation helps us understand something about the planet we live on called the `earth.'
The formula for the volume of a school is:
Since the radius `r' of the earth is 6,371.221 km we have: (r cubed = ((258623514676.49) x 4 x 3.14 )/3 = 1,082,770,448,112.82; Hmm, that is - 1 quadrillion dadada cubic kilometers.
Calculating the height of a pyramid
Recently a pyramid was found at Saqqara, each side of which measures 22 meters with a 51° angle (alpha) for the incline. How high was the pyramid? (Drawing not to scale)
Calculation: To calculate the height of a pyramid we use a bit of trigonometry,
We obtain 11 meters (b) diagonally to the mid-point of the pyramid where it forms a right angle with its base. The angle at the top (t) would be
t = 180 - (51 + 90); t = 39°The height of the pyramid would,
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