Help with kepler's law and gravitation

[nithin]

guys i need help with these problems.I have been trying to solve then for a long time and still cannot as i am very confused and have no where to go for help

1) On the way to the Moon , Apollo astronauts passed a point after which the moon's gravitational pull became stronger than the Earth's . a) what is the distance of that point from Earth's center. b) what is the acceleration due to the Earth's gravitation at this point?

i do not know at what distance to start and also i am not sure of what distance i should start at...

 

[interested_learner]

I would look at the relative sizes of the Earth and the Moon. That would be a good place to start looking. Then look at what the gravitational pull is for each body independently at that point. Are they equal? If not move in one direction or another.

I am sitting in a lab right now without a reference book so I can't help you with the formula you should use for the gravitational pull but it should be in your textbook and look something like G (constant) Mass_one Mass_two / distance**2

 

[andrevdh]

Have you tried equating the two forces using Newton's law of universal gravitational attraction?

$$\frac{m_{earth}}{x^2} = \frac{m_{moon}}{(D - x)^2}$$

Where D is the distance between the Earth and the moon.

Although I've got the sneaky feeling that this equation is not solveable.

 

[thiotimoline]

guys i need help with these problems.I have been trying to solve then for a long time and still cannot as i am very confused and have no where to go for help

1) On the way to the Moon , Apollo astronauts passed a point after which the moon's gravitational pull became stronger than the Earth's . a) what is the distance of that point from Earth's center. b) what is the acceleration due to the Earth's gravitation at this point?

i do not know at what distance to start and also i am not sure of what distance i should start at...

For 1), let X be the distance from, for eg, Earth to that point. Equate the 2 g-forces which are in opposite direction to find X. For 2), that point is where the astronaut feels nothing, so a should be 0.