Problem 1. Hohmann Transfer and Plane Changes. Geostationary orbits are circular with a period equal to...
Fantastic news! We've Found the answer you've been seeking!
Question:
Transcribed Image Text:
Problem 1. Hohmann Transfer and Plane Changes. Geostationary orbits are circular with a period equal to the length of a sidereal day (23 hr and 56 m), and an inclination of i = 0o. The minimum inclination that can be achieved for a spacecraft launched from the surface of the earth is equal to the latitude of the launch site. For American satellites, which are typically launched from Cape Canaveral (latitude = 28.50N), this means it is impossible to directly launch into an equatorial orbit i = 00. With this in mind, in order to send a spacecraft into a geostationary orbit from Florida, it is first launched into a circular Low Earth Orbit (LEO) with an altitude of 200 km and inclination i = 28.50. It then performs a series of orbital maneuvers to change the orbital plane and transfer to GEO. Consider the following four sets of possible maneuvers: I. A plane change burn is made to change the LEO orbit to a circular orbit with the same altitude but an inclination of i = 0o. In other words, the magnitude of v remains the same but its direction is changed. Now in the correct plane, the satellite is allowed to make one complete orbit, and then a Hohmann transfer is used to send the orbit out to GEO. II. In the original inclination of i = 28.50, a Hohmann transfer is performed to send the satellite to GEO. After the orbit has been circularized at GEO, the spacecraft is allowed to complete one orbit. A plane change is then performed to change the orbit to an inclination of i = 0o. III. At LEO, a plane change is implemented that simultaneously changes the inclination of the orbit to i = 0o and sets it on course for a Hohmann transfer in the new plane. In other words, both the magnitude and direction of v change. At GEO altitude, a burn is applied to circularize the orbit. IV. At LEO, a burn is applied to send the satellite on a Hohmann transfer in the same plane (i = 28.50). Once at GEO altitude, a burn is applied that simultaneously changes the inclination of the orbit to i = 0o and circularizes it. The first two maneuvers (I and II) require three burns (denoted 1, 2, and 3), and the maneuvers in the second set (III and IV) each require two burns (denoted 1 and 2). In all cases, let the initial circular orbit at LEO have a longitude of ascending nodes at 22 = 0o and assume the satellite has just enough fuel to complete the specified maneuvers. Problem 1. Hohmann Transfer and Plane Changes. Geostationary orbits are circular with a period equal to the length of a sidereal day (23 hr and 56 m), and an inclination of i = 0o. The minimum inclination that can be achieved for a spacecraft launched from the surface of the earth is equal to the latitude of the launch site. For American satellites, which are typically launched from Cape Canaveral (latitude = 28.50N), this means it is impossible to directly launch into an equatorial orbit i = 00. With this in mind, in order to send a spacecraft into a geostationary orbit from Florida, it is first launched into a circular Low Earth Orbit (LEO) with an altitude of 200 km and inclination i = 28.50. It then performs a series of orbital maneuvers to change the orbital plane and transfer to GEO. Consider the following four sets of possible maneuvers: I. A plane change burn is made to change the LEO orbit to a circular orbit with the same altitude but an inclination of i = 0o. In other words, the magnitude of v remains the same but its direction is changed. Now in the correct plane, the satellite is allowed to make one complete orbit, and then a Hohmann transfer is used to send the orbit out to GEO. II. In the original inclination of i = 28.50, a Hohmann transfer is performed to send the satellite to GEO. After the orbit has been circularized at GEO, the spacecraft is allowed to complete one orbit. A plane change is then performed to change the orbit to an inclination of i = 0o. III. At LEO, a plane change is implemented that simultaneously changes the inclination of the orbit to i = 0o and sets it on course for a Hohmann transfer in the new plane. In other words, both the magnitude and direction of v change. At GEO altitude, a burn is applied to circularize the orbit. IV. At LEO, a burn is applied to send the satellite on a Hohmann transfer in the same plane (i = 28.50). Once at GEO altitude, a burn is applied that simultaneously changes the inclination of the orbit to i = 0o and circularizes it. The first two maneuvers (I and II) require three burns (denoted 1, 2, and 3), and the maneuvers in the second set (III and IV) each require two burns (denoted 1 and 2). In all cases, let the initial circular orbit at LEO have a longitude of ascending nodes at 22 = 0o and assume the satellite has just enough fuel to complete the specified maneuvers.
Expert Answer:
Answer rating: 100% (QA)
To compare the four sets of possible maneuvers for sending a spacecraft into a geostationary orbit f... View the full answer
Related Book For
Essentials of Materials Science and Engineering
ISBN: 978-1111576851
3rd edition
Authors: Donald R. Askeland, Wendelin J. Wright
Posted Date:
Students also viewed these mechanical engineering questions
-
This case study on project evaluation is applicable for beginning courses in corporate finance or finance strategy. Two alternative investment options are available to evaluate. Challenges are...
-
Owner Shan Lo is considering franchising her Happy Wok restaurant concept. She believes people will pay $5 for a large bowl of noodles. Variable costs are $1.50 a bowl. Lo estimates monthly fixed...
-
Maritime Distributors created a $500 imprest petty cash fund. During the first month of use, the fund custodian authorized and signed petty cash tickets as shown below. Required Make general journal...
-
Using License Fees to Make Positive Profit: Suppose you own one of many identical pharmaceudical companies producing a particular drug x. A: Your production process has decreasing returns to scale...
-
Identify requirement categories.
-
Accounting Today identified the top accounting firms in 10 geographic regions across the United States. All 10 regions reported growth in 2013. the Southeast and Gulf Coast regions reported growth of...
-
Current Attempt in Progress The ledger of Cullumber, Inc. on March 31, 2027, includes the following selected accounts before adjusting entries. Debit Credit Prepaid Insurance $2,016 Supplies 2,100...
-
1. Should the chromatography serve to purify the sample? 2. Explain the formation of isomer Post-Lab Discussion/Analysis 1. Compare the TLC plates for the crude sample and the sample that was...
-
After estimating the model \(y=\beta_{1}+\beta_{2} x_{2}+\beta_{3} x_{3}+e\) with \(N=203\) observations, we obtain the following information: \(\sum_{i=1}^{N}\left(x_{i 2}-\bar{x}_{2}...
-
William Jones is evaluating three possible means of borrowing $1 million for one month: 1. Drawing down on a line of credit at 7.2% with a 1/2 percent commitment fee on the full amount with no...
-
Suppose a company has a current ratio of 2.5 times and a quick ratio of 1.5 times. If the companys current liabilities are h100 million, the amount of inventory is closest to: A. h50 million. B. h100...
-
An analyst gathered the following information about a company: If the company repurchases 1 million shares at the prevailing market price, the resulting book value per share will be closest to: A....
-
What do you know about the mathematical value of a project's future worth, relative to zero, under each of the following conditions? a. The present worth of the project is greater than 0. b. The...
-
II. Express the indicated variable in terms of the other variable/s. Show complete solutions. (2 points each) 1 Example: ==+ 1 f d d 1. F = C+32; C 2. y-y = m(x-x); x n 3. S = (2a + (n-1)d); d 4. A =...
-
A copper wire (density = 8.96 g/cm 3 ) has a diameter of 0.25 mm. If a sample of this copper wire has a mass of 22 g, how long is the wire?
-
We would like to produce an MgO-FeO ceramic that is 30 wt% solid at 2000 C. Determine the composition of the ceramic in wt%?
-
A cylindrical acetal polymer bar 20-cm-long and 1.5 cm in diameter is subjected to a vibrational load at a frequency of 500 vibrations per minute, with a load of 50 N. How many hours will the part...
-
Describe the relative tendencies of the following polymers to crystallize. Explain your answer. (a) Branched polyethylene versus linear polyethylene; (b) Polyethylene versus...
-
What is the main difference between a full-service and a limited-service supplier?
-
Discuss an ethical issue in marketing research that relates to each of the following stakeholders: (1) client, (2) the supplier, and (3) the respondent.
-
List two possible limitations when using social media for marketing research.
Study smarter with the SolutionInn App