Spatial velocity is simply the rate of surface change over time, so more careful and detailed looks at scientific practice have led us to realize that context plays a critical role in many explanations and that it is sometimes useful to think of explanations as answers to certain types of questions [Garfinkel, 1981]. Questions and their answers have an inevitable contextual component. When I ask, « Why did Adam eat the apple? » the question is ambiguous until I give the relevant contrast classes. Do I want to know why Adam and not Eve ate the apple? Do I want to know what Adam ate the apple instead of throwing it away? And so on. In addition, the basic knowledge of scientists looking for explanations determines what general information is relevant. For example, in physics before the advent of quantum mechanics, no response involving remote action would be considered relevant. If you stay clear about these contextual elements, you may find a more nuanced approach to the explanation, and we`ll see below that this can help clear up some standard confusions. Using Tycho Brahe`s precise data, Johannes Kepler carefully analyzed the positions of all known planets and the moon in the sky and recorded their positions at regular intervals. Based on this analysis, he formulated three statutes, which we will discuss in this section. In general, several tracking stations should be spread across the Earth so that satellite control and constellation information gathering can take place at any time. Caution should be exercised when calculating satellite orbits, as there are at least two different reference systems: the RA system, which indicates the satellite`s position r, and the conventional Earth system, used by positioning stations with the vector position R(φ, λ, h). We can calculate the topocentric region as The prevailing opinion in Kepler`s time was that all planetary orbits were circular. The data for Mars posed the greatest challenge to this view and ultimately encouraged Kepler to abandon the popular idea.
Kepler`s first law states that each planet moves along an ellipse, with the sun in a focus of the ellipse. An ellipse is defined as the set of all points such that the sum of the distance from each point to two foci is a constant. Figure 13.16 shows an ellipse and describes an easy way to create it. Since Fgrav = Fnet, the above expressions are the same for centripetal force and gravitational force. Thus, 2. Galileo is often credited with the early discovery of four of Jupiter`s many moons. Moons orbiting Jupiter follow the same laws of motion as planets orbiting the sun. One of the moons is called Io – its distance from Jupiter`s center is 4.2 units and orbits Jupiter in 1.8 Earth days. Another moon is called Ganymede; it is 10.7 units from the center of Jupiter.
Make a prediction of the Ganymede period using Kepler`s law of harmonies. The areas scanned by the sun vector to a planet are proportional to the time it takes to cover/overlap them. When a planet moves in orbit around the sun, the areas scanned by the planet are the same for equal time intervals. According to Kepler`s laws of planetary motion (see sections 2-4) of an ellipse, equal surfaces are swept at any point on the ellipse at the same time. As a circle is a special case of ellipse, this also applies to circular motion. The Sun is at the center of a circle and at the position of a focal point of an ellipse, as shown in Figure 3-16.6. First, consider the circular orbit. It should be obvious that for uniform motion along the circular trajectory, all areas scanned during a time interval are equal in size and shape, as indicated by the triangle filled with red. In the case of the ellipse, the surface A1 is equal to the surface A2, but the shapes of the surfaces are different. Since the distance from the Sun to the ellipse is closer for A1 than from the Sun to the ellipse for A2, it necessarily follows that the distance traveled along the trajectory is longer for A1 than for A2. In other words, for a complete orbit crossing, the Earth will spend more time farther from the Sun in the A2 region of the ellipse than in the A1 region.
