Every particle attracts every other particle with a force directly proportional to the product of their masses and inversely proportional to the square of the distance between their centers: F = G rac{m_1 m_2}{r^2}

An orbit where an object moves in a circle around another object, with constant speed and gravitational force always perpendicular to the velocity.

An orbit where an object moves in an ellipse around another object, with varying speed and gravitational force not always perpendicular to the velocity.

The velocity required for an object to maintain a stable orbit around a central body: $v = \sqrt{\frac{GM}{r}}$

The time it takes for an object to complete one full orbit around another object: $T = 2\pi \sqrt{\frac{r^3}{GM}}$

Half of the longest diameter of an ellipse. It is used in Kepler's Third Law to relate orbital period and orbital size.

A circular orbit above the equator with an orbital period equal to the rotation period of the central body, making the satellite appear stationary from the ground.

Circular: Constant speed, gravitational force always perpendicular to velocity. | Elliptical: Varying speed, gravitational force not always perpendicular to velocity.

First Law: Describes the shape of the orbit (ellipse). | Second Law: Describes the speed of the planet at different points in the orbit (equal areas in equal times).

1. Set gravitational force equal to centripetal force: G rac{Mm}{r^2} = m rac{v^2}{r}. 2. Solve for $v$: $v = \sqrt{\frac{GM}{r}}$

1. Use the formula: $T = \frac{2\pi r}{v}$. 2. Substitute the expression for orbital velocity: $T = 2\pi \sqrt{\frac{r^3}{GM}}$

1. Spacecraft approaches a moving planet. 2. Spacecraft interacts with the planet's gravitational field. 3. Spacecraft gains or loses kinetic energy, changing its speed and/or direction. 4. Planet's velocity change is negligible.