Orbits and Gravity

Question 1

Explain Brache

Answer 1

His extensive and precise observations enabled him to note that the positions of the planets varied from those given in published tables, which were based on the work of Ptolemy

Question 2

Briefly explain Keplers 3 laws

Answer 2

Described the behaviour of planets based on their paths through space

Question 3

Explain major axis

Answer 3

The widest diameter of the ellipse

Question 4

Explain semimajor axis

Answer 4

• Half this distance—that is, the distance from the centre of the ellipse to one end
• Is usually used to specify the size of the ellipse

Question 5

Explain eccentricity

Answer 5

The ratio of the distance between the foci to the length of the major axis

Question 6

State Kepler’s first law

Answer 6

Each planet moves around the Sun in an orbit that is an ellipse, with the Sun at one focus of the ellipse

Question 7

State Kepler’s second law

Answer 7

The straight line joining a planet and the Sun sweeps out equal areas in space in equal intervals of time

( known as the Law of Equal Areas )

Question 8

State Kepler’s third law

Answer 8

The square of a planet’s orbital period is directly proportional to the cube of the semi-major axis of its orbit

Question 9

Explain angular momentum

Answer 9

• Angular momentum is a measure of the rotation of a body as it revolves around some fixed point
• l = mvr
• As a planet approaches the Sun on its elliptical orbit and the distance to the spin centre decreases, the planet speeds up to conserve the angular momentum. Similarly, when the planet is farther from the Sun, it moves more slowly

Question 10

What are the two classes of objects in heliocentric orbits

Answer 10

Asteroids and comets

Question 11

Asteroid vs Comet

Answer 11

• Asteroids generally have orbits with smaller semi-major axes than those of comets
• Reside in the asteroid belt
• Comets have large orbits (elliptical, parabolic or hyperbolic) with larger eccentricity
• K2 therefore tells us they spend most of their time far from the Sun, moving very slowly.
• When comets approach the Sun, they get heated up and star ejecting gas. That’s when we see them

Question 12

Explain Perihelion

Answer 12

Point where a planet is closest to the Sun and has maximum orbital speed

Question 13

Explain Aphelion

Answer 13

Point where a planet is farthest from the Sun and has minimum orbital speed

Question 14

Explain why Newton had to determine the exact nature of the attraction

Answer 14

• Explain why/how planets move as described by Kepler’s Laws
• Predict correct behaviour of moving/falling bodies on Earth

Question 15

Breifly explain Kepers 3rd law

Answer 15

P^2 = a^3

• P is measured in years, and a is measured in astronomical units (AU), the two sides of the proportionality relation become equal to one another
• Says that a planet’s orbital period squared is proportional to the semi-major axis of its orbit cubed,

Question 16

Explain Keplers first 2 law

Answer 16

• Kepler’s first two laws of planetary motion describe the shape of a planet’s orbit and allow us to calculate the speed of its motion at any point in the orbit
• Second law deals with the speed with which each planet moves along its ellipse, also known as its orbital speed

-First law said that the orbits of all the planets are ellipses