The Science of Astronomy: Kepler and Newton

These flashcards cover the historical evolution of astronomical models from Tycho Brahe to Johannes Kepler, Kepler's three laws of planetary motion, basic physics of motion, and Newton's laws of motion and gravity.

What is the fundamental principle in astronomy regarding scientific laws?

The universe behaves by the same scientific laws everywhere.

What is the Copernican model?

A Sun-centered model of the solar system.

Who was the 1600s mathematician who used Tycho Brahe's observations to solve the motions of the planets?

Johannes Kepler

What was Tycho Brahe's primary strength as an astronomer?

He was the world’s best naked-eye astronomer and created an enormous catalog of exact planetary positions.

What specific measurement discrepancy led Kepler to abandon circular orbits in favor of ellipses?

An 8-arcminute discrepancy.

State Kepler’s First Law of Planetary Motion.

The orbit of each planet around the Sun is an ellipse with the Sun at one focus.

What is the definition of Kepler’s Second Law of Planetary Motion?

As a planet moves around its orbit, an imaginary line connecting the Sun and planet sweeps out equal areas in equal times.

According to Kepler’s Second Law, where does a planet move faster in its orbit?

A planet travels faster when it is nearer to the Sun (perihelion) and slower when it is farther from the Sun (aphelion).

What is the mathematical equation for Kepler’s Third Law?

$$p^2 = a^3$$

In Kepler’s Third Law formula, what do the variables $p$ and $a$ represent?

$p$ is the orbital period in years and $a$ is the average distance from the Sun in AU.

How does orbital speed change for planets that are more distant from the Sun?

More distant planets orbit the Sun at slower average speeds.

How is speed defined and what are its standard units?

Speed is how fast an object is moving regardless of its direction, defined as $\frac{\text{distance}}{\text{time}}$ in units such as $\text{m/s}$.

What is the difference between speed and velocity?

Speed is only how fast an object moves, while velocity describes both speed and direction.

What is the definition of acceleration?

The rate of change in velocity, measured in units of $\text{speed/time}$.

What is the acceleration of gravity ($g$) on Earth?

$g \approx 10\,\text{m/s}^2$ (more precisely $9.81\,\text{m/s}^2$), meaning speed increases by $10\,\text{m/s}$ for each second of falling.

What did Galileo demonstrate about the acceleration of falling objects of different masses?

He showed that the acceleration of gravity ($g$) is the same for all falling objects, regardless of their mass.

What was Sir Isaac Newton's specific realization regarding the laws of physics on Earth and in the heavens?

He realized the same physical laws that operate on Earth also operate in the heavens, building on the idea of one universe.

State Newton’s First Law of Motion.

An object moves at constant velocity unless a net force acts to change its speed or direction.

What is the formula for Newton’s Second Law of Motion?

$$\text{Force} = \text{mass} \times \text{acceleration}$$

What is the difference between mass and weight?

Mass is a measure of the amount of matter in an object, while weight is the gravitational force exerted on that mass.

How is weight calculated on Earth?

$\text{weight} = g \times \text{mass}$, where $g \approx 10\,\text{N/kg}$ on Earth.

What is the acceleration due to gravity on the Moon compared to Earth?

On the Moon, the acceleration due to gravity is $1.62\,\text{m/s}^2$, compared to $9.81\,\text{m/s}^2$ on Earth.

According to the lecture table, which body in the solar system has the highest acceleration due to gravity?

The Sun, with an acceleration of $274.13\,\text{m/s}^2$.