Physics Help Forum Explorer 1 Orbit

 Aug 6th 2017, 06:26 PM #1 Senior Member   Join Date: Nov 2013 Location: New Zealand Posts: 550 Explorer 1 Orbit Exercise taken from Caiken, pg 23 For part (a) I get (350+2549+2*6378)/2 = 7287.5 km for part (b) ... Used formula for conic sections $\displaystyle \frac{p}{r} = 1 + e \cos \theta$ assumed perigee when $\displaystyle \cos \theta = 0$ and apogee when $\displaystyle cos \theta = 1$. This gives two linear equations: p/(360+6378) - e = 1 p/(2549+6378) + e = 1 I get p = 7679.55646345356 and e = 0.139738270028726 for part (c) I get a bit stuck. I can't think of any formula that will help without knowing the mass of the satellite. Edit: Looks like Keplers 3rd law is a possible candidate for (c) $\displaystyle T^2 = \frac{4 \pi^2}{G M}a^3$ where a is the semi major axis and T is the period. That's a step closer anyway. Last edited by kiwiheretic; Aug 7th 2017 at 01:18 AM.
 Aug 7th 2017, 07:27 AM #2 Senior Member     Join Date: Aug 2008 Posts: 113 part (a) ... if the Earth's equatorial radius is 6378 km, the the semi-major axis is a = [360+2549+2(6378)]/2 = 7832.5 km part (b) ... focal length, c = 7832.5 - (360+6378) = 1094.5 km e = c/a = 1094.5/7832.5 = 0.1397... part (c) ... at the Earth's surface, $g = 9.81 \, m/s^2$ $g = \dfrac{GM}{R_e^2} \implies GM = g \cdot R_e^2$ $T^2 = \dfrac{4\pi^2}{GM} \cdot a^3 = \dfrac{4\pi^2}{g \cdot R_e^2} \cdot a^3$
 Aug 7th 2017, 07:18 PM #3 Senior Member   Join Date: Nov 2013 Location: New Zealand Posts: 550 Looks like you did something different for eccentricity that didn't involve a system of linear equations? you got a different answer for (a) but used same numbers? I just double checked with IPython as a calculator. Last edited by kiwiheretic; Aug 7th 2017 at 07:20 PM.
Aug 8th 2017, 05:03 PM   #4
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 Originally Posted by kiwiheretic Looks like you did something different for eccentricity that didn't involve a system of linear equations?

 you got a different answer for (a) but used same numbers? I just double checked with IPython as a calculator.
get a new calculator ...

Aug 8th 2017, 05:22 PM   #5
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 Originally Posted by kiwiheretic For part (a) I get (350+2549+2*6378)/2 = 7287.5 km
Oh, was a typo, I used a 350 instead of 360

Aug 8th 2017, 05:56 PM   #6
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 Originally Posted by kiwiheretic Oh, was a typo, I used a 350 instead of 360
 For part (a) I get (350+2549+2*6378)/2 = 7287.5 km
you also transposed the digits 2 and 8

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