- 3008 - MATH - shuttle to the Moon? - Does the Space Shuttle have the payload capacity to carry enough extra fuel for this one-way trip? No, the Shuttle does not have enough capacity to lift all of the required fuel to Earth orbit. Here is why that is true:
-------------------------- 3008 - MATH - shuttle to the Moon?
- Near Earth orbits, what do we mean? We can think of successive orbits at increasing distance from Earth as representing a ladder. A spacecraft needs to expend more energy the higher up the ladder its orbit is from the surface of earth. This means that more distant orbits require larger launch vehicles and longer ‘burn’ times to get to them, than orbits close to Earth.
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- Think of the process of changing from one orbit to the other as a series of speed (velocity) changes. For example, the orbit of the Space Shuttle at an altitude of 380 kilometers (236 miles) has an orbital speed of 7.68 km/s (17,179 miles per hour).
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- The more distant orbits of the commercial geostationary communications satellites, located 35,800 km (22,245 miles)from Earth’s surface, represent an orbital speed of 3.07 km/sec (6,867 miles per hour)
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- You might think that, since the GEO satellite orbit speed is slower than the Space Shuttle, all you have to do is ‘slow down’ the Space Shuttle by decreasing its kinetic energy, and it will move out to GEO satellite orbits.
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- In fact, because of the way that kinetic energy changes in a gravitational field, you actually have to increase the kinetic energy of the Space Shuttle to make this orbit change.
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- This is done by turning on its rockets for enough time to move it outwards from Earth. Once its orbit speed has dropped 4.61 km/s (10,312 miles per hour) to the new value of 3.07 km/s (6,867 miles per hour), it will find itself at GEO orbit altitude.
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------------------------ Lunar distance : 384,000 km
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------------------------ Shuttle Orbital Speed : 17,500 miles / hr
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------------------------ Maximum cargo mass : 55,000 pounds
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- Knowing that the Moon is ‘located’ at an orbit speed of 1.0 km/sec 92,237 miles per hour). What must be the Space Shuttle speed change to reach lunar orbit?
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----------------- Delta-V = 1.0 – 7.68 = - 6.68 km/sec. (-14,943 miles per hour)
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- When the Shuttle “Orbital Maneuvering System” (OMS) is turned on, it can cause a speed change of 0.6 meters / second for every second that the engines are burning. How many seconds would the OMS have to remain on in order for the Space Shuttle to build up the necessary velocity change to reach the Moon?
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---------------- The delta-V to get to the moon is 6,680 meters/sec. The OMS can produce 0.6 m/s every second, so the total burn time would have to be T = 6,680 / 0.6 or about 11,000 seconds or 3 hours of continuous thrust.
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- The OMS can produce a maximum delta-V of 1,000 meters / second before consuming all of its 9,700 pounds of fuel. How many pounds of fuel will the OMS have to expend to get to the Moon?
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------------------- We need a total delta-V of 6,680 m/s, so 9,700 pounds x (6,680/1,000) = 64,796 pounds of fuel.
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- Does the Space Shuttle have the payload capacity to carry enough extra fuel for this one-way trip?
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------------------------ The maximum cargo mass is 55,000 pounds, so the OMS fuel would require 64,796 / 55,000 = 1.2 times the maximum load of the Space Shuttle cargo bay
---------------------- No, the Shuttle does not have enough capacity to lift all of the required OMS fuel to Earth orbit.
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- Now you high school students can figure out how big a rocket we need to take astronauts to the Moon. Then sign up after graduation. Here are some more reviews:
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- 2969 - MATH - for a Rocket Launch? - You give your students a photo of a rocket launch at Kennedy Space Center. The night time exposure was 2.5 minutes. How far from launch did the rocket reach its orbit at 300 miles altitude? Well let’s do the math:
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- 2966 - MATH - Invented to Solve Problems? This review discusses the languages of math and how they were invented to solve problems. Mathematics is a language. It can be used to explain observations, to solve problems, to find results and to predict results in the future.
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- 1235 Equations are sentences in sort hand
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- 1213 How to calculate odds for poker hands.
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- 1086 Formulas for space time, velocity.
- 1095 Math is a learned discipline.
- 1042 Calculate areas by connecting the dots, Pick’s Theorem
- 1041 The star with the golden ratio
- 1042 The calculus of a circle.
- 853 Math, the golden ratio
- 803 Transcendental numbers, “e” and “pi”.
- 649 The Greeks invented numbers.
- 805 Gambling
- 796 Science and Math, Part I
- 798 Science and Math, Part II.
- 799 Science and Math, Part III.
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January 30, 2021 MATH - shuttle to the Moon? 3008
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