3A6 Kepler's Laws of Orbital Motion Flashcards
Describe Kepler's three laws of orbital motion.
What shape do planetary orbits take according to Kepler’s First Law?
Elliptical
An ellipse is an oval shape with two foci.
How did Kepler’s First Law disprove the geocentric model?
It proved planets orbit the Sun in elliptical paths, not circles around Earth.
## Footnote
This law supported the heliocentric model proposed by Copernicus.
What ellipse components define a planet’s orbit?
- Foci
- Major axis
- Minor axis
- Perihelion
- Aphelion
The major axis is the longest diameter of the ellipse.
What are the foci of an ellipse?
Two fixed points that shape the ellipse’s orbit.
## Footnote
The Sun sits at one focus of a planet’s orbit.
Fill in the blank:
The ______ describes the point of an elliptical orbit farthest from the Sun.
aphelion
Perihelion is the closest point to the Sun.
Fill in the blank:
In an elliptical orbit, the Sun is located at one ______ of the ellipse.
focus
The two foci define the shape of the ellipse; the other focus is empty.
How does the elliptical shape of Earth’s orbit affect its distance from the Sun?
The distance varies, with Earth being closest at perihelion and farthest at aphelion.
Perihelion occurs in January, and aphelion occurs in July.
How does the eccentricity of the Earth’s orbit affect its motion?
It makes Earth move faster at perihelion and slower at aphelion.
## Footnote
Earth’s low eccentricity (0.0167) results in minimal effects on seasonal lengths and solar energy.
How do the orbits of Mercury and Venus compare to those of more distant planets?
Mercury and Venus have orbits close to being circular, while farther planets have more pronounced elliptical orbits.
The measurements for Mercury and Venus were impressively accurate, but still had a margin of error compared to modern measurements.
What factor primarily influences Earth’s seasonal variations?
Earth’s axial tilt
Earth’s orbit and the distance from the sun both have minimal impact on seasonal variations.
What does Kepler’s Second Law state?
A planet sweeps out equal areas in equal times in its orbit.
Planets move faster near perihelion and slower near aphelion.
Fill in the blank:
Kepler’s Second Law is also known as the law of ______ _____.
equal areas
This describes the varying speed of a planet in its orbit.
Why do planets move faster near perihelion?
The Sun’s gravitational pull is stronger when the planet is closer.
Gravitational force increases as distance decreases.
Fill in the blank:
The changing speed of Earth’s orbit, explained by Kepler’s Second Law, affects the length of ______.
seasons
Northern Hemisphere summers are longer due to slower orbital speed near aphelion.
How does Kepler’s Second Law relate to conservation of angular momentum?
A planet’s angular momentum remains constant as it moves in its orbit.
Faster motion near perihelion compensates for smaller orbital radius.
What happens to a planet’s velocity as it approaches the Sun?
It increases.
Gravitational pull grows stronger as the distance decreases.
How does the law of equal areas apply to comets?
Comets move very fast near the Sun and slow down as they travel away.
This is why comets spend most of their time far from the Sun.
Why is Kepler’s Second Law important for space missions?
Kepler’s Second Law helps calculate precise travel times and trajectory.
It is crucial for space missions as it describes how objects in orbit move at varying speeds, being faster closer to the orbiting body and slower farther away.
What does Kepler’s Third Law state?
The square of a planet’s orbital period is proportional to the cube of its semi-major axes.
T² ∝ r³, where T is the period and r is the semi-major axes of that orbit. Larger orbits implies longer periods.
Fill in the blank:
Kepler’s Third Law connects a planet’s orbital ______ to its average distance from the Sun.
period
This relationship holds true for all planets orbiting the Sun.
What is the orbital period of Earth?
365.25 days
This accounts for the need for a leap day every four years.
True or false:
Planets farther from the Sun have shorter orbital periods.
False
Planets farther from the Sun take longer to complete their orbits.
How does Kepler’s Third Law apply to the Moon’s orbit?
The law can predict the Moon’s orbital period based on its average distance from Earth.
This applies to any satellite orbiting a central body.
Why do outer planets have slower orbital speeds?
They are farther from the Sun, leading to a weaker gravitational pull and a longer orbital period.
Greater orbital radius results in a longer period.
What happens if a satellite slows down in its orbit?
Gravity’s pull will overcome the inertia needed to maintain the orbit, causing it to spiral inwards towards the planet.
Conversely, if it goes faster, the orbit will become elliptical rather than circular.
How is Kepler’s Third Law used in astronomy?
It determines the distance of exoplanets from their stars by observing orbital periods.
This helps locate potentially habitable planets.
How did Kepler’s Third Law influence Newton’s work?
It helped Newton derive the universal law of gravitation.
Newton explained Kepler’s laws using gravitational forces.
What is the significance of Kepler’s Third Law for satellite launches?
It helps calculate the orbital period for specific satellite distances.
Accurate placement is crucial for communication and GPS satellites.
How do Kepler’s laws influence satellite motion?
The laws describe the orbits of satellites:
- They follow elliptical orbits with Earth at one focus (First Law).
- Satellites move faster near Earth and slower farther away (Second Law).
- The farther a satellite is, the longer its orbital period (Third Law).
Kepler’s laws apply universally to any object orbiting another due to gravity, including artificial and natural satellites.
