Kepler’s first law replaced the long-standing idea that planets must follow perfect circles. Using Tycho Brahe’s precise observations, Kepler concluded that planetary paths are ellipses with the Sun at one focus. This lesson introduces ellipses, orbital landmarks, and the broader family of conic-section paths.
An ellipse is the set of points for which the sum of the distances to two fixed points, called the foci, is constant. Kepler’s first law states that every planet moves in an elliptical orbit with the Sun at one focus. The Sun is not generally at the center of the ellipse; it is at one of its foci.
All flashcards
State Kepler’s first law.
Every planet moves in an elliptical orbit with the Sun located at one focus of the ellipse.
What defines an ellipse?
It is the set of points for which the sum of the distances from each point to two fixed foci is constant.
What are perihelion and aphelion?
Perihelion is the point in an orbit closest to the Sun; aphelion is the point farthest from the Sun.
What does orbital eccentricity describe?
Eccentricity describes the shape of a conic orbit. For an ellipse, e=0 is a circle, and values closer to one indicate a more elongated ellipse.
How do energy and eccentricity classify conic orbits?
Negative energy gives a bound orbit with 0≤e<1; zero energy gives a parabola with e=1; positive energy gives a hyperbola with e>1.
Quiz questions
For a Hohmann transfer between two circular orbits around the same body, where do the transfer ellipse’s apsides lie?Answer: Perihelion at the inner orbit and aphelion at the outer orbit.
Why does a spacecraft need a second velocity change at the end of a Hohmann transfer?Answer: To match the destination circular orbit’s velocity.
In a two-body gravitational system, where do both bodies trace conic paths?Answer: Around their shared center of mass.
For the same spacecraft mass, how does total orbital energy compare between two circular orbits when one has a larger radius?Answer: The larger-radius orbit has energy that is less negative.
For a spacecraft to meet a destination planet at the far end of a transfer ellipse, what must be coordinated?Answer: The planet’s arrival time with the spacecraft’s travel time.
Based on University Physics Volume 1 by William Moebs, Samuel J. Ling, Jeff Sanny (OpenStax), licensed CC BY 4.0. Adapted into a summary, flashcards and quizzes.