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Determine the time needed for the space probe of …

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Problem 112 Easy Difficulty

The Clementine spacecraft described an elliptic orbit of minimum altitude $h_{A}=400 \mathrm{km}$ and maximum altitude $h_{B}=2940 \mathrm{km}$ above the surface of the moon. Knowing that the radius of the moon is $1737 \mathrm{km}$ and that the mass of the moon is 0.01230 times the mass of the earth, determine the periodic time of the spacecraft.

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Video Transcript

everyone here it is. Given element time. Spacecraft described elliptical orbit with minimum altitude. 400 kilometer and maximum amplitude. Sorry altitude 2940 kilometer have of the surface of the moon radius of the moon is given 1737 kilometers and mark off moon it Find the beautiful 123 times that of the earth. Calculate the riptide for art. G m. It's called G R Square, that is 9.81 in tow. 656 737 Turned to the power six. It is 3. 98.6 Tend to the power 12 meter cubed per second square for months G while the 00 123 years math of the art 398 while 06 So this valley you will get a four point 8964.8 96 in tow. 10 to the power 12 meter queue for second square. I mean are a 1737 plus altitude. Yeah, it will be 2137 kilometer are 2.137 tent of our 6 m. Similarly, are we? You will find 1737 plus 2940 that is 46 double seven kilometers on in meter. Be with right, 4.6 double seven. 10 to the power 6 m. No. One upon our a Young better than its the M upon 80 square unless see cars off. Peter eight on burn upon our weekend. Britain's the M upon 80 square C pillars. Horse off data be here. Peter B. Is Uh huh 1 80 plus theater A. But for one upon are weak and return it GM upon 80 square minus. See into cars off Peter A adding bar entry one. Upon our A plus, Bon upon RV. It's called toe price off GM upon edges square. So from here, edge ability toe gm are a in tow RV over. GM is poor white. 896 to 10 to the power off 12 are a but let's RV on solving angular momentum Pary red marks. You will get 3.27 8983 came to the power night meter squared per second. It's Puerto half up our A plus Army, which is who like 137 and to 10 to the power six. So you will get three points or 02 in tow, 10 to the power 6 m. Similarly, you can find the value of the the root off our A in tow RV are it 2.137 And to the power six value of RV is four point 677 Tend to the power six. So value off the you will get 3.161 45 10 to the power 6 m and time period will be will fight a B upon edge. He is 3.40 to 10 to the power six b is 3.16145 in tow. 10 to the power six upon edge 3.78 983 The time period you will get 17.831 This is the answer for this problem. Thanks for watching it.

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03:28
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09:37
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Isaac Newton (4 January 1643 – 31 March 1727) was an English mathematician, physicist, astronomer, theologian, and author (described in his own day as a "natural philosopher") who is widely recognised as one of the most influential scientists of all time and a key figure in the scientific revolution. His book Philosophiæ Naturalis Principia Mathematica ("Mathematical Principles of Natural Philosophy"), first published in 1687, laid the foundations of classical mechanics. Newton also made seminal contributions to optics, and he shares credit with Gottfried Wilhelm Leibniz for developing the infinitesimal calculus.
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