The Moon describes an elliptical path around the Earth and a complete orbit is 29d 12h 44m 3s Approximately!
At its closest during this orbit it is termed Perigee and at its farthest Apogee. However there must be 2 other points opposite Perigee & Apogee where the moon is at its 2nd closest and 2nd farthest. Are these points of any significance? Do they have a name?
Thanks
Mike
The Moon describes an elliptical path around the Earth and a complete orbit is 29d 12h 44m 3s Approximately!
At its closest during this orbit it is termed Perigee and at its farthest Apogee. However there must be 2 other points opposite Perigee & Apogee where the moon is at its 2nd closest and 2nd farthest. Are these points of any significance? Do they have a name?
I never heard of 2 other points opposite Perigee and Apogee where the Moon is aledgedly 2nd closest and 2nd farthest. Might you be thinking of the precession of the orbit such that Perigee and Apogee rotate about the Moon? Also, might you be thinking about the Lagrange Points?
The moon revolves around the earth on an elliptical path with the earth at one of the foci of the ellipse. At the point on the elliptical path closest to the earth, the perigee, the moon is ~221,463 miles from the earth. At the point on the elliptical path farthest from the earth, the apogee, the moon is ~252,710 miles from earth. The moon travels this path in a counterclockwise direction, looking down on the ecliptic plane (the plane of the earth's orbit). The moon's orbit is inclined ~5.145 degrees to the ecliptic plain. The two points at which the moon's path crosses the ecliptic plane are called nodes. The line connecting these nodes, the Nodal line, rotates clockwise in the ecliptic plane, taking ~18.6 years to complete one revolution.
At what distance from the earth toward the moon will the gravitational force of attraction towards the moon be equal and opposite to the gravitational force of attraction towards the earth?
The Law of Universal Gravitation states that each particle of matter attracts every other particle of matter with a force which is directly proportional to the product of their masses and inversely proportional to the square of the distance between them. Expressed mathematically,
F = GM(m)/r^2
where F is the force with which either of the particles attracts the other, M and m are the masses of two particles separated by a distance r, and G is the Universal Gravitational Constant. The product of G and, lets say, the mass of the earth, is sometimes referred to as GM or mu (the greek letter pronounced meuw as opposed to meow), the earth's gravitational constant. Thus the force of attraction exerted by the earth on any particle within, on the surface of, or above, is F = 1.40766x10^16 ft^3/sec^2(m)/r^2 where m is the mass of the object being attracted and r is the distance from the center of the earth to the mass.
The gravitational constant for the earth, GM(E), is 1.40766x10^16ft^3/sec^2. The gravitational constant for the moon, GM(M), is 1.7313x10^14ft^3/sec^2. Using the average distance between the earth and moon of 239,000 miles, let the distance from the moon, to the point between the earth and moon, where the gravitational pull on a 32,200 lb. satellite is the same, be X, and the distance from the earth to this point be
(239,000 - X). Therefore, the gravitational force is F = GMm/r^2 where r = X for the moon distance and r = (239000 - X) for the earth distance, and m is the mass of the satellite. At the point where the forces are equal, 1.40766x10^16(m)/(239000-X)^2 = 1.7313x10^14(m)/X^2. The m's cancel out and you are left with 81.30653X^2 = (239000 - X)^2 which results in 80.30653X^2 + 478000X - 5.7121x10^10 = 0. From the quadratic equation, you get X = 23,859 miles, roughly one tenth the distance between the two bodies from the moon. So the distance from the earth is ~215,140 miles.
Checking the gravitational pull on the 32,200 lb. satellite, whose mass m = 1000 lb.sec.^2/ft.^4. The pull of the earth is F = 1.40766x10^16(1000)/(215,140x5280)^2 = 10.91 lb. The pull of the moon is F = 1.7313x10^14(1000)/(23858x5280)^2 = 10.91 lb.
This point is sometimes referred to as L2. There is an L5 Society which supports building a space station at this point between the earth and moon. There are five such points in space, L1 through L5, at which a small body can remain in a stable orbit with two very massive bodies. The points are called Lagrangian Points and are the rare cases where the relative motions of three bodies can be computed exactly. In the case of a body orbiting a much larger body, such as the moon about the earth, the first stable point is L1 and lies on the moon's orbit, diametrically opposite the earth. The L2 and L3 points are both on the moon-earth line, one closer to the earth than the moon and the other farther away. The remaining L4 and L5 points are located on the moon's orbit such that each forms an equilateral triangle with the earth and moon.
If you find what you are lookijg for, please let us know.
The moon is pretty! :)
Yes, the points opposite Perigee and Apogee do have a name. They are called the "nodal points" or "lunar nodes." These points are where the Moon's orbit intersects the plane of the Earth's orbit around the Sun, also known as the ecliptic plane.
The lunar nodes are of significance because they are the locations in the Moon's orbit where eclipses can occur. Specifically, a solar eclipse can happen when the Moon is near one of the lunar nodes and aligns with the Sun in such a way that it casts a shadow on the Earth. Conversely, a lunar eclipse can occur when the Moon is near one of the lunar nodes and the Earth blocks the sunlight from reaching the Moon.
There are two types of lunar nodes: the ascending node and the descending node. The ascending node is the point where the Moon's orbit crosses the ecliptic from south to north, while the descending node is the point where it crosses from north to south.
So, while the lunar nodes may not be as well-known as Perigee (closest) and Apogee (farthest), they do play a crucial role in determining when and where eclipses can occur.