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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

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if a ball is thrown straight up into the air with an initial velocity of 8080 ft/s, its height in feet after tt second is given
yanalaym [24]

The average velocity for the time period beginning when t=1 and lasting

(i) 0.01 seconds = 63.84 ft/s

(ii) 0.001 seconds = 63.984 ft/s

Given that a ball is thrown with an initial velocity = 80 ft/s

Let 'y' be the height in feet after 't' seconds.

Given,  y=80t-16t^2 gives the height in 't' seconds.

Average velocity = Rate of change of distance

                             = Change in distance/Change in time.

The initial time can be taken as 0 s.

When t =1 s, y = 80 - 16 = 64 ft

(1)  t = 0.01 s

    y = 80 x 0.01 - 16 x 0.01 x 0.01 = 0.7984 ft

    Average velocity = (64 - 0.7984) / (1 -0.01) = 63.84 ft/s

(2) t = 0.001 s

    y = 80 x 0.001 - 16 x 0.001 x 0.001 = 0.079984 ft

    Average velocity = (64 - 0.079984) / (1 -0.001) = 63.984 ft/s

The question is incomplete. Find out the complete question below:

If a ball is thrown straight up into the air with an initial velocity of 80 ft/s, it height in feet after t second is given by  y=80t-16t^2 .Find the average velocity for the time period beginning when t=1 and lasting

(i) 0.01 seconds

(ii) 0.001 seconds

Learn more about average velocity at brainly.com/question/6504879

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Calculate the amount of heat (in kJ) required to convert 97.6 g of water to steam at 100° C. (The molar heat of vaporization of
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221.17 kJ

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N = 97.6 ÷ 18

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This is approximately 221.17 kJ

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Answer:

demand (an amount) as a price for a service rendered or goods supplied.

Explanation:

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The Jensens dccided to spend their family vaeation white water rafting. During one segment of their trip down the river, the raf
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Answer:

24,187.04 J ≈ 24,200 J

Explanation:

mass (m) = 544 kg

initial speed (u) = 6.75 m/s

final speed (v) = 15.2 m/s

change in height (Δh) = -14 m (negative sign is because there is a decrease in height )

acceleration due to gravity (g) = 9.8 m/s^{2}

How much work was done on the raft by non conservative forces?

work done = change in energy of the system = change in kinetic energy + change in potential energy

work done = (0.5m(v^{2} -u^{2} )) + (mgΔh)

work done = (0.5x544x(15.2^{2} -6.75^{2} )) + (544 x 9.8 x (-14))

work done = 50449.76 - 74,636.8

work done = 24,187.04 J ≈ 24,200 J

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