Physics Help Forum Newton and motion of satellites

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 Dec 9th 2010, 03:02 PM #1 Junior Member   Join Date: Dec 2010 Posts: 1 Newton and motion of satellites I need help with the second part of a two part question. Using Newton's thought on the motion of satellites: a. Calculate the speed that a satellite shot from the cannon must have in order to orbit Earth 150 km above its surface. The mass of the Earth is 5.97 x 10²⁴ kg and the radius of the Earth is 6.52 x 10⁶ m. I got this: V=√((6.7 x 10-ıı)(5.97 x 10²⁴)/(6.52 x 10⁶)) V=7,832.50 m/s Is that correct? b. How long, in minutes, would it take for the satellite to complete one orbit and return to the cannon? I have so far: T=2pi√((6.52 x 10⁶)³/(6.7 x 10-ıı)(5.97 x 10²⁴)) T=5235 Is 5235 in m/s? If so how do i get it into minutes?
 Dec 11th 2010, 12:25 AM #2 Member   Join Date: Oct 2010 Location: Sri Lanka Posts: 63 a)(1/2)mv^2=GMm/r^2 substitute the values Last edited by BAdhi; Dec 11th 2010 at 12:28 AM.
 Dec 11th 2010, 01:48 AM #3 Physics Team     Join Date: Jun 2010 Location: Mauritius Posts: 609 a. I do not agree. The formula for the gravitational potential energy is U = -GMm/r The change in gravitational energy equals the initial kinetic energy provided. Hence, this gives (mv^2)/2 = - (GMm)/(r+h) + (GMm)/r b. The centripetal force on the satellite is provided by the gravitational force. Hence; mRω^2 = (GMm)/(R^2) Simplifying gives indeed T = 2pi \sqrt{R^3/(GM)} And here, R = r + h And the T that you got is in seconds, not m/s And one assumption here is that the Earth is not rotating on itself then. Because otherwise, you'll have another value, lower or higher depending whether it is rotating in the same direction as the Earth or rotating in the opposite direction. __________________ Jerry (Got my results!) It is easier to protect your feet with slippers than to cover the earth with carpet. No one can go back and change a bad beginning; but anyone can start now and create a successful ending. If a problem can be solved, no need to worry about it. If it cannot be solved what is the use of worrying?

 Tags motion, newton, satellite, satellites

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