I still cannot solve this problem:
Consider a spaceship located on the Earth-Moon center line (i.e. a line that intersects the centers of both bodies) such that, at that point, the tugs on the spaceship from each celestial body exactly cancel, leaving the craft literally weightless. Take the distance between the centers of the Earth and Moon to be 3.90E+5 km and the Moon-to-Earth mass ratio to be 1.200E-2. What is the spaceship's distance from the center of the Moon?
Bobpursely told me that:
Mm/Me=(d2/d)^2
where mm is mass moon, me mass earth, d2 is distance from craft to moon, and d is the distance from craft to earth.
My online homework site wants me to use ONLY the info given and solve for what I don't have. So I'm trying to get the distance from the craft to earth using the numbers given, but I can't seem to figure it out.
The ratio of distances to the centers of Moon and Earth is the square root of the mass ratio.
Sqrt 0.012 = 0.1095 = d2/d
d + d2 = d + 0.1095 d = 1.0955 d = 3.90*10^5 km
d = 3.56*10^5 km
d2 = 0.39*10^5 km
BobPursley suggested that you use the law of gravity. That is not "new information". it is what you needed to do to solve the problem.
To find the distance from the craft to Earth (d), you can rearrange the equation provided by Bobpursely:
Mm/Me = (d2/d)^2
First, let's substitute the given values:
Mm/Me = mass moon / mass earth = 1.200E-2
d2 = distance from craft to moon
d = distance from craft to earth (unknown)
Now solve for d:
Mm/Me = (d2/d)^2
Taking the square root of both sides:
sqrt(Mm/Me) = sqrt((d2/d)^2)
Simplifying:
sqrt(Mm/Me) = d2/d
Cross multiplying:
d * sqrt(Mm/Me) = d2
Now, let's substitute the known values:
d * sqrt(1.200E-2) = d2
Now you have an equation with only one unknown (d). You can solve this equation algebraically to find the value of d.