1 answer

# 1. (Coding problem) Consider the satellite equations GMx (x2 + y2)3/2' GMY (x2 + y2)3/2" with...

###### Question:

1. (Coding problem) Consider the satellite equations GMx (x2 + y2)3/2' GMY (x2 + y2)3/2" with the initial condition x(0) = 0, x'(0) = v, y(0) = 20000m + R, y'(0) = 0, where G = 6.67408 x 10-11mºkg-15-2, M = 5.974 x 1024 kg, R= 6378.1 x 10°m. The initial condition is such that at time t = 0, the satellite is 20km above our head with a velocity v in the direction perpendicular to vertical. If the velocity v is too small, the satellite's orbit will crash onto the Earth (when (x2 + y2) falls below the Earth’s radius R). This problem is to numerically determine the minimal velocity v so that the satellite does not crash onto the Earth. (1) First, choose a large value of v = 10,000m/s, and use the Runge-Kutta-4 method to compute the solution to time t = 10 hours. Verity in this case that the distance of the satellite from the center of the Earth V (x2 + y2) is always larger than R. Choose your time step h carefully so that the solution at t = 10 hours has relative accuracy less than 10-6. Then plot your solution in the (x,y) plane. (2) Now, gradually decrease your velocity v, and for each v, check its full orbit to decide if it crashes onto the Earth or not. From this, determine the minimum velocity Vmin so that the satellite does not crash onto the Earth.

## Answers

#### Similar Solved Questions

1 answer
##### E and f please 14) (20) Does the presence of others affect people's willingness to assume...
e and f please 14) (20) Does the presence of others affect people's willingness to assume responsibility for the welfare of others? For example, does the presence of other people affect our reaction to potentially dangerous smoke seeping from a wall vent? To answer this question, a researcher me...
1 answer
##### 4· C and CO2 are kept at constant pressure at 1000 K. The following reaction takes...
4· C and CO2 are kept at constant pressure at 1000 K. The following reaction takes place and reaches equilibrium C(s) + CO2(g)-- 2CO(g) If Keq- 0.021, calculate the equilibrium concentration of CO if the concentration of CO2 was initially 0.012 M....
1 answer
1 answer
##### Below is a Eh-pH diagram for sulfur species (at 25C, 1bar). What is the stable species...
Below is a Eh-pH diagram for sulfur species (at 25C, 1bar). What is the stable species at Eh = 0.5 V and pH = 7? 1.0 HSO; SO- Eh (V) Hys -0.5 6 8 10 12 14 In acid mine drainage, oxidation of exposed pyrite leads to the leaching of sulfuric acid (HSO4) in the effluent. By looking at the Eh-pH diagram...
1 answer
##### Homework 1 Due October 8 (Monday , at the beginning of the class) Consider the data...
Homework 1 Due October 8 (Monday , at the beginning of the class) Consider the data below. r 0.91.31.92.12.63.0 3.94.4 4.75.06.0 f) 1.3 1.51.85 2.1 2.62.7 2.4 2.15 2.05 2.1 2.25 r 7.0 8.09.2 10.5 11.311.6 12.0 12.6 13.0 13.3 f(x) 2.3 2.25 1.95 1.4 0.90.70.6 0.5 0.4 0.25 Obtain a smooth curve by usin...
1 answer
##### 7. Of the ultraviolet transitions in the Bohr hydrogen atom, which transition results in the emission...
7. Of the ultraviolet transitions in the Bohr hydrogen atom, which transition results in the emission of photons with a wavelength of 97.3nm? Hint, the Rydberg equation may be helpful. Note that this transition is part of the Lyman series. 1,097x107...
1 answer
##### Marginal benefit Marginal social The table below shows information about the costs and benefits of a...
Marginal benefit Marginal social The table below shows information about the costs and benefits of a steel smelter that pollutes the air of a city. The marginal external cost of this pollution is \$10 per ton at every quantity of steel produced. Use this information to answer questions 33-35. Quantit...
1 answer
##### 1. It is known that has a Fversion of the test. Find the limt lim (Vx+&+1...
1. It is known that has a Fversion of the test. Find the limt lim (Vx+&+1 -2 +2 -1 ) Show your work in the PDF version of the best. Done 2 of 13 10:55 1 of 3 CO 2020 VIPadron...
1 answer
##### Dimentional Analysis 5) Water is dripping through a small hole in a bottom of a cyllindrical...
Dimentional Analysis 5) Water is dripping through a small hole in a bottom of a cyllindrical container with a diameter D [m]. Find the form of the relationship between the diameter of drops o [m] and the remaining parameters: - diameter of the hole d [m] - height of the water surface in the contain...
1 answer
##### A capacitor of 10 mF capacitance is being discharged through a resistor. It is observed that...
A capacitor of 10 mF capacitance is being discharged through a resistor. It is observed that the current in the circuit drops to 50% of its initial value in 12 seconds. Calculate the resitor's resistance....
1 answer
##### /portal/site/MAU 47 101 20 1 930/tool/30722679-ba57-42b-a52d-e7a32e4006cdjtidelivery/delnerAssessmentp1q4 When the supply of HDTVs increases, ceteris paribus, the equilibrium...
/portal/site/MAU 47 101 20 1 930/tool/30722679-ba57-42b-a52d-e7a32e4006cdjtidelivery/delnerAssessmentp1q4 When the supply of HDTVs increases, ceteris paribus, the equilibrium price will decrease because: O A. A shortage exists at the old equilibrium price. O B. A surplus exists at the old equilibri...
1 answer
##### Exercise: 1) Determine the rank of the following matrices -21 a) 2 3 5 2 -5...
Exercise: 1) Determine the rank of the following matrices -21 a) 2 3 5 2 -5 -8 -12 3 1 5 -1 2 2 6 rank=2 3 1 b) -4 7 -2 -3 -1 3 5 2 1 4 rank=3 5 9 c) 6 11 16 6 7 12 17 7 8 13 18 8 9 14 19. 2) Determine the value of P such that the rank of 0 1 -1 -3 2 P 4 P 9 is 3 4 2 9 2 3...
1 answer
##### Usi ng the method of (d) on p. 215, show that f (x) = 2x2 is...
Usi ng the method of (d) on p. 215, show that f (x) = 2x2 is integrable on to, is and soflolda = 3 that 3 and (d) Consider the function f(x) = x, x € (0,1). For n E N, let P, be the partition {0,1...,1}. Since ſ is increasing on [0, 1], its infimum and supremum on each interval ( 4.4) are ...
1 answer
##### 10. Part A. (9 pt) Fill in any necessary reagents or intermediates in the empty boxes...
10. Part A. (9 pt) Fill in any necessary reagents or intermediates in the empty boxes in the scheme below. 2) DMS 1) LAH 52) H30+ / H20 PCC/ CH2Cl2 W + En сон 1) OsO4 2) NaHSO3 /H20 + 3 other stereoisomers....
1 answer
##### 1. Why is a Thorpe tube flowmeter not used with an adjustable regulator?
1. Why is a Thorpe tube flowmeter not used with an adjustable regulator?...
1 answer
##### Following are four economic states, their likelihoods, and the potential returns. Economic States Probability Return Fast...
Following are four economic states, their likelihoods, and the potential returns. Economic States Probability Return Fast Growth 0.33 56% Slow Growth 0.42 15% Recession 0.15 -12% Depression    0.10 -42% Calculate the expected return and Standard Deviation (round answers to two decimal plac...
1 answer
##### MİNDTAP Homework (Ch 02) Artempts Do No Harm:13 2. The circular-flow model The following diagram presents...
MİNDTAP Homework (Ch 02) Artempts Do No Harm:13 2. The circular-flow model The following diagram presents a circular-fow model of a simple economy. The outer set of arrows (shown in green) shows the flow of dolars, and the nner set of errows (shown in red) shows the corresponding flow of inputs...