Linear Polynomials and Gravitation Review

Vocabulary flashcards covering linear equations from polynomial studies and gravitational physics concepts including field intensity, universal gravitation, and orbital periods.

Linear Equations in Two Variables

Algebraic equations representing straight lines on a coordinate plane, such as $y = -3x + 4$, $2y = 4x + 7$, and $5y = 6x - 10$.

Newton's Law of Gravitation

The law stating that the gravitational force between two bodies of masses $m_1$ and $m_2$ separated by distance $r$ is proportional to the product of their masses and inversely proportional to the square of the distance, expressed as $F = G \frac{m_1 m_2}{r^2}$.

Universal Constant of Gravitation ($G$)

The constant of proportionality in Newton's law of gravitation, which is numerically equal to the force of attraction between two unit masses placed at unit distance apart.

Femtometer ($fm$)

A unit of distance defined by the relation $1\,fm = 10^{-15}\,m$.

Time Period of Revolution ($T$)

The time period of revolution of a planet around the sun of mass $M$, defined by $T = 2\pi \sqrt{\frac{r^3}{GM}}$, where $r$ is the average radius of the orbit.

Action at a Distance Viewpoint

The classical assumption that a body directly exerts a gravitational force on another body kept at a distance without an intermediate field.

Gravitational Field

A physical entity created by a body in the space around it that has its own existence, energy, and momentum, and exerts a force on any other mass placed within it.

Intensity of Gravitational Field

The gravitational force exerted per unit mass placed at a point in a field, defined by $\vec{E} = \frac{\vec{F}}{m}$ with an SI unit of $\text{N/kg}$.

Vector Addition of Gravitational Fields

The principle stating that if $\vec{E}_1$ is the field due to source $S_1$ and $\vec{E}_2$ is the field due to source $S_2$, the resultant gravitational field is $\vec{E} = \vec{E}_1 + \vec{E}_2$.

Relationship between Field Intensity and Acceleration due to Gravity

The concept that intensity of gravitational field and acceleration due to gravity are two separate physical quantities having equal magnitudes and directions, related near Earth's surface by $\vec{E} = \frac{\vec{F}}{m} = \frac{m\vec{g}}{m} = \vec{g}$.

Gravitational Field due to a Point Mass

The field intensity created by a particle of mass $M$ at a point distance $r$ away, given by $E = \frac{GM}{r^2}$ along $PO$ (or in vector form $\vec{E} = -\frac{GM}{r^2}\hat{r}$, where $\hat{r}$ is the unit vector along $\vec{r} = \vec{OP}$).