Sub Points Support and Explain Once you have the main points in your essay on your outline, you can then add sub point under each of these. As you develop through the writing process, sub points build up, support and explain the main points in your essay subpoint (pl. subpoints) A point (proposition in a debate etc.) that forms part of a larger point. , Courtland L. Bovée, Contemporary Public Speaking. Each subpoint has a direct, specific relation to its major point, which you can make clear by the organizational method you choose for your subpoints Subsolar point definition is - the point on the surface of the earth or a planet at which the sun is at the zenith
Subpoints Meaning | Best 1 Definitions of Subpoints
By Dr. Kelso Last time, we worked through the process of calculating the ECI Earth-Centered Inertial coordinates of an observer's position on the Earth's surface, starting with the observer's latitude and longitude. Then, we used those coordinates to calculate look angles azimuth and elevation from the observer's position to an orbiting satellite.
The most difficult part of that process was in calculating the sidereal time, a quantity necessary to determines the Earth's orientation in inertial space, subpoints definition. In the process of performing those calculations, subpoints definition, however, we made one simplifying assumption: that the Earth is a sphere.
Unfortunately, subpoints definition, this assumption is not a good one. Ignoring the fact that the Earth's shape can more accurately be described as an oblate spheroid a flattened sphere can have a significant effect in certain types of satellite tracking applications. In this column, we will examine the implications of our initial assumption by modifying our calculations to allow for the Earth's flattening at the poles and then tackle the related problem of determining the sub-point of an orbiting satellite.
Let's start by looking at a cross-section of the Earth and defining some terms. Figure 1 is an exaggerated view of the cross-section of the Earth, subpoints definition. For an observer on the Earth's surface, we can define a couple of terms fairly easily. The first subpoints definition the local zenith. The local zenith direction is just a fancy way of saying "straight up, subpoints definition. On a sphere, this direction is always directly away from the Earth's center.
However, on an oblate spheroid, subpoints definition, this subpoints definition not the case since a line from the center of the Earth to the observer's position would not point to the local zenith except on the equator and at the poles. Since the local zenith direction depends upon the local horizon, let's take some time to better define it, as well.
The local horizon is a plane subpoints definition is tangent touching at a point to the Earth's surface at the observer's position. For our purposes, we will consider the local horizon to be the plane tangent to the reference spheroid. The term reference spheroid is used to define the oblate spheroid which 'best' defines the shape of the Earth. How 'best' is defined is a complicated process and depends upon whether the fit of the reference spheroid is regional or global.
We will use the reference spheroid defined in WGS World Geodetic System, for our standard, subpoints definition. In WGS, the Earth's equatorial radius, ais defined to be 6, The Earth's polar radius, bis related to the equatorial radius by something called the flattening, fwhere.
Using this value, the Earth's polar radius would be 6, The first real subpoints definition of using an oblate spheroid instead of a sphere to define the Earth's shape comes in determining the observer's latitude. On a sphere, latitude is defined as the angle between the line going from the center of the Earth to the observer and the Earth's equatorial plane.
However, on an oblate spheroid, geodetic latitude is the angle between the local zenith direction and the Earth's equatorial plane, subpoints definition.
Subpoints definition angle, φ, is the latitude used on maps; the angle formed by the observer's position, the Earth's center, and the equatorial plane is more properly referred to as the geocentric latitudeφ'.
The impact of this change is subpoints definition in order to calculate the observer's ECI position, we must determine the geocentric latitude from the geodetic latitude. Knowing the geocentric latitude, φ', we can then calculate the geocentric radius, subpoints definition, ρ, and from that calculate the z coordinate ρ sin φ' and the projection in the equatorial plane ρ cos φ', subpoints definition. Let's start by developing the relationship between φ and φ' since we'll usually be given φ.
that is, the normal to the tangent of the spheroid. Differentiating the equation of the ellipse. So, knowing the geodetic latitude and the flattening, we can now determine the subpoints definition latitude. Now, let's see how much of a difference results from using an oblate spheroid. Figure 2 plots the difference between geodetic and geocentric latitude as a function of geodetic latitude, subpoints definition. That's it? All that work and the maximum error is less than two-tenths of a degree?
It would hardly seem worth the effort to perform the calculation. But let's explore a little further. Using the example of calculating the ECI coordinates of 40° N geodetic latitude, 75° W longitude on October 01 at 9 h UTC, subpoints definition. Although close to our calculations assuming a spherical Earth, we find this simplification resulted in a position error of What we really want to know, however, is just how big an error will result when generating look angles to a satellite from an observer's position on the Earth's surface if we assume a spherical Earth.
From Figure 2, subpoints definition, we would expect to have the largest errors for observers around 45° N latitude, subpoints definition, so let's use a location near Minneapolis at 45° N latitude and 93° W longitude for our example. On a pass of the Mir space station over Minneapolis on November 18, Mir passed almost directly overhead. Calculating the look angles for both a spherical and oblate Earth yields the results shown in Table 1.
The pointing error produced by subpoints definition a spherical Earth is 3. For most applications, this error might not be significant. However, in applications involving tracking with high-gain, typically narrow-beamwidth, antennas, an error of 3 degrees can result in a loss of communications. So, now that we've completed the calculation of a satellite look angle for an oblate Earth, let's look at how to calculate the sub-point subpoints definition a satellite in Earth orbit.
We'll begin by examining the calculations for a spherical Earth first before looking at the case for an oblate Earth. First, let's be sure we understand what we're looking for. The subpoints definition sub-point is that point on the Earth's surface directly below the satellite. For the case of a spherical Earth, this point is the intersection of the line from the center of subpoints definition Earth to the satellite and the Earth's surface, as shown in Figure 3.
where θ g is the Greenwich Mean Sidereal Time GMST. The altitude subpoints definition the satellite would be, subpoints definition. As seen in Figure 4, the calculation for an oblate Earth is somewhat more complicated.
The first thing we notice is that our definition of satellite sub-point requires some refinement. The point on the Earth's surface directly below the satellite is not on a line joining the satellite and the center of the Earth. Instead, it is that point on the Earth's surface where the satellite would appear at the zenith. Calculating the longitude of the satellite's sub-point doesn't change. However, to calculate the geodetic latitude of the satellite sub-point, we'll want to begin by approximating φ with φ' as calculated above and letting for computational efficiency.
Then, we'll want to loop through the following calculations. until is within the desired tolerance. To compute the altitude of the satellite above the sub-point. Using our example of Mir passing over Minneapolis subpoints definition November 18 at 12 h 46 m UTC yields subpoints definition sub-point at And while we cannot solve for the sub-point directly, the number of iterations required is typically quite small, subpoints definition.
For this example, subpoints definition, the value of after the first iteration is 0, subpoints definition. Admittedly, some of the differences we've found may seem small, subpoints definition, but that will depend upon your tracking requirements.
And, since they are not that much more difficult to calculate, there is little reason not to use them. As always, subpoints definition, if you have questions or comments on this column, feel free to send me e-mail at TS. Kelso celestrak. com or write care of Satellite Times. Until next time, keep looking up!
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How to create a \
, time: 3:32Defining Main And Sub Points In An Essay
Sub Points Support and Explain Once you have the main points in your essay on your outline, you can then add sub point under each of these. As you develop through the writing process, sub points build up, support and explain the main points in your essay Subpoints meaning Plural form of subpoint Definition from Wiktionary, the free dictionary. Jump to navigation Jump to search. English [] Noun []. subpoints. plural of subpoint
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