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VCE Stuff => VCE Science => VCE Mathematics/Science/Technology => VCE Subjects + Help => VCE Physics => Topic started by: KeyMan on June 07, 2009, 07:44:59 pm

Title: When gravitation field strength = 0
Post by: KeyMan on June 07, 2009, 07:44:59 pm: Hey, I have no idea where to begin when I get questions asking me to calculate R when the gravitational field strength is 0 so can you guys please help me with these 2 questions?

There is a point between the Earth and the Moon where the total gravitational field is zero.Given that the mass of Earth is 6.0 × 10^24 kg, the mass of the Moon is 7.3 × 10^22 kg and the radius of the Moon’s orbit is 3.8 × 10^8 m, calculate the distance of this point from the centre of the Earth.

(http://img14.imageshack.us/img14/7760/gravamz.jpg)
Title: Re: When gravitation field strength = 0
Post by: kamil9876 on June 07, 2009, 08:10:25 pm: question 8:

Let this distance between the the centre of Alpha and Y be D. If body of mass m was at point Y, the gravitational force between the body and alpha would be:

$F_1=G\frac{mM}{D^2}$

However the distance between Beta and Y is $R-D$ . Hence the gravitational force between the body and Beta would be:

$F_2=G\frac{m(0.01M)}{(R-D)^2}$

Now forces $F_1$ and $F_2$ act on the body at Y and they act in opposite directions. However the net force must be zero and so the the magnitudes of these two forces must be equal. Equating the two equations gives:
$<br />G\frac{mM}{D^2}=G\frac{m(0.01M)}{(R-D)^2}$
$\frac{1}{D^2}=\frac{0.01}{(R-D)^2}$

$\frac{1}{D}=\frac{0.1}{R-D}$

$R-D=0.1D$
$R=1.1D$
$D=\frac{10R}{11}$
Title: Re: When gravitation field strength = 0
Post by: anonuser0511 on June 07, 2009, 10:38:14 pm: would this also be a place where true weightlessness could occur? (this and deep space where G theoretically = 0, although it really approaches doesn't it?
-seeing as
F = GMm/r^2
  = GMm/(really big number)^2
only equals zero with calculus eh.)

Also i got

3.42249E8m for the first Q

using
X = distance from earth where gravitational field = 0
Me = Mass of the Earth
Mm = Mass of the Moon

Dx = R(moon's orbit)*sqrt(Me/Mm)
   _________________________
   (1 + sqrt(Me/Mm)