Orbital Mechanics and Ellipses Quiz

<p>e = 0 (B)</p> Signup and view all the answers

<p>Eccentricity (D)</p> Signup and view all the answers

<p>The ellipse's eccentricity. (D)</p> Signup and view all the answers

<p>Circle (B)</p> Signup and view all the answers

<p>0 ≤ e &lt; 1 (A)</p> Signup and view all the answers

<p>Semi-major axis ($a$) and eccentricity ($e$) (A)</p> Signup and view all the answers

<p>The orientation of the orbit and the orbital plane (B)</p> Signup and view all the answers

<p>The angle between the orbital plane and the observer's line of sight. (A)</p> Signup and view all the answers

<p>The angle measured in the observer's plane, defining the orientation of the orbital plane. (B)</p> Signup and view all the answers

<p>Perigee (C)</p> Signup and view all the answers

<p>Periastron (B)</p> Signup and view all the answers

<p>Apapsis (B)</p> Signup and view all the answers

<p>The relative orientation of the orbit within its plane and the position of the body along the orbit. (B)</p> Signup and view all the answers

<p>$P_b^2 = \frac{4\pi^2}{GM} a^3$ (B)</p> Signup and view all the answers

<p>The time evolution of orbital elements in a binary system. (A)</p> Signup and view all the answers

<p>They can be measured independently of any specific gravity model and then compared to theoretical predictions. (C)</p> Signup and view all the answers

<p>The angle between the orbital plane and the plane of the sky. (A)</p> Signup and view all the answers

<p>$a = \left( \frac{GM P_b^2}{4\pi^2} \right)^{1/3}$ (A)</p> Signup and view all the answers

<p>The system is well-described by Newtonian gravity with no perturbations. (B)</p> Signup and view all the answers

<p>Conservation of angular momentum (D)</p> Signup and view all the answers

<p>The orbital speed is fastest when the stars are closest together. (A)</p> Signup and view all the answers

<p>The approximate lifetime of stars, given their energy source. (D)</p> Signup and view all the answers

<p>That stars must be powered by a different energy source than just gravity due to geological data indicating earth's age. (C)</p> Signup and view all the answers

<p>An approximation of a star's age based on its total energy and rate of energy loss. (C)</p> Signup and view all the answers

<p>The timescale of energy production due to gravitational contraction. (B)</p> Signup and view all the answers

<p>It provided observational evidence supporting the mass-luminosity relation. (B)</p> Signup and view all the answers

<p>$U = -3GM_{\star}^2 / 5R_{\star}$ (C)</p> Signup and view all the answers

<p>The Sun must be powered by a different, more long-lasting energy source than gravitational contraction alone. (E)</p> Signup and view all the answers

<p>$L(M) ∝ M^{3.5}$ (D)</p> Signup and view all the answers

<p>Both components are detectable and spatially resolved. (B)</p> Signup and view all the answers

<p>Through the oscillation of the detectable component in space. (A)</p> Signup and view all the answers

<p>A dip is seen in the light curve over time. (B)</p> Signup and view all the answers

<p>The lines are Doppler shifted in opposite directions due to the orbital motion. (B)</p> Signup and view all the answers

<p>Distance measurements combined with angular separations. (D)</p> Signup and view all the answers

<p>It allows for easy detection of both components. (D)</p> Signup and view all the answers

<p>Double stars are not generally considered binary systems. (B)</p> Signup and view all the answers

<p>The period related to the motion of the stars in the system. (B)</p> Signup and view all the answers

<p>Creates sinusoidal variations (C)</p> Signup and view all the answers

<p>Detection is possible over long distances in this scenario (D)</p> Signup and view all the answers

<p>Δν/v = ν/c (A)</p> Signup and view all the answers

<p>If v/c is much less than 1 (C)</p> Signup and view all the answers

<p>The frequency of the signal (B)</p> Signup and view all the answers

<p>Resolution finer than 1 MHz (A)</p> Signup and view all the answers

<p>Temperature and composition (B)</p> Signup and view all the answers

<p>By observing binary interactions (A)</p> Signup and view all the answers

A star system consisting of two stars orbiting a common center of mass.

Three laws that describe the motion of planets around the sun, also applicable to binary stars.

Different classifications of binary star systems based on visibility and interaction.

The change in frequency or wavelength of waves in relation to an observer moving relative to the source.

Six parameters that define the size, shape, and orientation of an orbit.

A measure of how much an orbit deviates from a perfect circle, ranging from 0 to greater than 1.

Half of the longest diameter of an ellipse, key in defining orbits.

Calculated using the formula πab where 'a' is semi-major and 'b' is semi-minor axis.

Half of the longest diameter of an ellipse; defines size of the orbit.

A parameter that measures the deviation of an orbit from a perfect circle.

The tilt of an orbital plane regarding the reference plane, typically the equatorial plane.

The angle from a reference direction to the ascending node of the orbit.

The angle from the ascending node to the point of closest approach in an orbit.

The angle between the direction of periapsis and the current position of the body.

Various terms referring to the closest point in an orbit, e.g., perihelion (sun), perigee (Earth).

The time it takes for a binary system to complete one full orbit around its center of mass.

The angle between the orbital plane of a binary system and the plane of reference (the sky).

Parameters that modify Kepler's laws to account for additional effects in binary systems over time.

The classical theory of gravity describing the force between two masses as proportional to their masses and inversely proportional to the square of their distance.

The combined mass of both objects in a binary system, measured in solar masses (M⊙).

An orbit where the relative velocity of the objects involved approaches a significant fraction of the speed of light (v/c).

A potential energy field created by a central mass around which objects orbit.

The velocity of one object as observed from another object.

The ability to distinguish between different wavelengths in a spectrum.

An orbit with varying distance from the central body, causing more complex spectral variations.

A graphical representation of stars showing the relationship between luminosity and temperature.

The total amount of energy emitted by a star across all wavelengths.

The mass of a star divided by its volume, indicating how compact it is.

A law describing the power radiated by a black body in terms of its temperature.

A binary system where both stars can be seen and resolved.

A binary system where one component is visible and the other is inferred from its gravitational effects.

A binary system where stars pass in front of each other, causing a dip in brightness.

A binary system detected by observing the Doppler shifts in the spectral lines of stars.

The angle between the two components in a binary system as seen from Earth.

The apparent shift in position of a star against the background due to Earth's movement.

A graph showing brightness of a star system over time; used for analyzing eclipsing binaries.

A significant portion of main sequence stars exist in binary or multiple star systems.

The relationship stating luminosity (L) is proportional to mass (M) raised to the power of approximately 3.5.

An important 1924 plot demonstrating the mass-luminosity relation discovered by Sir Arthur Eddington.

The calculation of a star's age based on its energy source, represented by age ≈ E/L.

The estimated age of a star based on gravitational potential energy and luminosity: tKH = |U|/L.

The energy stored due to the gravitational attraction of a star's mass: U = -3GM²/(5R).

The process by which stars generate energy, leading to the discovery of their long lifetimes.

A conclusion derived from repeated observations, such as the empirical mass-luminosity relation.