Compare Gravity Scales - Middle School Earth and Space Science
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What is the formula for orbital speed of a circular orbit around mass $M$ at radius $r$?
What is the formula for orbital speed of a circular orbit around mass $M$ at radius $r$?
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$v = \sqrt{\frac{GM}{r}}$. Derived by balancing gravitational and centripetal forces.
$v = \sqrt{\frac{GM}{r}}$. Derived by balancing gravitational and centripetal forces.
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In a gravity model, what does a deeper gravitational potential well represent?
In a gravity model, what does a deeper gravitational potential well represent?
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Stronger gravity and more energy needed to escape. Deeper wells require more energy to climb out of.
Stronger gravity and more energy needed to escape. Deeper wells require more energy to climb out of.
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Which comparison is correct: typical gravity binding planets to the Sun or binding stars to the Milky Way?
Which comparison is correct: typical gravity binding planets to the Sun or binding stars to the Milky Way?
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Both are gravity-bound orbits, but the Milky Way’s gravity comes from distributed mass. Solar system has central mass; galaxy has distributed mass throughout.
Both are gravity-bound orbits, but the Milky Way’s gravity comes from distributed mass. Solar system has central mass; galaxy has distributed mass throughout.
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If distance to a mass triples, by what factor does gravitational field strength change?
If distance to a mass triples, by what factor does gravitational field strength change?
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It becomes $\frac{1}{9}$ as large. Inverse square law: $3^2 = 9$ times weaker.
It becomes $\frac{1}{9}$ as large. Inverse square law: $3^2 = 9$ times weaker.
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What is the escape velocity formula from a spherical mass $M$ at radius $r$?
What is the escape velocity formula from a spherical mass $M$ at radius $r$?
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$v_e = \sqrt{\frac{2GM}{r}}$. Minimum speed to overcome gravity and reach infinity.
$v_e = \sqrt{\frac{2GM}{r}}$. Minimum speed to overcome gravity and reach infinity.
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Identify the correct statement about galaxy rotation: do outer stars move much slower than inner stars?
Identify the correct statement about galaxy rotation: do outer stars move much slower than inner stars?
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No; outer stars often move at similar speeds (flat rotation curve). Dark matter causes unexpected constant speeds at all radii.
No; outer stars often move at similar speeds (flat rotation curve). Dark matter causes unexpected constant speeds at all radii.
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Which model best represents Milky Way gravity: one point mass or distributed mass across a disk and halo?
Which model best represents Milky Way gravity: one point mass or distributed mass across a disk and halo?
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Distributed mass across the galaxy (disk, bulge, and halo). Galaxy mass spreads throughout spiral arms and dark matter halo.
Distributed mass across the galaxy (disk, bulge, and halo). Galaxy mass spreads throughout spiral arms and dark matter halo.
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Which model best represents solar system gravity: one dominant mass or many equal masses?
Which model best represents solar system gravity: one dominant mass or many equal masses?
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One dominant mass (the Sun) with smaller orbiting bodies. Planets orbit the massive Sun, not each other equally.
One dominant mass (the Sun) with smaller orbiting bodies. Planets orbit the massive Sun, not each other equally.
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What does Kepler’s third law state for orbits around the same central mass?
What does Kepler’s third law state for orbits around the same central mass?
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$T^2 \propto r^3$. Period squared is proportional to radius cubed for all orbits.
$T^2 \propto r^3$. Period squared is proportional to radius cubed for all orbits.
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If orbital radius increases, what happens to orbital period according to $T \propto r^{\frac{3}{2}}$?
If orbital radius increases, what happens to orbital period according to $T \propto r^{\frac{3}{2}}$?
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Orbital period increases. The $r^{3/2}$ relationship means farther orbits take longer.
Orbital period increases. The $r^{3/2}$ relationship means farther orbits take longer.
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What is the formula for the gravitational force between two masses separated by distance $r$?
What is the formula for the gravitational force between two masses separated by distance $r$?
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$F = G\frac{m_1m_2}{r^2}$. Newton's law shows force depends on both masses and inverse square of distance.
$F = G\frac{m_1m_2}{r^2}$. Newton's law shows force depends on both masses and inverse square of distance.
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What does the constant $G$ represent in $F = G\frac{m_1m_2}{r^2}$?
What does the constant $G$ represent in $F = G\frac{m_1m_2}{r^2}$?
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The universal gravitational constant. A fundamental constant that makes gravitational calculations work universally.
The universal gravitational constant. A fundamental constant that makes gravitational calculations work universally.
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Which change increases gravitational force more: doubling $m_1$ or doubling $r$?
Which change increases gravitational force more: doubling $m_1$ or doubling $r$?
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Doubling $m_1$ increases; doubling $r$ decreases by a factor of $4$. Doubling mass doubles force; doubling distance quarters it due to $r^2$ term.
Doubling $m_1$ increases; doubling $r$ decreases by a factor of $4$. Doubling mass doubles force; doubling distance quarters it due to $r^2$ term.
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Identify the relationship between gravitational force and distance in $F = G\frac{m_1m_2}{r^2}$.
Identify the relationship between gravitational force and distance in $F = G\frac{m_1m_2}{r^2}$.
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Inverse-square: $F \propto \frac{1}{r^2}$. Force decreases with the square of distance, not linearly.
Inverse-square: $F \propto \frac{1}{r^2}$. Force decreases with the square of distance, not linearly.
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What is the formula for gravitational field strength (acceleration) at distance $r$ from mass $M$?
What is the formula for gravitational field strength (acceleration) at distance $r$ from mass $M$?
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$g = G\frac{M}{r^2}$. Gravitational acceleration depends only on source mass and distance.
$g = G\frac{M}{r^2}$. Gravitational acceleration depends only on source mass and distance.
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Which object mainly provides the gravitational force that keeps planets in orbit in our solar system?
Which object mainly provides the gravitational force that keeps planets in orbit in our solar system?
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The Sun. The Sun contains 99.86% of the solar system's mass.
The Sun. The Sun contains 99.86% of the solar system's mass.
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Which object mainly provides the gravitational force that keeps the Sun orbiting the galaxy?
Which object mainly provides the gravitational force that keeps the Sun orbiting the galaxy?
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The Milky Way’s combined mass (especially near the galactic center). Stars orbit the galaxy's center of mass, not a single object.
The Milky Way’s combined mass (especially near the galactic center). Stars orbit the galaxy's center of mass, not a single object.
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Which has the stronger gravitational pull on Earth: the Sun or Jupiter?
Which has the stronger gravitational pull on Earth: the Sun or Jupiter?
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The Sun. The Sun's much greater mass outweighs Jupiter's closer distance.
The Sun. The Sun's much greater mass outweighs Jupiter's closer distance.
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Which has the stronger gravitational pull on Earth: the Moon or the Sun?
Which has the stronger gravitational pull on Earth: the Moon or the Sun?
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The Sun. Despite being farther, the Sun's enormous mass creates stronger pull.
The Sun. Despite being farther, the Sun's enormous mass creates stronger pull.
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What is the formula for orbital period of a circular orbit around mass $M$ at radius $r$?
What is the formula for orbital period of a circular orbit around mass $M$ at radius $r$?
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$T = 2\pi\sqrt{\frac{r^3}{GM}}$. Combines orbital circumference with velocity formula.
$T = 2\pi\sqrt{\frac{r^3}{GM}}$. Combines orbital circumference with velocity formula.
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What is the main reason stars in the Milky Way do not orbit a single star like planets orbit the Sun?
What is the main reason stars in the Milky Way do not orbit a single star like planets orbit the Sun?
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They orbit the galaxy s combined mass, not one star. Unlike planets, stars orbit distributed mass throughout the galaxy.
They orbit the galaxy s combined mass, not one star. Unlike planets, stars orbit distributed mass throughout the galaxy.
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What does the variable $G$ represent in the equation $F=G\frac{m_1m_2}{r^2}$?
What does the variable $G$ represent in the equation $F=G\frac{m_1m_2}{r^2}$?
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The universal gravitational constant. A constant ($6.67 \times 10^{-11}$ N⋅m²/kg²) that makes the equation work.
The universal gravitational constant. A constant ($6.67 \times 10^{-11}$ N⋅m²/kg²) that makes the equation work.
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Which change increases gravitational force more: doubling $m_1$ or doubling $r$ (with other values fixed)?
Which change increases gravitational force more: doubling $m_1$ or doubling $r$ (with other values fixed)?
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Doubling $m_1$ increases force more. Doubling mass doubles force, but doubling $r$ reduces force to $\frac{1}{4}$.
Doubling $m_1$ increases force more. Doubling mass doubles force, but doubling $r$ reduces force to $\frac{1}{4}$.
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Identify the relationship between gravitational force and distance $r$ in $F=G\frac{m_1m_2}{r^2}$.
Identify the relationship between gravitational force and distance $r$ in $F=G\frac{m_1m_2}{r^2}$.
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Inverse-square: $F\propto\frac{1}{r^2}$. Force decreases with the square of distance, not linearly.
Inverse-square: $F\propto\frac{1}{r^2}$. Force decreases with the square of distance, not linearly.
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What happens to gravitational force when distance increases from $r$ to $2r$ (masses unchanged)?
What happens to gravitational force when distance increases from $r$ to $2r$ (masses unchanged)?
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It becomes $ \frac{1}{4}$ of the original. When $r$ becomes $2r$, denominator becomes $4r^2$, reducing force by factor of 4.
It becomes $ \frac{1}{4}$ of the original. When $r$ becomes $2r$, denominator becomes $4r^2$, reducing force by factor of 4.
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