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The moon does not fall to earth because of its tangential velocity. The following video explains it well.
The initiative http://lunarscience.nasa.gov/ask-a-scientist/ by NASA will answer all your doubts on moon.
Is the gravitational force between moon & earth are equal ?
If the question is- “Is the force exerted by earth on moon is equal to the force exerted by moon on earth?” then the answer is “Yes”
I hope that more questions will follow.
Please post your questions as comments to this post.
Why does the sun appear to rise and set though it is actually not moving?
First of all I would like to remind you that it is incorrect to say that “sun is not moving”. Sun is also moving. But the question here is, “Sun appears to rise and set not because of its motion”.
Sunset and sunrise are caused by the rotation of earth. When earth rotates, the position of sun appears to change and it seems as if the sun is revolving around the earth; just like we feel that the ground is revolving around us when we are looking out from a rotating merry-go-round.
Can you please explain about paralax method?
How to use it to calculate the distance between two astronomical objects?
Parallax is the change in the apparent position of an object due to change iv view point.
Read more here
The parallax method is a way of measuring distances of far-away objects.
WHAT IS THE WAY TO MEASURE THE DISTANCE OF DISTANT OBJECTS LIKE STARS WITH THE HELP OF PARALLAX METHOD
Parallax is a displacement or difference in the apparent position of an object viewed along two different lines of sight, and is measured by the angle or semi-angle of inclination between those two lines.
Astronomers use the principle of parallax to measure distances to celestial objects including to the Moon, the Sun, and to stars beyond the Solar System.
See the animation below to understand the parallax method for determining the stellar distances
Find more information here