Compare Gravity Scales - Middle School Earth and Space Science

Identify the correct statement about galaxy rotation: do outer stars move much slower than inner stars?

No; outer stars often move at similar speeds (flat rotation curve). Dark matter causes unexpected constant speeds at all radii.
What does the constant $G$ represent in $F = G\frac{m_1m_2}{r^2}$ ?

The universal gravitational constant. A fundamental constant that makes gravitational calculations work universally.
Which factor mainly makes the Sun dominate planetary orbits in the solar system: mass or distance to each planet?

Mass (the Sun has far greater mass). The Sun contains 99.86% of the solar system's mass.
What is the formula for gravitational force between two masses $m_1$ and $m_2$ separated by $r$ ?

$F=G\frac{m_1m_2}{r^2}$ . Newton's law shows force depends on both masses and inverse square of distance.
Which object mainly provides the gravitational force that keeps planets in orbit in our solar system?

The Sun. The Sun contains 99.86% of the solar system's mass.
In a galaxy model, what mass components contribute to the Milky Ways gravity besides stars?

Gas, dust, and dark matter. Dark matter contributes ~85% of the galaxy's gravitational mass.
What does Kepler's third law state for orbits around the same central mass?

$T^2 \propto r^3$ . Period squared is proportional to radius cubed for all orbits.
What is the formula for weight $W$ of an object of mass $m$ in a gravitational field $g$ ?

$W=mg$ . Weight equals mass times local gravitational field strength.
Which object mainly provides the gravitational force that keeps the Sun orbiting the galaxy?

The Milky Way's combined mass (especially near the galactic center). Stars orbit the galaxy's center of mass, not a single object.
If two equal masses are separated by $3r$ instead of $r$ , what is the new force relative to the original?

It becomes $\frac{1}{9}$ of the original. Force varies as $\frac{1}{r^2}$ , so tripling $r$ divides force by 9.
Which has the stronger gravitational pull on Earth: the Moon or the Sun?

The Sun. Despite being farther, the Sun's enormous mass creates stronger pull.
What is the formula for gravitational field strength (acceleration) at distance $r$ from mass $M$ ?

$g = G\frac{M}{r^2}$ . Gravitational acceleration depends only on source mass and distance.
In a gravity model, what does a deeper gravitational potential well represent?

Stronger gravity and more energy needed to escape. Deeper wells require more energy to climb out of.
What is the key similarity between a solar system model and a galaxy model regarding orbits?

Gravity provides the inward (centripetal) pull for orbits. Both use gravity as the centripetal force maintaining circular motion.
What is the main reason stars in the Milky Way do not orbit a single star like planets orbit the Sun?

They orbit the galaxys combined mass, not one star. Unlike planets, stars orbit distributed mass throughout the galaxy.
Which comparison is correct: typical gravity binding planets to the Sun or binding stars to the Milky Way?

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.
Identify the correct comparison: which has a larger central mass, the Sun (solar system) or the Milky Way (galaxy)?

The Milky Way has a much larger total mass. The galaxy contains ~400 billion solar masses.
Which change increases gravitational force more: doubling $m_1$ or doubling $r$ (with other values fixed)?

Doubling $m_1$ increases force more. Doubling mass doubles force, but doubling $r$ reduces force to $\frac{1}{4}$ .
What is the formula for orbital speed of a circular orbit around mass $M$ at radius $r$ ?

$v = \sqrt{\frac{GM}{r}}$ . Derived by balancing gravitational and centripetal forces.
Choose the correct model conclusion: if total enclosed mass increases, orbital speeds at a given $r$ tend to do what?

Increase. More mass creates stronger gravity, requiring faster orbits for stability.
What happens to gravitational force when distance decreases from $r$ to $\frac{r}{2}$ (masses unchanged)?

It becomes $4$ times the original. When $r$ becomes $\frac{r}{2}$ , denominator becomes $\frac{r^2}{4}$ , multiplying force by 4.
Identify the relationship between gravitational force and distance $r$ in $F=G\frac{m_1m_2}{r^2}$ .

Inverse-square: $F\propto\frac{1}{r^2}$ . Force decreases with the square of distance, not linearly.
If orbital radius increases, what happens to orbital period according to $T \propto r^{\frac{3}{2}}$ ?

Orbital period increases. The $r^{3/2}$ relationship means farther orbits take longer.
What is the escape velocity formula from a spherical mass $M$ at radius $r$ ?

$v_e = \sqrt{\frac{2GM}{r}}$ . Minimum speed to overcome gravity and reach infinity.
If distance to a mass triples, by what factor does gravitational field strength change?

It becomes $\frac{1}{9}$ as large. Inverse square law: $3^2 = 9$ times weaker.
Which change increases gravitational force more: doubling $m_1$ or doubling $r$ ?

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.
Which model best represents Milky Way gravity: one point mass or distributed mass across a disk and halo?

Distributed mass across the galaxy (disk, bulge, and halo). Galaxy mass spreads throughout spiral arms and dark matter halo.
What happens to gravitational force when distance increases from $r$ to $2r$ (masses unchanged)?

It becomes $\frac{1}{4}$ of the original. When $r$ becomes $2r$ , denominator becomes $4r^2$ , reducing force by factor of 4.
Identify the relationship between gravitational force and distance in $F = G\frac{m_1m_2}{r^2}$ .

Inverse-square: $F \propto \frac{1}{r^2}$ . Force decreases with the square of distance, not linearly.
Which object exerts the largest gravitational pull on Earth: the Sun or Jupiter?

The Sun. The Sun's mass is ~1000× Jupiter's, overwhelming the distance advantage.
Which has the stronger gravitational pull on Earth: the Sun or Jupiter?

The Sun. The Sun's much greater mass outweighs Jupiter's closer distance.
What is the formula for the gravitational force between two masses separated by distance $r$ ?

$F = G\frac{m_1m_2}{r^2}$ . Newton's law shows force depends on both masses and inverse square of distance.
Which model best represents solar system gravity: one dominant mass or many equal masses?

One dominant mass (the Sun) with smaller orbiting bodies. Planets orbit the massive Sun, not each other equally.
What is the formula for orbital period of a circular orbit around mass $M$ at radius $r$ ?

$T = 2\pi\sqrt{\frac{r^3}{GM}}$ . Combines orbital circumference with velocity formula.
What is the primary gravitational force that keeps stars orbiting within the Milky Way?

Gravity from the galaxys total mass. Stars orbit the combined gravitational pull of billions of stars.
Identify the key difference in typical distances: are solar system orbits measured in AU or light-years?

Solar system orbits are typically measured in AU. Galaxy orbits span thousands of light-years, not AU.
What model statement best compares scales: is $r$ typically larger for stargalaxy interactions or planetSun interactions?

$r$ is typically larger for stargalaxy interactions. Galactic distances are thousands of times larger than planetary distances.
Which gravitational interaction is stronger: EarthMoon or SunEarth (considering real solar system values)?

SunEarth is stronger. Sun's huge mass outweighs its greater distance from Earth.
What does the variable $G$ represent in the equation $F=G\frac{m_1m_2}{r^2}$ ?

The universal gravitational constant. A constant ( $6.67 \times 10^{-11}$ N⋅m²/kg²) that makes the equation work.

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