A8 - Planetary motion and gravity

Question 1

What did Tycho Brahe do?

Answer 1

did lots of observational work to aid the transition from a geocentric model to the heliocentric model of the Solar System

Question 2

What did Copernicus do?

Answer 2

mathematically modelled the heliocentric (Sun-centered) solar system

Question 3

How did Copernicus’s model of the solar system improve on earlier models?

Answer 3

it made predictions of the planet’s positions easier and quicker to calculate

Question 4

Who was Kepler, and what did he do?

Answer 4

-he was Tycho Brahe’s assistant, and after he died, Kepler used Brahe’s measurements to formulate his 3 laws of planetary motion

-he first thought that planets had elliptical orbits, and this explained Brahe’s observations

Question 5

What was Kepler’s first law?

Answer 5

a planet’s orbit is always elliptical, with the Sun at one of its foci

Question 6

What was Kepler’s second law?

Answer 6

-rate of area swept out across the orbit is constant

-ie for equal changes in time, the area sweeped out (WRT the Sun) across any part of the orbit will be equal

Question 7

What was Kepler’s third law?

Answer 7

the square of the orbital period in years, T², is proportional to the cube of the length of the semi-major axis, a³

T²/a³ = a constant

Question 8

What does the constant in Kepler’s third law depend on? How does it affect the time period of the orbiting body?

Answer 8

-it depends inversely on the mass of the central body (eg the Sun)

-increasing the central body’s mass would decrease the time period of the orbiting body

Question 9

If you know the ratio between the masses of 2 separate bodies, what can you deduce about their constants from Kepler’s third law?

Answer 9

the ratio between the masses are equal to the inverse of the ratio of the constants

Question 10

Name 2 important points on a planet’s orbit around the Sun, or a satellite’s orbit around the Earth:

Answer 10

-perihelion (closest to the Sun) and aphelion (furthest)

-perigee (closest to the Earth) and apogee (furthest)

The body moves fastest at perihelion/perigee

Question 11

What did Newton do to enhance the understanding of the forces in the Solar System model?

Answer 11

-used his law of universal gravitation to explain Kepler’s Laws

-the law stated that the gravitational force between 2 bodies is proportional to the product of their masses, and inversely proportional to the square of their separation