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Chapter 3: Problem 30

What is the eccentricity of a circular orbit?

Short Answer

Expert verified
The eccentricity of a circular orbit is 0.

Step by step solution

01

Understanding Eccentricity

Eccentricity is a measure of how much an orbit deviates from being circular. It is denoted as the letter 'e'.
02

Characteristics of a Circular Orbit

In a circular orbit, the distance between the orbiting object and the focus (e.g., the center of the Earth) is constant. This implies that the orbit is a perfect circle.
03

Eccentricity Formula

The formula for eccentricity is \[ e = \frac{\text{distance from center to focus}}{\text{semi-major axis}} \].
04

Applying to Circular Orbit

For a circular orbit, the distance from the center to any point on the orbit is the same, which makes the distance from the center to the focus equal to zero.
05

Calculate Eccentricity

Using the formula, if the distance from the center to the focus is zero, then \[ e = \frac{0}{\text{semi-major axis}} = 0 \]. Therefore, the eccentricity of a circular orbit is 0.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Orbit Eccentricity
Orbit eccentricity is a key concept in understanding different types of orbits around celestial bodies. It determines how much an orbit deviates from being a perfect circle and is denoted by the letter 'e'.
Eccentricity can range from 0 to 1:
  • An orbit with an eccentricity of 0 is a perfect circle.
  • Orbits with eccentricity between 0 and 1 (but not 0) are elliptical.
  • An orbit with an eccentricity of exactly 1 is parabolic, meaning the object escapes the gravitational pull of the primary body.
  • If eccentricity exceeds 1, the orbit becomes hyperbolic.
Understanding eccentricity is critical because it affects the orbital characteristics, such as the speed and distance of the orbiting object throughout its path.
Circular Orbit
A circular orbit is an orbit with an eccentricity of 0, meaning it is a perfect circle.
In a circular orbit:
  • The distance between the orbited object and the orbiter is constant, meaning the orbiting object stays a fixed distance from the focus point.
  • There is uniform motion, as the speed of the orbiting body remains constant due to the constant gravitational pull.
The key characteristics of a circular orbit are valuable for understanding stable and predictable pathways, like many artificial satellites around the Earth. They help ensure steady communication and observation in space missions.
Orbit Deviation
Orbit deviation refers to how much an orbit diverges from a circular path. This is largely dictated by the eccentricity of the orbit.
The further an orbit deviates from 0 (circular), the more elongated or stretched it becomes. This elongation has several effects:
  • Increased distance variation, leading to parts of the orbit being closer or farther from the focus point than others.
  • Varying orbital speeds, as objects move faster when closer to the focus (periapsis) and slower when farther away (apoapsis).
  • Potential for complications in mission planning, as irregular intervals might necessitate additional calculations and contingencies.
Comprehending how deviations impact orbits is vital for tasks like satellite deployment, space travel, and even predicting celestial events.

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Most popular questions from this chapter

Go to the Museo Galileo website (http://brunelleschi.imss .fi.it/telescopiogalileo/index.html), and view the exhibit on Galileo's telescope. What did his telescope look like? What other instruments did he use? From the museum page you can link to short videos (in English) on his science and his trial (http://catalogue.museogalileo.it). Why is Galileo considered the first modern scientist? Why is his middle finger on display in the museum?

Suppose a planet is discovered orbiting a star in a highly elliptical orbit. While the planet is close to the star it moves _______, but while it is far away it moves _______. a. faster; slower b. slower; faster c. retrograde; prograde d. prograde; retrograde

When Earth catches up to a slower-moving outer planet and passes it in its orbit in the same way that a faster runner overtakes a slower runner in an outside lane, the planet a. exhibits retrograde motion. b. slows down because it feels Earth's gravitational pull. c. decreases in brightness as it passes through Earth's shadow. d. moves into a more elliptical orbit.

Galileo observed that Venus had phases that correlated with its size in his telescope. From this information, you may conclude that Venus a. is the center of the Solar System. b. orbits the Sun. c. orbits Earth. d. orbits the Moon.

Imagine you throw a ball straight up in the air. At the top of its flight, it stops and then falls again. What is the acceleration of the ball at the top of its flight?
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