Planets and other celestial bodies follow elliptical orbits around the Sun, as described by Kepler’s laws of planetary motion. Because of this elliptical path, the velocity of a planet changes depending on its position in orbit. The perihelion and aphelion are two key points in this journey, where the planet moves at its fastest and slowest speeds, respectively.
Understanding the velocity at perihelion and aphelion is crucial for astronomy, physics, and space exploration. This topic explains why these velocity differences occur and how they relate to gravitational forces and orbital mechanics.
What Are Perihelion and Aphelion?
Perihelion: The Closest Point to the Sun
The perihelion is the point in a planet’s orbit where it is closest to the Sun. At this position:
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The gravitational force from the Sun is strongest.
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The planet moves at its fastest speed due to increased gravitational pull.
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For Earth, perihelion occurs around early January, when it is approximately 147 million km from the Sun.
Aphelion: The Farthest Point from the Sun
The aphelion is the point where a planet is farthest from the Sun. At this position:
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The gravitational pull is weaker.
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The planet moves at its slowest speed.
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Earth reaches aphelion around early July, at a distance of about 152 million km from the Sun.
Why Does Velocity Change at Perihelion and Aphelion?
Kepler’s Second Law: The Law of Equal Areas
Johannes Kepler’s second law states that a planet sweeps out equal areas in equal times. This means:
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When the planet is closer to the Sun (perihelion), it must move faster to cover the same area.
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When it is farther from the Sun (aphelion), it moves slower because the area it sweeps is wider.
Newton’s Laws and Gravitational Forces
According to Newton’s law of universal gravitation, the force between two objects depends on:
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The mass of the objects.
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The distance between them.
Since gravity weakens with distance, planets experience the strongest gravitational pull at perihelion, accelerating their motion. Conversely, at aphelion, gravity is weaker, slowing them down.
How to Calculate Orbital Velocity at Perihelion and Aphelion
The orbital velocity (v) of a planet is determined using the formula:
Where:
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v = orbital velocity
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mu = standard gravitational parameter of the Sun (approximately 1.327 à 10¹¹ km³/s²)
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r = distance from the Sun
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a = semi-major axis of the orbit
From this equation:
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At perihelion, r is smaller, making velocity higher.
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At aphelion, r is larger, making velocity lower.
For Earth:
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Velocity at perihelion: ~30.29 km/s
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Velocity at aphelion: ~29.29 km/s
This difference may seem small, but it significantly affects Earth’s seasons and climate.
Examples of Other Planets’ Orbital Speeds
Different planets experience varying speed differences due to their elliptical orbits.
Mercury (Most Eccentric Orbit)
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Perihelion velocity: ~58.98 km/s
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Aphelion velocity: ~38.86 km/s
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Mercury’s orbit is highly elliptical, causing a dramatic speed difference.
Mars
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Perihelion velocity: ~26.50 km/s
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Aphelion velocity: ~21.97 km/s
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Mars also has an elliptical orbit, leading to noticeable seasonal changes.
The Impact of Perihelion and Aphelion on Earth
1. Seasonal Differences
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Many assume that Earth’s seasons are caused by perihelion and aphelion, but this is not true.
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Seasons are primarily caused by Earth’s axial tilt (23.5°).
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However, the small change in distance affects the intensity of sunlight received.
2. Climate and Weather Patterns
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When Earth is at perihelion, it moves faster, shortening winter in the Northern Hemisphere and summer in the Southern Hemisphere.
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When at aphelion, the slower movement extends the opposite seasons.
3. Space Missions and Satellite Orbits
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Understanding velocity changes at perihelion and aphelion is critical for space missions.
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Spacecraft must adjust their speed when moving closer or farther from the Sun to maintain orbit stability.
The velocity at perihelion and aphelion plays a crucial role in planetary motion and orbital mechanics. Due to gravitational forces, planets move fastest at perihelion and slowest at aphelion, following Kepler’s laws. This concept not only explains how planets move but also helps scientists plan space missions, predict climate effects, and understand celestial mechanics.
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