AP Physics 1 universal gravitation and orbits key terms

What does Newton's law of universal gravitation state?

Every mass attracts every other mass with a force proportional to the product of their masses and inversely proportional to the square of the distance between them.

Fill in the blank: The gravitational force formula is ______.

F = G \frac{m_1 m_2}{r^2}, where G is the gravitational constant.

True or False: Gravitational force is stronger with greater distance.

False - Gravitational force decreases as distance increases, following an inverse square relationship.

Compare gravitational force and electric force.

Gravitational force is always attractive; electric force can be attractive or repulsive, depending on charge.

What is the gravitational constant (G)?

G = 6.674 imes 10^{-11} ext{ N(m/kg)}^2, a key value in the gravitational force formula.

How does mass affect gravitational force?

Gravitational force increases with greater mass, as it is directly proportional to the product of the masses involved.

What is the shape of orbits due to gravity?

Orbits are elliptical, as described by Kepler's laws, not perfectly circular.

Cause → Effect: Increase in distance between two masses?

Effect: Decrease in gravitational force acting between them.

What are Kepler's first and second laws?

First: Orbits are ellipses with the Sun at one focus. Second: A line segment joining a planet and the Sun sweeps out equal areas in equal times.

What happens to gravitational force when mass doubles?

The gravitational force also doubles, as force is directly proportional to mass.

True or False: Weight is the same on all planets.

False - Weight varies with gravitational acceleration, which differs by planet.

What is escape velocity?

The minimum velocity needed to break free from a celestial body's gravitational influence, calculated using $\displaystyle v_e = \frac{GM}{R}$.

Define gravitational potential energy (U).

U = -G \frac{m_1 m_2}{r}, the energy due to the position of masses in a gravitational field.

How does gravitational acceleration vary with altitude?

Gravitational acceleration decreases with altitude, as it is inversely proportional to the square of the distance from the center of the mass.

What role does gravity play in tides?

Gravity from the Moon and Sun causes ocean tides, creating bulges on Earth.

Fill in the blank: Gravitational force is ______ to distance squared.

Inversely proportional, meaning as distance increases, force decreases.

What is an orbit?

An orbit is the curved path of an object around a point in space, typically due to gravitational forces.

Define escape velocity.

Escape velocity is the minimum speed needed for an object to break free from a celestial body's gravitational pull. Formula: $\displaystyle v_e = \frac{GM}{r}$.

True or False: Orbits can be circular or elliptical.

True. Orbits can be circular (constant distance) or elliptical (varying distance) based on energy and velocity.

What factors affect the period of an orbit?

The period depends on the mass of the central body and the radius of the orbit. Formula: $\displaystyle T = 2\pi\sqrt{\\frac{r^3}{GM}}$.

Fill in the blank: The gravitational force between two objects is ______ proportional to the product of their masses.

Directly. It also inversely varies with the square of the distance between them.

Compare geostationary and polar orbits.

Geostationary: stays above the same point on Earth. Polar: passes over the poles, covering the entire Earth.

What is the centripetal force in an orbit?

The centripetal force required to keep an object in orbit is provided by gravity. $\displaystyle F_c = \\frac{mv^2}{r}$.

Question: What is Kepler's Third Law?

Kepler's Third Law states that the square of the orbital period ($\displaystyle T^2$) of a planet is directly proportional to the cube of the semi-major axis ($\displaystyle r^3$) of its orbit: $\displaystyle T^2 \propto r^3$.

What is the significance of orbital eccentricity?

Eccentricity measures the deviation of an orbit from circularity. Range: 0 (circle) to 1 (parabola), with higher values indicating more elongated orbits.

Cause → Effect: Increasing the orbital radius affects what?

Increasing the orbital radius decreases the gravitational force and increases the orbital period.

What is a satellite's kinetic energy in orbit?

Kinetic energy ($\displaystyle KE$) of a satellite is given by: $\displaystyle KE = \\frac{1}{2}mv^2$, where $\displaystyle m$ is mass and $\displaystyle v$ is orbital speed.

True or False: All orbits are stable.

False. Orbits can be perturbed by gravitational influences, leading to instability.

What determines the shape of an orbit?

The shape is determined by the total energy (kinetic + potential) and angular momentum of the orbiting object.

Explain the concept of gravitational assist.

Gravitational assist uses the gravity of a planet to increase a spacecraft's speed and change its trajectory.

Calculate the orbital speed of an object at radius r.

Orbital speed ($\displaystyle v$) is calculated using: $\displaystyle v = \sqrt{\\frac{GM}{r}}$. Where $\displaystyle G$ is the gravitational constant and $\displaystyle M$ is the mass.

What is an apogee?

Apogee is the point in an orbit where the satellite or object is farthest from the Earth or central body.