Now that the satellite has been launched (i.e. Ch. 12 Lab), Earth is hopeful to get...

Now that the satellite has been launched (i.e. Ch. 12 Lab), Earth is hopeful to get a more reliable eye on space anomalies. Shortly after the satellite's course around Jupiter, communication started to get more and more sporadic and weaker in signal. To counter this, a new satellite dish will be designed, specifically targeting the new satellite. Satellite dishes follow the shape of a paraboloid. The equation of a paraboloid is as follows: z=x^2/a^2+y^2/b^2 Where a and b could be the same number (depending on the desired shape). When you are designing this dish, where should you place the receiver? The receiver is like the ‘antenna’, receiving the data signals. Could the effectiveness of the receiver be changed if the ratio a/b is changed? A preliminary design is started with the dish’s circular radius of 20 feet, and a depth of 5 feet. What is the equation for this paraboloid? Hint: a = b, for this design. When the dish is a circular paraboloid (again a = b), a two-dimensional model could be viewed with the equation: x^2=4py , where p is the distance from the parabola's vertex to its focus. This equation can be revolved around the y-axis to form the shape of the satellite dish. Using the dimensions of the dish in #2, find the equation of the parabola in two-dimensions. Where should the receiver be placed? If the graph is revolved around the y-axis, what is the surface area of the satellite dish? From #3, find the cost of the dish itself when the material to make the dish costs $1,500 per square foot (it is a high quality satellite dish!). Many satellite dishes today are elliptic paraboloids (now a ≠ b), for reasons of reducing interference. But, would this change of shape also change where to place the receiver? Let’s use a satellite dish which has a 20-foot radius in the x-direction, and has a 10-foot radius in the y-direction. If a single receiver is placed at 10 feet from the vertex, what must the depth be in the x-direction and y-direction, separately, in order that the signal is maximized? What would a function look like for the depth of the dish at any particular place on the rim? Is there any theoretical reason to use an elliptic paraboloid vs. a circular paraboloid? Explain your reasoning. Thank you.

Expert Solution

Do check with the answer which i have uploaded which gives answers for almost all questions asked.

genius_generous answered 2 years ago

A satellite which has a weight of 35000 N on the surface of the earth is...

A satellite which has a weight of 35000 N on the surface of the earth is moving in a circular orbit around the earth. The radius of the orbit is 2R where R approx 6,400 km is the radius of the earth. Derive and find the period of the satellite from Newton’s second law. What is the angular momentum of the satellite as it orbits the earth? If we now desire to push the satellite into a higher orbit with a...

NASA has launched a mission to a newly discovered object, spherical in shape. A satellite is...

NASA has launched a mission to a newly discovered object, spherical in shape. A satellite is given a gravitationally driven circular orbit around the object. The altitude of the satellite in its orbit is equal to the radius of the object, and it takes 19.4 × 103 ??? for the satellite to complete one orbit. At the same time, a rover lands on the surface of the object. NASA engineers notice one of the support arms on it is broken...

A satellite moves in a circular earth orbit that has a radius of 7.49 x 106...

A satellite moves in a circular earth orbit that has a radius of 7.49 x 106 m. A model airplane is flying on a 24.1-m guideline in a horizontal circle. The guideline is nearly parallel to the ground. Find the speed of the plane such that the plane and the satellite have the same centripetal acceleration.

1. The parking orbit of an Earth satellite has apogee and perigee altitudes of 850 km...

1. The parking orbit of an Earth satellite has apogee and perigee altitudes of 850 km and 250 km, respectively (this orbit is sometimes referred to as an 850 km x 250 km orbit). (a) Determine the delta v required to circularize the orbit using a single-impulse burn at perigee. What is the period of the resulting circular orbit? Sketch the two orbits, indicating the point where the impulsive burn occurs. (b) Determine the delta v required to circularize the...

Calculate at what distance from the centre a satellite has to orbit Earth (of mass 6...

Calculate at what distance from the centre a satellite has to orbit Earth (of mass 6 x 10 24 kg) if it period or revolution is to equal Earth’s rotation period of 23h 56m (about 86, 160 seconds.) What is important about such a satellite? c) The mass of the moon is 81 times smaller (7.4074x 10 22 kg) and the period of orbit is 27.3 days. (Convert using 86, 400 sec = 1 day.) What should the radius of...

Dr. Strangelove has created a device that predicts whether or not a missile has been launched....

Dr. Strangelove has created a device that predicts whether or not a missile has been launched. Given that a missile has been launched, the device will correctly report that a missile has been launched 95 percent of the time. Given that a missile has not been launched, there is a 2 percent chance that the device will incorrectly report that a missile has been launched. There is a 1 percent chance that a missile will be launched. What is the...

Now that the turkey has been in the oven for quite some time, it is now...

Now that the turkey has been in the oven for quite some time, it is now time to get the gravy ready. First, you will need to put a circular aluminum sauce pan with a 12-cm diameter and a thickness of 8-mm on the stovetop and turn on the burner. Now you 120-gram mix the gravy contents with 360-grams of water. Assume that the latent heat of evaporation for gravy is similar to that of water, which is ?v=2260 KJ/Kg...

A spherical satellite has 12 identical monopropellant thrust chambers for attitude control with the following performance...

A spherical satellite has 12 identical monopropellant thrust chambers for attitude control with the following performance characteristics: thrust (each unit): 5 lbf; Is (steady state or more than 2 sec): 240 sec; Is (pulsing duration 20 msec): 150 sec; Is (pulsing duration 100 msec): 200 sec; satellite weight: 3500 lbf; satellite diameter: 8 ft; satellite internal density distribution is essentially uniform; disturbing torques, Y and Z axes: 0.00005 ft-lbf average; disturbing torque, for X axis: 0.001 ft-lbf average; distance between...

It has been said that biodiversity (or the loss of biodiversity, i.e. the loss of a...

It has been said that biodiversity (or the loss of biodiversity, i.e. the loss of a species to extinction) is the most important issue that humans face. The argument goes something like this: we can change our population growth rates (if we want to)...we can fix acid rain, even global climate change, we can stop dumping wastes into rivers...but when we lose a species to extinction..... it is forever (there is no getting the species back). Since we are reading...

Thomas Friedman argues that the world has been flattened, i.e., the economic playing field has been...

Thomas Friedman argues that the world has been flattened, i.e., the economic playing field has been made more level to more people than ever before. On the other hand, academics like Richard Florida argue that the playing field is not level but highly uneven. Who, and what sector of the economy is Friedman really referring to? What are some of the ways that the world is and is not flat?

Question