Calculate the magnitudes of the gravitational forces exerted...

Name: Problem 63, Chapter 12: University Physics with Modern Physics
Uploaded: 2021-05-27T07:24:46-08:00
Duration: 4 min
Channel: Ajay Singhal
Description: Calculate the magnitudes of the gravitational forces exerted on the Moon by the Sun and by the Earth when the two forces are in direct competition, that is, when the Sun, Moon, and Earth are aligned with the Moon between the Sun and the Earth. (This alignment corresponds to a solar eclipse.) Does the orbit of the Moon ever actually curve away from the Sun, toward the Earth?

Calculate the magnitudes of the gravitational forces exerted on the Moon by the Sun and by the Earth when the two forces are in direct competition, that is, when the Sun, Moon, and Earth are aligned with the Moon between the Sun and the Earth. (This alignment corresponds to a solar eclipse.) Does the orbit of the Moon ever actually curve away from the Sun, toward the Earth?

Key Concepts

Newton's Law of Universal Gravitation

This fundamental principle states that every two masses attract each other with a force proportional to the product of their masses and inversely proportional to the square of the distance between their centers. It provides the mathematical framework (F = GMm/r²) used to calculate the gravitational forces between bodies.

Gravitational Forces in Multi-Body Systems

In systems where more than two bodies interact, each body experiences gravitational forces from all others. Analyzing such systems requires calculating individual force contributions and understanding how these forces combine vectorially, which is essential for determining the overall dynamics and stability of the system.

Orbital Dynamics and Perturbations

Orbital dynamics studies the motion of objects under the influence of gravity, including how orbits evolve over time. Perturbations refer to deviations from a simple, ideal orbit due to additional forces from other bodies, highlighting that orbits can be slightly altered without a complete change in their overall trajectory.

Alignment of Gravitational Forces

This concept involves the configuration where objects line up such that the gravitational forces they exert are in direct competition. Such alignments are significant because they can produce noticeable effects, like eclipses or temporary imbalances in gravitational influence, but do not typically result in a dramatic change in the inherent orbital path.

Transcript

00:01 Belongs to the gravitational chapter and according to this question we have to calculate the magnitude of gravitational force fg on the moon due to sun and earth so suppose this is the diagram for this condition okay so this is the diagram in which this is the sun and this is the moon and this is the earth okay so the gravitational force on the moon due to sun will be in this direction and the gravitational force on the moon due to earth will be in this direction.

00:30 These are the distance between earth and moon and sun and earth.

00:34 So, now we can calculate the gravitational force applied by the sun f s.

00:39 This will be equals to g mass of sun, mass of moon, divided by r .s .e minus r small r we can take as per the diagram.

00:51 So rse minus r e m whole square.

00:55 Okay.

00:56 So this will become the distance from here to here.

01:00 So, substituting values, so we will get that force applied by the sun f s, this will be equals to 6 .67 into 10 to the power minus 11.

01:08 This is the value for the g and mass of the sun which is 1 .99 into 10 to the power 30 kg and mass of the moon which is 7 .3 double 4 multiplied by 10 to the power 22 kg divided by distance between sun and earth which is 1 .496 into 10 to the power 11 meter and distance between in earth and moon which is 3 .8 double 4 multiplied by 10 to the power 8 meters.

01:35 So whole is where.

01:36 So from here after solving, we will get that force applied due to the sun on the moon f s equals to minus 4 .381 multiplied by 10 to the power 20 newton into x -capped direction minus x kept direction.

01:50 Suppose this is our x direction and this is the y direction...

Please give Ace some feedback