1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
jarptica [38.1K]
2 years ago
9

Io and Europa are two of Jupiter's many moons. The mean distance of Europa from Jupiter is about twice as far as that for Io and

Jupiter. By what factor is the period of Europa's orbit longer than that of Io's?
TEu/TIo =
Physics
1 answer:
Anastaziya [24]2 years ago
6 0

The universal gravitation law and Newton's second law allow us to find that the answer for the relation of the rotation periods of the satellites is:

        \frac{T_{Eu}}{T_{Io}} = 2.83

The universal gravitation law states that the force between two bodies is proportional to their masses and inversely proportional to their distance squared

           F = G  \frac{Mm}{r^2}

Where G is the universal gravitational constant (G = 6.67 10⁻¹¹ \frac{N m^2 }{kg^2}), F the force, m and m the masses of the bodies and r the distance between them

Newton's second law states that force is proportional to the mass and acceleration of bodies

          F = m a

Where F is the force, m the mass and the acceleration

In this case the body is the satellites of Jupiter and the planet,

            G \frac{Mm}{r^2} = m a

Suppose the motion of the satellites is circular, then the acceleration is centripetal

           a = \frac{v^2}{r}r

Where v is the speed of the satellite and r the distance to the center of the planet

     

we substitute

      G \frac{Mm}{r^2} = m \frac{v^2}{r}  \\G \frac{M}{r}  = v^2

Since the speed is constant, we can use the uniform motion ratio

      v = \frac{\Delta x}{t}

In the case of a complete orbit, the time is called the period.

The distance traveled is the length of the orbit circle

           Δx = 2π r

We substitute

           G \frac{M}{r} = (\frac{2 \pi  r}{T} )^2 \\T^2 = (\frac{4 \pi ^2}{GM}) \ r^3

           

Let's write this expression for each satellite

Io satellite

Let's call the distance from Jupiter is  

            r = r_{Io}  

           T_{Io}^2 = (\frac{4 \pi ^2}{GM} ) \ r_{Io}^3TIo² = (4pi² / GM) rIo³

Europe satellite

Distance from Jupiter  is

         r_{Eu} = 2 \ r_{Io}

We calculate

         T_{Eu} = ( \frac{4\pi ^2 }{GM} (2 \ r_{Io})^3\\T_{Eu} = ( \frac{4 \pi ^2 }{GM}) r_{Io} \ 8

         

         T_{Eu}^2 = 8 T_{Io}^2            

         

         \frac{ T_{Eu}}{T_{Io}} = \sqrt{8}  = 2.83

           

In conclusion, using the universal gravitation law and Newton's second law, we find that the answer for the relationship of the relation periods of the satellites is:

        \frac{T_{Eu}}{T_{Io}} = 2.83

Learn more about universal gravitation law and Newton's second law here:

brainly.com/question/10693965

You might be interested in
The diagram below shows a 5.00-kilogram block
bixtya [17]

The name and strength of the force holding the block up is 50 N upward - Normal force.

The given parameters:

  • <em>Mass of the block, m = 5 kg</em>

The weight of the block acting downwards due to gravity is calculated as follows;

W = mg

where;

  • <em>g is acceleration due to gravity = 10 m/s²</em>

W = 5 x 10

W = 50 N <em>(</em><em>downwards</em><em>)</em>

Since the block is at rest, an a force equal to the weight of the block must be acting upwards. This force is known as normal reaction.

Fₙ = 50 N <em>(</em><em>upwards</em><em>)</em>

Thus, the name and strength of the force holding the block up is 50 N upward - Normal force.

Learn more about Normal force here: brainly.com/question/14486416

4 0
2 years ago
Read 2 more answers
Main function of gametes?
vichka [17]
Sexual reproduction. thats the answer i think
3 0
2 years ago
A plastic box has an initial volume of 2.00 m 3 . It is then submerged below the surface of a liquid and its volume decreases to
nikitadnepr [17]

Answer:

Volume strain is 0.02

Explanation:

Volume strain is defined as the change in volume to the original volume.

It is given that,

Initial volume of the plastic box is 2 m³

It is then submerged below the surface of a liquid and its volume decreases to 1.96 m³

We need to find the volume strain on the box. It is defined as the change in volume divided by the original volume. So,

\delta V=\dfrac{V_f-V_i}{V_i}\\\\\delta V=\dfrac{1.96-2}{2}\\\\\delta V=0.02

So, the volume strain on the box is 0.02.

6 0
3 years ago
How much power is used by a car engine if it does 48496 J of work in 4 min?
elena-14-01-66 [18.8K]

<em>Hope this will help u</em><em>.</em><em>.</em><em>.</em><em>.</em><em>.</em><em>✌</em><em>✌</em><em>✌</em>

8 0
3 years ago
Read 2 more answers
Like the filters falling through the air, a car on the freeway represents an object with a high Reynolds number traveling throug
Goshia [24]

Answer:

ΔF=125.22 %

Explanation:

We know that drag force on the car given as

F_D=\dfrac{1}{2}\rho C_DA v^2

C_D=Drag coefficient

A=Projected area

v=Velocity

ρ=Density

All other quantity are constant so we can say that drag force and velocity can be given as

\dfrac{F_D_1}{F_D_2}=\dfrac{v_1^2}{v_2^2}

Now by putting the values

\dfrac{F_D_1}{F_D_2}=\dfrac{v_1^2}{v_2^2}

\dfrac{F_D_1}{F_D_2}=\dfrac{50^2}{75^2}

\dfrac{F_D_1}{F_D_2}=0.444

Percentage Change in the drag force

\Delta F=\dfrac{F_D_2-F_D_1}{F_D_1}\times 100

\Delta F=\dfrac{F_D_2-0.444F_D_2}{0.444F_D_2}\times 100

\Delta F=\dfrac{1-0.444}{0.444}\times 100

ΔF=125.22 %

Therefore force will increase by 125.22  %.

3 0
3 years ago
Other questions:
  • Restate newton's first law in terms of acceleratin
    11·1 answer
  • How are different types of radiation arranged along the electromagnetic spectrum
    6·1 answer
  • When a spring is compressed, the energy changes from kinetic to potential. Which best describes what is causing this change?
    9·2 answers
  • Auroras are frequently seen
    5·1 answer
  • How do you find initial velocity?
    13·1 answer
  • Which material is likely to slow the flow of electric charges the most ? explain.
    15·2 answers
  • How would the force of gravity between two objects change if the distance
    14·1 answer
  • What is air resistance means explain it with free falling body​
    10·1 answer
  • 39. What is the change in momentum for a 5,000 kg ship in
    9·1 answer
  • Select all that apply.
    6·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!