Kepler's Third Law can be expressed mathematically as follows:
[tex]\[ T^2 = k \cdot d^3 \][/tex], the constant of proportionality for our planet is approximately [tex]1.711 \times 10^{-19} \text{ miles}^{-3}[/tex] and the period of Neptune is approximately [tex]6.252 \times 10^4 \text{ miles}^{4.5}[/tex].
(a) Expressing Kepler's Third Law as an equation:
Kepler's Third Law can be expressed mathematically as follows:
[tex]\[ T^2 = k \cdot d^3 \][/tex]
where T is the period of the planet (in units of time), d is the average distance of the planet from the sun (in units of length), and k is the constant of proportionality.
(b) Finding the constant of proportionality:
To find the constant of proportionality, we can use the fact that for our planet (Earth), the period is approximately 365 days and the average distance is about 93 million miles.
Using these values, we can plug them into the equation:
[tex]\[ (365 \text{ days})^2 = k \cdot (93 \text{ million miles})^3 \][/tex]
Simplifying the equation, we have:
[tex]\[ 133,225 = k \cdot (778,500,000,000,000,000,000,000 \text{ miles}^3) \][/tex]
Dividing both sides of the equation [tex](778,500,000,000,000,000,000,000 \text{ miles}^3)[/tex], we get:
[tex]k = 133,225/(778,500,000,000,000,000,000,000 miles^3)[/tex]
Calculating this expression, we find:
[tex]\[ k \approx 1.711 \times 10^{-19} \text{ miles}^{-3} \][/tex]
Therefore, the constant of proportionality for our planet is approximately [tex]1.711 \times 10^{-19} \text{ miles}^{-3}[/tex].
(c) Finding the period of Neptune:
Given that the average distance of Neptune from the sun is about 2.79 × 10^9 miles, we can use Kepler's Third Law to find the period of Neptune.
Using the equation [tex]\[ T^2 = k \cdot d^3 \][/tex] and plugging in the values:
[tex]\[ T^2 = (1.711 \times 10^{-19} \text{ miles}^{-3}) \cdot (2.79 \times 10^9 \text{ miles})^3 \][/tex]
Simplifying the expression, we have:
[tex]\[ T^2 = 1.711 \times 10^{-19} \text{ miles}^{-3} \cdot 2.79^3 \times 10^{9 \cdot 3} \text{ miles}^{3 \cdot 3} \][/tex]
[tex]\[ T^2 = 1.711 \times 2.79^3 \times 10^{-19 + 27} \text{ miles}^9 \][/tex]
[tex]\[ T^2 \approx 1.711 \times 22.796 \times 10^{8} \text{ miles}^9 \][/tex]
[tex]\[ T^2 \approx 39.108 \times 10^{8} \text{ miles}^9 \][/tex]
Taking the square root of both sides to solve for T, we get:
[tex]\[ T \approx \sqrt{39.108 \times 10^{8}} \text{ miles}^{4.5} \][/tex]
Calculating the square root, we find:
[tex]\[ T \approx 6.252 \times 10^4 \text{ miles}^{4.5} \][/tex]
Therefore, the period of Neptune is approximately [tex]6.252 \times 10^4 \text{ miles}^{4.5}[/tex]
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PlEaSe HeLp MeE
What is the gpe of a rock weighing 100N that is sitting on top pf a hill 300 m high?
Answer:
Gpe = 30000J
Explanation:
Given the following data;
Weight = 100N
Height = 300m
To find the gravitational potential energy (gpe);
Gravitational potential energy can be defined as an energy possessed by an object or body due to its position above the earth surface.
Mathematically, potential energy is given by the formula;
[tex] G.P.E = mgh[/tex]
Where,
G.P.E represents potential energy measured in Joules.
m represents the mass of an object.
g represents acceleration due to gravity measured in meters per seconds square.
h represents the height measured in meters.
Gpe = mgh
But weight = mg = 100N
Substituting into the equation, we have:
Gpe = 100*300
Gpe = 30000J
What is the kinetic energy of a 5kg ball that is rolling 3m/s?
Answer:
22.5
Explanation:
As the mass is 5 kg,velocity is 3m/s so the derivation use for kinetic energy is 1÷2 mv*2 . By this derivation we will find out the kinetic energy
the organelles are giving their job description to you can you identify which organelle are they? write your answers in your answer sheet.
1. Hi! My responsibility is to add stability and protection to plant cells. What am I?
2. Hi! produce proteins inside the cell. What am I ?
3. Hello! I have a green pigment called the clorophyll. I also absorb solar energy to do the process of photosynthesis. What am I?
4. Good morning po! my work is to store food materials and excretes waste materials. I take a large space on plants. I make the leaves of plants fresh. what am i?
5. Hi! All organelles are embedded in me. I am a "jelly- like" substance. What am I?
Please real answer
1. cell wall?
2. ribosomes?
3. chloroplast
4. vacuoles
5. cytoplasm
A tractor pulls a 1,000 kg wagon with a force of 4,000N. What is the wagon’s acceleration in m/s2? *
Answer:
4m/s^2
Explanation:
acceleration=force/mass
therefore a=4000/1000
=4m/s^2
what is the wavelength of the wave
Explanation:
it is equal to the speed (v) of a wave train in a medium divided by its frequency (f): λ = v/f. Waves of different wavelengths.
Answer:
It is measured in the direction of the wave. Description: Wavelength is the distance from one crest to another, or from one trough to another, of a wave (which may be an electromagnetic wave, a sound wave, or any other wave).
the force required to lift a load of 800 Newton by using a Lever having a mechanical advantage of 1.6 is
Answer:force required to lift the load = 500N
Explanation:
Mechanical advantage for a lever is given by the formulae
= force output/force input
or
Mechanical Advantage = Load / Effort
where
Force output / Load= 800 N
mechanical advantage = 1.6
Force input / Effort =??
Force input= Force output /Mechanical advantage
= 800N / 1.6
=500N
OR
Effort = Load/ Mechanical Advantage = 800/ 1.6 = 500N
An object spins with an angular momentum of 8.9 kg⋅m2 /s. A torque on the object causes it to slow to a stop in 5.2 s. What was the angular impulse on the object? What was the average torque on it? Analyze and Sketch the Problem
List Knowns and Unknowns Knowns Unknowns Li = ____________________ Lf = ________________ _____________ = ? ∆t = _________________ _____________ = ? SOLVE FOR THE UNKNOWNS a. Determine the angular impulse from the change in angular momentum b. Apply the impulse-momentum theorem to determine the Torque EVALUATE THE ANSWER Is the unit of torque correct? ______________________________________________________________ Is the magnitude of the torque realistic? _____________________________________________________
Answer:
Explanation:
Li = 8.9 kg m² /s , Lf = 0
Time = Δt = 5.2 s
Angular impulse = change in angular momentum = Li - Lf
= 8.9 - 0 = 8.9 kg.m²/s .
Average torque = angular impulse / time
= 8.9 / 5.2 = 1.711 kg m² / s²
Li = 8.9 kg m² /s , Lf = 0
Δt = 5.2 s
unit of torque = force x distance = mass x acceleration x distance
= kg . m /s² x m
= kg m² / s²
give three example what are the aims of each team in playing basketball?
Answer:
The main objective of basketball is to make a goal and score points.Each team should not only try to make a goal and prevent the opposite team from taking control of the ball, but should also try to protect the basket in their court and prevent the opponent from making a goal.
hope that helps..
which two criteria are least important for engineers to consider when developing a process to produce an important chemical
Answer:
Chemical engineering is a multi-disciplinary branch of engineering that combines natural and experimental sciences such as chemistry and physics, along with life sciences such as biology, microbiology and biochemistryplus mathematics and economics to design, develop, produce, transform, transport, operate
Explanation:
Answer:
A. the process needs to produce significant amounts of ammonia
C. the process needs to be able to be performed safely
Explanation:
a p e x
What causes a liquid to freeze? A. When particles speed up and get closer together. B. When particles stop moving. C. When particles slow down and get closer together. D. When particles speed up and get farther apart.
Answer:The answer is C
Explanation:
what type force does this depict?
Answer:
c. gravitational force
Explanation:
How many total molecules are present in the formula below
2H2O
I'm guessing 6.
the coefficient of two turns our hydrogen into 4 and our oxygen into 2 which makes a total of 6 molecules.
plsss anyone help I BEG. its not that hard im just lazy and don't feel like thinking3
Answer:
Well I think you should think
example of unlile parallel forces
Answer:
Explanation:
In mechanical engineering, a parallel force system is a situation in which two forces of equal magnitude act in the same direction within the same plane, with the counter force in the middle. An example of this is a see saw.
Forces which are parallel and acting a similar way are called like parallel forces. Like Parallel forces are the forces that are parallel to each other and have the same direction. Unlike parallel forces are the forces that parallel yet have directions inverse to each other.
when the parallel force system is a situation in which two forces of equal magnitude act in the same direction within the same plane, Two forces that are parallel can either be in the same direction or in opposite directions.
(hope this helps can i plz have brainlist :D hehe)
Select the correct answer.
Which pair of atoms has the highest electronegativity difference?
OA.
H-S
B.
H-Cl
o c.
N-H
OD.
О – Н
O E.
C-H
Answer:O – H
Explanation:
calculate the change in gravitational potential energy of a stone of mass 0.55 kg as it falls through a distance of 2.7 m. ignore air resistance (mention formula)
Answer:
14, 85 J
Explanation:
The formula of potential Energy (P.E.) is
P.E. = m * g * h, where m is the mass in kilograms, g is the acceleration due to gravity (about 10 m / [tex]s^{2}[/tex] at the surface of the earth) and h is the height in meters.
Here P.E. is 0,55 kg * 10 m/s * 2,7 m = 14, 85 J
Wave Properties
With the help of their science teacher, Kaden and Mariam made a machine that can move a slinky back and forth. This motion
creates a fast-moving wave in the slinky. The image below is a model of a wave that is generated by the machine. The frequency of
the wave modeled in the image is 4 Hz.
3 m
What is the speed of the wave?
OA. 24 m/s
ОВ.
1.25 m/s
OC.
0.75 m/s
OD
12 m/s
the wave has a speed of 12 m/s.
Explanation:
Speed is directly proportional to wavelength and frequency. The wave has a frequency of 4 Hz. One Hertz (Hz) is equal to one cycle per second. The image shows that the wave has a wavelength of 3 m. Using the given speed and frequency, the wavelength can be calculated as shown below.
speed= wave length x frequency
speed = 3m x 4Hz
speed = 12m m/6
Una pieza de platino metalico con densidad 21.5 g/cm3 tiene un volumen de 4.49 cm3. Cual es su masa
Answer:
m = 96.53 grams
Explanation:
Given that,
The density of metallic platinum, d = 21.5 g/cm³
Volume, V = 4.49 cm³
We need to find the mass. Let it is m. We know that the density is equal to the mass per unit volume. So,
[tex]d=\dfrac{m}{V}\\\\m=d\times V\\\\m=21.5\times 4.49\\\\m=96.53\ g[/tex]
So, the required mass is 96.53 grams.
One of the largest planes ever to fly, and the largest to fly frequently, is
the Ukrainian-built Antonov An-124 Ruslan. Its wingspan is 73.2 m
and its length is 69.2 m. The gravitational potential energy associated
with the plane at an altitude of 1.45 km is 3.36 x 10^9 J. What is the airpanes mass
Show work pls :)
The gravitational potential energy associated with the plane is 2.36 x [tex]10^{5}[/tex] J
What is gravitational potential energy?Gravitational potential energy is energy an object possesses because of its position in a gravitational field.
It is given by P.E = mgh
where m = mass
g= acceleration due to gravity
h = height of the object
Here,
h = 1.45km = 1450 m
P.E = 3.36 x [tex]10^{9}[/tex] J
g = 9.8m/[tex]s^{2}[/tex]
therefore, m = P.E/ gh = (3.36 x [tex]10^{9}[/tex]s J)/ 9.8 x 1450
m = 2.36 x [tex]10^{5}[/tex]
Hence mass of the airplane is 2.36 x [tex]10^{5}[/tex]
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Importance of Forest
Answer:
to help keep fresh air
Explanation:
what is the unit scientist use to measure energy?
answer:
scientists use a measurement called BTU to measure energy
Energy is defined as ____________.
The ability of an object to produce a change in the environment or itself
motion
the effort required to perform work
power
Answer:
The effort required to perform work
Explanation:
Two photographers are competing for business in town. Andrea uses only film photography and Keira uses only digital photography. Keira claims that the digital technology is superior, and her advertisement claims that the images can be stored, shared, and copied more easily. They can even be sent long distances using a series of wave pulses to transmit the information. Andrea replies that digital images can be stolen and altered more easily.
Do the advantages outweigh the disadvantages, or do both sides have valid points? Support your answer with at least three reasons
There is no right or wrong answer, your teacher wants you to support your own answer with points. As long as the reasons make logical sense you are fine.
I think they both have valid points. Their replies are both true, but from a buyer's perspective who would you purchase services from? You would get different answers depending on who you ask.
If you choose to go old school, obviously you get an actual photo that can be stored physically. This means it is a memory that can be preserved, and it might feel more nostalgic being able to touch the photo.
On the other hand, a digitally stored photo can be altered (photoshop), but it is forever as long as the internet still exists. A physical photo would fade with time, which doesn't happen with a digital photo.
It is definitely easier to argue that digital photography has more advantages (they do, it is why nobody uses film anymore)
Points you can consider:
Can be transferred to the other side of the world instantly
Ability to make copies and print as many photos as you want
Can be stored on cloud/devices and be like that forever
Compare them with film photography to give a more solid response.
What is the main reason people and bears slip and fall on ice, be careful when outside in the snow/ice.
Answer:
Both ice and snow have a lower coefficient of friction in comparison with grass, wood or pavement.
Explanation:
The main reason why people and bears, slip and fall on ice/snow is that both ice and snow have a lower coefficient of friction in comparison with grass, wood or pavement. We present below a comparative chart of coefficients of friction associated with different materials:
Material Coefficient of Friction - Static
Ice/Snow 0.05 - 0.3
Wood 0.2 - 0.6
Asphalt 0.5 - 0.7
Grass 0.3 - 0.5
An element carries a_____charge
Answer:
The charge of an element is equal to the number of protons minus the number of electrons. The number of protons is equal to the atomic number of the element given in the periodic table. The number of electrons is equal to the atomic number minus the charge of the atom.
Explanation:
Answer:
hydrogen sometimes has a charge of zero or (less commonly) -1. Although noble gas atoms almost always carry a charge of zero, these elements do form compounds, which means they can gain or lose electrons and carry a charge.
Explanation:
Please help with this !!!!!!
Answer:
answer is d from my guess
A 9Ω resistance is cut into three equal parts and connected in parallel. Find the equivalent resistance of the combination.
Answer:
the ans i 1 ohm
Explanation:
if i cut a resistor of 9 ohm into 3 equal parts then each resistor will have a resistance of 3 ohm and if they are in parallel combination the net resistance will be R
so 1/R=1/R1+1/R2+1/R3
1/R=1/3+1/3+1/3
R=1
What is potential energy?
Motion Quiz 1
Part I. Vocabulary (5 points each)
1. The location of an object.
2. A change in the position of an object in reference to a starting point. 3. A change in the position of an object that includes distance and direction. 4. North, south, right, and down are all examples of ________. 5. How fast or slow something moves over a given distance per unit of time. 6. A unit of measurement for time.
Part II. Multiple Choice (10 points each)
Direction
Displacement Meters
Minutes
Motion
Position
Speed
A toy robot moved from a starting point, traveling in a straight line at different speeds and then turning around and returning to the starting point at different speeds.
7. What is the total distance that the toy robot traveled?
A. 12 m
B. 24 m
C. 48 m
D. 96 m
8. A cyclist travels 3 km north in 25 minutes. What does this information describe?
A. mass
B. force
C. motion
D. gravity
9. A book is lying on a seat in a car that is moving at 50 kilometers per hour (km/h). The driver says that the book is not moving. An outside observer says the book is moving at 50 km/h because it is in the car. Which is the most logical conclusion for these two statements?
A. Motion is detected only if the car accelerates and is measured by the observer.
B. Motion is absolute, and the driver is incorrect saying that the book has no motion.
C. Motion is relative to a given frame of reference, and both the driver and observer are correct.
D. Motion is constantly changing so neither person’s statement will be correct when the car slows down.
10. Which measurement describes the speed of a rubber ball?
A. 5 cm
B. 10 m/s
C. 15 newtons
D. 50 grams
11. A change in the position of an object as time changes best describes
A. direction.
B. waves.
C. motion.
D. frequency.
12. A school bus moves past a parked car at a speed of 30 km/h. Which of the following best describes the observation made by a passenger on the bus?
A. The car appears to be moving 30 km/h in the same direction as the bus.
B. The car appears to be moving 30 km/h in the opposite direction of the bus. C. The car appears to be moving 15 km/h in the same direction as the bus.
D. The car appears to be moving 15 km/h in the opposite direction of the bus.
13. Calculate the speed when the distance travelled is 800 km and the time is 40 seconds. A. 200 km/sec
B. 320 m/sec
C. 20 km/sec
D. 32 m/sec
Two spheres are moving towards each other. Which of the following is the
best evidence that the spheres have transferred energy from one to the other?
A.The friction of the surface decreases
B.Gravity is always acting on the spheres
C.The motion of the sphere changes
Or
D.Both of the spheres have the same mass
Answer:
D
Explanation:
If they are both moving at the same speed then its D.