Question

activity c: radius and period
get the gizmo ready

• click reset
• set the sun mass to medium, close to the mass of our sun

instruction: keplers last law relates the period (t) of a planet, or the time it takes to complete an orbit, to the planets orbital radius (a), or average distance from the sun
question: how does the period of a planet relate to its average distance from the sun?

1. predict: how do you expect the period of a planet to change as its average distance from the sun increases?
2. measure: place the planet at - 4.00 au and set the velocity to - 15.00 km/s (does not have to be exact). click play, and then click pause when the planet completes one orbit

a. what is the approximate period of the planet in days?
b. select the table tab and click record data. what is the actual period (t) of the planet in earth days and years? ____ days ____ years
c. what is the orbital radius (a) of the planet?
d. click reset. place the planet at - 2.00 au and set the velocity to - 20.0 km/s. click play and record data. what is the period now? ____ days ____ years
e. what is the new orbital radius?
f. how does the distance between the planet and the sun affect its period?

1. gather data: experiment with the gizmo to create a series of larger and larger orbits. record each orbits radius (a) and period (t). leave the last two columns blank for now

orbit	a (au)	t (years)
2
3
4
5

Explanation:

Step1: Recall Kepler's third law

Kepler's third - law states that $T^{2}\propto a^{3}$, where $T$ is the period of the planet's orbit and $a$ is the semi - major axis (average distance from the Sun).

Step2: Answer prediction question

As the average distance ($a$) of a planet from the Sun increases, according to $T^{2}\propto a^{3}$, the period ($T$) of the planet will increase.

Step3: For part 2A

This requires actual measurement from the Gizmo simulation. Without running the simulation, we can't give a numerical answer. But conceptually, we would observe the time it takes for one orbit.

Step4: For part 2B

Again, requires simulation data. After running the simulation and recording from the table, we can convert the period from days to years (1 year = 365.25 days approximately).

Step5: For part 2C

The orbital radius ($a$) is given as 4.00 AU in the setup.

Step6: For part 2D

After resetting and new setup (planet at 2.00 AU), run the simulation to get the period in days and convert to years.

Step7: For part 2E

The new orbital radius is 2.00 AU as given in the setup.

Step8: For part 2F

Based on Kepler's third law $T^{2}\propto a^{3}$, as the distance ($a$) between the planet and the Sun increases, the period ($T$) of the planet's orbit increases.

Answer:

1. The period of the planet will increase as its average distance from the Sun increases.
2. A. (To be filled by running the Gizmo simulation)

B. (To be filled by running the Gizmo simulation and converting units)
C. 4.00 AU
D. (To be filled by running the Gizmo simulation and converting units)
E. 2.00 AU
F. As the distance between the planet and the Sun increases, the period of the planet's orbit increases.

1. (To be filled by running multiple simulations with the Gizmo to gather data on different orbits)