Repeat the previous problem, this time finding the magnitude and direction of the net force acti

step 1 The moon is in its third quarter phase. The sun, the earth, and the moon are in the positions as

Repeat the previous problem, this time finding the magnitude...

Key Concepts

Gravitational Force

Gravitational force is the mutual attractive force between objects with mass, described by Newton's law of universal gravitation. This concept is essential in astrophysics, as it explains how bodies like the Sun, Moon, and planets interact through their masses, exerting forces that result in orbital motions and other dynamics in the solar system.

Net Force

The net force on an object is the vector sum of all individual forces acting on it. In the context of astrophysical bodies, determining the net force involves calculating and combining contributions from multiple gravitational interactions. This overall force dictates the acceleration and motion of the object according to Newton's second law of motion.

Vector Decomposition and Addition

Vector decomposition and addition involve breaking down forces into their components along chosen coordinate axes and then summing these components to obtain the resultant force. This process is critical when dealing with forces that act in different directions, enabling the determination of both the magnitude and direction of the net force in a systematic way.

Reference Frames for Direction Analysis

A reference frame or reference axis provides a basis to describe the direction of forces. In problems involving celestial bodies, directions are often specified relative to significant lines, such as the line connecting two major bodies. This approach allows the direction of net forces to be expressed in terms that are physically meaningful and easier to interpret in the context of the system's geometry.

Transcript

00:01 The moon is in its third quarter phase.

00:02 The sun, the earth, and the moon are in the positions as shown, and i've drawn the masses of the sun, earth, moon, and their distances relative to each other on the right side.

00:14 The problem wants us to find the magnitude and direction of the net force acting on the sun.

00:20 Here, we will want to find the distance between the sun and the moon, and since the earth is not in only the x or, or only in the y direction with respect to the sun.

00:35 We will also want to find this angle here for calculations later on.

00:41 So for rsm, we can use the pythagorean theorem where it is just rse squared minus rme squared, and we take the square root of that, and we get about 1 .48 times 10 to the 11 meters.

01:01 For the angle, we can go ahead and use the inverse sign between rme and rse.

01:18 This would give us an angle of about 0 .15 degrees.

01:26 So now the problem, let's write down what the problem wants us to find, which is the force acting on the sun.

01:34 So this will be equal to the force acting on the sun by the moon plus the force acting on the sun by the earth.

01:45 Let's go ahead and look at the force by the moon first.

01:49 This is purely in the x direction and the sun is being pulled in the positive x direction.

01:55 So it'll be a positive g.

01:58 M1 will be the sun.

02:01 So ms, m.

02:03 M over distance, which is r.

02:06 S m squared in the x direction...

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