7 Gravitation and Orbits Free Online FlashCards

What is Newton’s law of universal gravitation?

$F=G\frac{m_1m_2}{r^2}$, where $r$ is the distance between the masses’ centers and $G$ is the gravitational constant.

What forces do two gravitating bodies exert on each other?

The forces are equal in magnitude and opposite in direction, acting along the line joining the bodies’ centers.

How does gravitational force change when separation doubles?

The force is proportional to $\frac{1}{r^2}$, so doubling the separation makes it one-fourth as strong.

How can a spherical body’s external gravitational effect be modeled?

Outside a spherically symmetric body, its gravitational effect is the same as if its mass were concentrated at its center.

What is the gravitational field around a spherical mass?

$\vec g=-\frac{GM}{r^2}\hat r$. The minus sign means the field points inward, toward the mass.

What is gravitational potential energy when zero is defined at infinity?

With zero potential energy at infinity, $U=-\frac{GMm}{r}$. Its negative value indicates a bound system; energy must be added to separate the masses to infinity.

When is $\Delta U\approx mgh$ a good gravitational-energy approximation?

For a small height change $h$ near Earth’s surface, $\Delta U\approx mgh$. This approximation applies when the height change is small compared with Earth’s radius.

How does gravity produce an orbit?

An object’s sideways motion carries it forward while gravity continually accelerates it toward the body it orbits. Gravity supplies the inward, centripetal acceleration.

What sets circular-orbit speed, and does the orbiting mass matter?

For a circular orbit, $v=\sqrt{\frac{GM}{r}}$. The orbiting object’s mass cancels, so objects at the same radius around the same central mass have the same ideal speed.

How does circular-orbit period depend on radius?

For a circular orbit, $T=2\pi\sqrt{\frac{r^3}{GM}}$. A larger orbital radius means a longer period.

What is the total energy of an object in a circular orbit?

The total mechanical energy is $E=-\frac{GMm}{2r}$. Negative total energy corresponds to a bound orbit.

What does Kepler’s law of orbits state?

A planet follows an ellipse with the central body at one focus; a circle is a special case of an ellipse.