Ay [T6.5] - Kepler's Laws

Question 1

Name law 1 of the 3 laws of planetary motion

Answer 1

The orbit of all the planets is an ellipse with the sun at one foci.

Question 2

Name law 2 of the 3 laws of planetary motion

Answer 2

An imaginary line connecting the planet to the sun “sweeps out” equal areas in equal times

Question 3

Name law 3 of the 3 laws of planetary motion

Answer 3

The square of the orbital period is proportional to the cube of it’s mean distance from the sun

T²∝R³

Question 4

Define aphelion

Answer 4

The furthest point from the sun on an orbit

Question 5

Define perihelion

Answer 5

The closest point to the sun on an orbit

Question 6

Define eccentricity

Answer 6

A measure of how stretched an elliptical orbit is

Question 7

When is the aphelion for Earth’s orbit?

Answer 7

In the summer

Question 8

When is the perihelion for Earth’s orbit?

Answer 8

In the winter

Question 9

In the 2nd law of the 3 laws of planetary motion, where is a celestial body in it’s orbit moving the slowest and where is it moving the fastest?

Answer 9

Closer to the object that it’s orbiting, the celestial body moves quicker. (It’ll have the most kinetic energy here.)

Further away from the object that it’s orbiting, the celestial body moves slower. (It’ll have the least kinetic energy here.)

Question 10

What is the equation related to Kepler’s 3rd law for anything that orbits the sun?

Answer 10

T(y)² / R(AU)³ = 1

T measured in years (y)
R measured in AU

Question 11

If T² / R³ = k, and you’re using the data of 2 objects that orbit the same object, what can you do?

Answer 11

If constant doesn’t change, you can remove it.

(T1²) / (R1³) = (T2²) / (R2³)

Question 12

The k in Kepler’s 3rd law depends on what?

Answer 12

The mass of the central object - the bigger the mass, the smaller k is

Question 13

What is the ratio of masses equations for Kepler’s 3rd law?

Answer 13

k1 / k2 = m2 / m1

1 = the sun
2 = the new star

Question 14

In Newton’s Universal Law of Gravitation, the size of the force acting between bodies depends on what things?

Answer 14

The mass of each body in the situation

The distance between the two bodies

Question 15

In Newton’s Law of Universal Gravitation, what is force proportional to (both words and equations)?

Answer 15

Force is directly proportional to both masses of both objects, and force is inversely proportional to distance squared

F ∝ (m1 × m2) / r²

Question 16

In Newton’s Law of Universal Gravitation, what happens if you double one of the masses of one of the objects?

Answer 16

The magnitude of the forces on each object doubles

Question 17

In Newton’s Law of Universal Gravitation, what happens if you double both masses of both objects at the same time?

Answer 17

The magnitude of the forces on each object quadruples

Question 18

In Newton’s Law of Universal Gravitation, what happens if you half the distance between the objects?

Answer 18

The magnitude of the forces on each object quadruples

Question 19

In Newton’s Law of Universal Gravitation, what happens if you double the distance between the objects?

Answer 19

The magnitude of the forces on each object is divided by 4

Question 20

In Newton’s Law of Universal Gravitation, what happens if you triple the distance between the objects?

Answer 20

The magnitude of the forces on each object is divided by 9