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Reil [10]
3 years ago
7

The first artificial satellite to orbit the Earth was Sputnik I, launched October 4, 1957. The mass of Sputnik I was 83.5 kg, an

d its distances from the center of the Earth at apogee and perigee were 7330 km and 6610 km, respectively. Find the difference in gravitational potential energy for Sputnik I as it moved from apogee to perigee.
Physics
1 answer:
9966 [12]3 years ago
4 0

Answer:

-4.941*10^8J.

Explanation:

To solve this exercise it is necessary to take into account the concepts related to gravitational potential energy, as well as the concept of perigee and apogee of a celestial body.

By conservation of energy we know that,

\Delta U = \Delta_{perogee}-\Delta_{Apogee}

Where,

U= \frac{-GmM_e}{r}

Replacing

\Delta U = \frac{-GmM_e}{r_p}- \frac{-GmM_e}{r_a}

\Delta U = GmM_e (\frac{1}{r_A}-\frac{1}{r_p})

Our values are given by,

m = 85.5Kg

M_e = 5.97*10^{24}Kg

r_A = 7330Km

r_p = 6610Km

G = 6.67*10^{-11}Nm^2/Kg^2

Replacing at the equation,

\Delta U = (6.67*10^{-11})(85.5)(5.97*10^{24}) (\frac{1}{7330}-\frac{1}{6610})

\Delta U = -4.941*10^8J

Therefore the Energy necessary for Sputnik I as it moved from apogee to perigee was -4.941*10^8J.

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Answer:

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b) m₁ << m₂   F₂ₓ =0

Explanation:

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     ∑ F = m a

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we must write the expression for the center of mass

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now let's use the derivatives

      a_{cm} = d² x_{cm}/dt² = 1 / M (m₁ a₁ + m₂a₂)

where M is the total mass M = m₁ + m₂

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               0 = 1 / M (m₁ a₁ + m₂a₂)

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   F₁ₓ = -F₂ₓ

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      acm = d2 xcm / dt2 = 1 / M (m1 a1 + m2a2)

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               m1 a1 = - m 2 a2

with the initial condition, we can despise m₁, therefore

                0 = m₂a₂

 if we use Newton's second law

              F₂ = 0

       

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The correct answer between all the choices given is the last choice or letter D. I am hoping that this answer has satisfied your query and it will be able to help you in your endeavor, and if you would like, feel free to ask another question.

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3 years ago
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