Recent content by ArbazAlam

Ok, so: P(R_{e})=2 \pi \sqrt{R_{e}^{3}/(GM)} = P_{0} P'(R_{e})=3 \pi \sqrt{R_{e}/(GM)} So, P(h+R_{e}) \approx P(R_{e}) + P'(R_{e})(h) = 2 \pi \sqrt{R_{e}^{3}/(GM)}(1+(3h)/(2R_{e})) = P_{0}[1+(3h)/(2R_{e})]

Sweet! Finally got it. Here is how I got it for future reference. I took the Taylor series of P(h+R_e) about R_e and got: P\approx 2\pi R_{e}\sqrt{(h+R_{e})/(GM)}(1+(3h)/(2R_{e}))The next question asks what the value of P_0 is. I take that to be: P_{0}=2\pi R_{e}\sqrt{(h+R_{e})/(GM)} The...

Yes, I can compute a Taylor expansion like the example you presented. So in this problem, I take f(h) = P^2 and then compute the Taylor series for f(h) about R_e [to n=1]. Once I do that, I can take the square root of the polynomial. Is this correct?

I made a dumb mistake. There is no root in the period approximation and I edited accordingly. D H, I'm afraid I still don't understand. :( Thank you for bearing with me.

Doesn't the original function have to have a root to begin with?

Homework Statement Use Kepler's Third Law and a Taylor expansion to derive the following approximation for the orbital period of a satellite in low Earth orbit with a constant height h above the surface of the Earth. h << R_earth : P \approx P_{0}(1+3h/2R_{e}) Homework Equations Kepler's...

Thank you! I didn't even notice those units canceled out. And thank you for the theta.

Homework Statement A fire hose held near the ground shoots water at a speed of 7.5 m/s. At what angle(s) should the nozzle point in order that the water would land 3.0 m away? The attempt at a solution I remember from engineering there was a single equation you could use to find the...

A ball is thrown straight up from the edge of the roof of a building. A second ball is dropped from the roof 2.00 s later. Air resistance may be ignored. (a) If the height of the building is 60 m, what must be the initial speed of the first ball if both are to hit the ground at the same...

This problem has really been bugging me. After several attempts, I don't even know where to start anymore. A ball is thrown straight up from the edge of the roof of a building. A second ball is dropped from the roof 2.00 s later. Air resistance may be ignored. (a) If the height of the...