Gravitational interactions play a fundamental role in shaping the dynamics of our solar system. As objects with mass exert gravitational forces on each other, these interactions influence celestial bodies' orbits, movements, and stability.

Question

Figure 1. Planet Nine.

Planet Nine, also known as Planet X, is a hypothetical celestial body theorized to exist in our solar system, positioned beyond the orbit of Neptune. The concept emerged to account for gravitational anomalies observed in the orbits of distant Kuiper Belt objects. If it exists, Planet Nine is believed to be a sizable planet, potentially 9.5 times the mass of Earth, and its proposed orbit would place it in the distant reaches of the Kuiper Belt.  It is believed that Planet 9 is between 400 to 800 Astronomical Units from the sun.

Figure 2. Distance of planets from the sun.

Figure 3. The mass of the planets in our Solar System.

The equation for gravitational pull is:  F=G m1m2r2

Where G is the gravitational constant of  6.674 × 10−11 Nm2kg2

m1 and m2 are the masses of objects 1 and 2

r is the distance between the objects

Correctly complete the sentences.

(5 points)
The formula for gravitational force includes two factors: 
 and
.
Based on the information provided, Earth is 
 the Sun than Planet 9.
Although Planet 9’s mass is 
 times Earth’s, the 
 has a greater impact on gravitational force because it is squared in the equation.
Question 2
The formula for weight is W= m x g
where:

W is the weight (N)
m is the mass (kg)
g is the acceleration due to gravity (m/s²)
You know that you weigh 45 kg. What would your weight be on Saturn if the acceleration due to gravity on Saturn is 10.44 m/s²?
Show your work.

(1 point)
W=m×g = 
 
N
Question 3
If scientists were able to prove that Planet 9 was indeed out there, between which two planets would Planet 9 fall if you ordered the planets by gravitational pull? Why did you choose those two planets?(1 point)
Responses

Between Jupiter and Saturn
Between Jupiter and Saturn

Between Earth and Uranus
Between Earth and Uranus

Between Venus and Earth
Between Venus and Earth

Uranus and Neptune
Uranus and Neptune
Question 4
Planet 9 is assumed to be around 9.5 times more massive than Earth.  If we were to add planet 9 to Table #2 to which point would we graph it on the X-axis?(1 point)
Responses

95
95

0.95
0.95

9.5
9.5

950
950
Question 5
Suppose an object with a mass of 100 kg is placed on the hypothetical Planet 9. How would the gravitational force on this object compare to a similar object on Earth? (2 points)
Planet 9 would have about a 9.5 times 
 gravitational interaction with the object because of its mass. The object would have a 
 weight on Planet 9 than Earth. 
Question 6
Correctly completed the sentences. (3 points)
Because Planet 9 has a gravity that is much stronger than Earth’s, a human traveler would likely move 
 and with 
 effort because 
.
Question 7
Use the figure to answer the question.

Figure 3. Planet mass.

Rank the planets in order by mass. Place the planet with the highest mass at the top of the list, and the planet with the lowest mss at the bottom of the list.

(4 points)
Arrange responses in the correct order to answer the question. Select a response, navigate to the desired position and insert response at that position. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can be moved using the up and down arrow keys or by dragging with a mouse.
Question 8
If you dropped a feather and a bowling ball at the same time in an environment with no air resistance, how would they fall?(1 point)
Responses

The bowling ball would land first. 
The bowling ball would land first.

The feather would land first. 
The feather would land first.

The bowling ball and feather would land at the same time.

GPT-4o mini · Answer

Here are the answers to your questions based on the provided information:

Question 1

The formula for gravitational force includes two factors: the masses of the objects (m1 and m2) and the distance between them (r).

Based on the information provided, Earth is closer to the Sun than Planet 9.

Although Planet 9’s mass is 9.5 times Earth’s, the distance (r) has a greater impact on gravitational force because it is squared in the equation.

Question 2

To calculate weight on Saturn: \[ W = m \times g \]
\[ W = 45 , \text{kg} \times 10.44 , \text{m/s²} \]
\[ W = 470.8 , \text{N} \]

Question 3

If scientists were able to prove that Planet 9 was indeed out there, between which two planets would Planet 9 fall if you ordered the planets by gravitational pull?

Between Jupiter and Saturn

Why: Jupiter has the strongest gravitational pull among the planets, and Saturn is next. Given Planet 9's significant mass, it would likely have a gravitational pull greater than that of Saturn, but less than Jupiter.

Question 4

Planet 9 is assumed to be around 9.5 times more massive than Earth. If we were to add Planet 9 to Table #2, to which point would we graph it on the X-axis?

9.5

Question 5

Suppose an object with a mass of 100 kg is placed on the hypothetical Planet 9. How would the gravitational force on this object compare to a similar object on Earth?

Planet 9 would have about a 9.5 times stronger gravitational interaction with the object because of its mass. The object would have a greater weight on Planet 9 than on Earth.

Question 6

Because Planet 9 has a gravity that is much stronger than Earth’s, a human traveler would likely move more slowly and with more effort because the gravitational pull is stronger, making it harder to lift and move limbs.

Question 7

Rank the planets in order by mass:

Jupiter (highest mass)
Saturn
Uranus
Neptune
Earth
Venus
Mars
Mercury (lowest mass)

(Note: The specific order can vary slightly depending on the exact mass values, but this is the general consensus based on their typical masses.)

Question 8

If you dropped a feather and a bowling ball at the same time in an environment with no air resistance, how would they fall?

The bowling ball and feather would land at the same time.

In the absence of air resistance, all objects fall at the same rate regardless of their mass.