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As per this The Gravitational Force of the Earth and Moon on Each Other Moon is pulling us with a force equal to 1/300,000th of our weight. I have read this Is the fuel burn for a satellite launch affected by the position of the moon relative to the launch site? NASA do no wait for moon to come overhead of rocket.(why?)

Considering this heavy rocket http://www.spacex.com/falcon-heavy have mass of 1394000 kg .

If the rocket is launched when moon is overhead it can save upto 13661200/300000 = 4.64 kg of load or might be more? (as we go above in space the gravity of moon increases and earth gravity decrease.)

Update : removed W = 1394000 * 9.8 = 13661200 kg as it was in 1g environment.

How to calculate pulling force to rocket when below planets are in line?(diagram just for reference)

Gravity on rocket

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  • $\begingroup$ Consider, for a moment the fluctuation in the total atmospheric drag at launch due to differing weather conditions. Are these larger or small than the concerns you ask about? By what factor? $\endgroup$ Jan 31, 2016 at 15:53
  • $\begingroup$ i understand the weather condition. i guess small concern. pulling gravity on rocket by moon, venus, mercury and sun. $\endgroup$
    – gaganyaan
    Jan 31, 2016 at 16:38

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First, when calculating force, the unit produced is newtons (N), not kg. You can use kg(force) if you're willing to risk getting confused, and your calculation of the falcon weight shows that you did get confused. In a 1g environment, 1 kg of mass produces 1 kg of force, so there is no multiplication by 9.8.

The gravitational attraction between any two bodies of masses m and M, separated by a distance R, is $$F=\frac{GmM}{R^2}$$ and in the case of the moon and a body on the surface of the earth this amounts to $$F = \frac{6.67\times 10^{-11}\times 7.34\times 10^{22}\times m}{{(3.8\times10^8)}^2} = m\times({3.4\times{10^{-5})}} $$ and your second calculation, although generally correct, provides a force in newtons, as well. To compare this to the weight of the rocket, you need to divide by 9.8, so the gravitational attraction of the moon on the rocket is the equivalent of about 4.5 kg mass attraction to the earth. Since the Falcon weighs (as you have noted, $1.4\times 10^6$ kg, this amounts to a mass reduction of .0003%.

So the simple answer to your question "NASA do no wait for moon to come overhead of rocket.(why?)" is "It's not worth it." Waiting for the moon to be overhead is the equivalent of saving 10 pounds on a Falcon, and paint alone weighs a lot more than that. Compared to the restriction on launch windows (you can only launch at a certain time each day) this is simply not worth it.

As for your conjunction question, you simply use the equation for gravitational attraction between the rocket and each of the bodies, then sum them.

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  • $\begingroup$ I did get confused 1g environment. 4.64 km seems very less now comparing to the paint :) but considering if we can add more 4.5 kg payload to the rocket can save upto 4.64*3333.33 =15466$ as per en.wikipedia.org/wiki/Space_Launch_System (projection 2012) $\endgroup$
    – gaganyaan
    Jan 31, 2016 at 21:05
  • $\begingroup$ We don't have to wait for moon once per month because it is rotating around the earth. I believe we can see moon everyday except when it dark. space.com/24871-does-the-moon-rotate.html $\endgroup$
    – gaganyaan
    Feb 1, 2016 at 7:06
  • $\begingroup$ @editinit - Ooops. You are, of course, correct, and I have edited to reflect this. My apologies. $\endgroup$ Feb 1, 2016 at 19:49

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