Elliptical Orbits in Astronomy

Questions and Answers

at aphelion

at a point where the Sun is directly overhead

at perihelion (correct)

halfway between aphelion and perihelion

Law of Elliptical Orbits

Law of Equal Areas

Law of Harmonies in Planetary Motion (correct)

Law of Universal Gravitation

hyperbolic

circular

parabolic

elliptical (correct)

A planet sweeps out equal areas in equal times. Signup and view all the answers

It increases by a factor of the cube root of 2. Signup and view all the answers

It states that planets move faster when they are closer to the Sun. Signup and view all the answers

Law of Equal Areas Signup and view all the answers

Study Notes

Law of Elliptical Orbits: Kepler's first law states that the orbits of the planets are elliptical in shape, with the Sun at one of the two foci.
Characteristics of Elliptical Orbits:
- The planet's distance from the Sun varies throughout its orbit.
- The planet moves fastest when closest to the Sun (perihelion) and slowest when farthest from the Sun (aphelion).
- The shape of the orbit is a closed curve, with the planet returning to the same position after one complete orbit.

Law of Equal Areas: Kepler's second law states that the line connecting the planet to the Sun sweeps out equal areas in equal times.
Orbital Period: The time it takes a planet to complete one orbit around the Sun.
Relationship between Orbital Period and Semi-Major Axis:
- The orbital period of a planet is proportional to its semi-major axis (average distance from the Sun).
- The farther a planet is from the Sun, the longer its orbital period.

Harmony in Planetary Motion: Kepler's third law states that the square of a planet's orbital period is proportional to the cube of its semi-major axis.
Mathematical Representation: P² ∝ a³, where P is the orbital period and a is the semi-major axis.
Implications of Harmony:
- The harmony in planetary motion reveals a underlying order in the solar system.
- The law allows astronomers to calculate the orbital periods of planets and their relative distances from the Sun.

Planets have elliptical orbits with the Sun at one of the two foci.
A planet's distance from the Sun varies throughout its orbit.
A planet moves fastest at perihelion (closest point to the Sun) and slowest at aphelion (farthest point from the Sun).
Elliptical orbits are closed curves, with the planet returning to the same position after one complete orbit.

The line connecting a planet to the Sun sweeps out equal areas in equal times.
Orbital period is the time it takes a planet to complete one orbit around the Sun.
A planet's orbital period is proportional to its semi-major axis (average distance from the Sun).
The farther a planet is from the Sun, the longer its orbital period.

The square of a planet's orbital period is proportional to the cube of its semi-major axis (P² ∝ a³).
The harmony in planetary motion reveals an underlying order in the solar system.
This law allows astronomers to calculate orbital periods of planets and their relative distances from the Sun.