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At apogee, the center of the moon is 406,395 km from the center of Earth and at perigee, the moon is 357,643 km from the center of Earth. What is the orbital speed of the moon at perigee and at apogee?

Respuesta :

Answer:

orbital speed of the moon v = 1.08 km/s

orbital speed of the moon v  = 9.5 × 10² m/s

Explanation:

given data

At apogee moon distance r  = 460,395 km from the earth

at perigee moon distance r  = 357,643 km from the earth

solution

we consider here orbital period is 27.3 day

we get here orbital speed of the moon that is

orbital speed of the moon v  = rω

orbital speed of the moon v  = [tex]\frac{2\pi r}{T}[/tex]   ...................1

put here value for apogee in equation 1

orbital speed of the moon v  = [tex]\frac{2\pi *406395}{2358720}[/tex]

here we know 1 day = 86,400 second so 27.3 day = 2358720 seconds

orbital speed of the moon v = 1.08 km/s

and

now we put put here value for perigee in equation 1

orbital speed of the moon v  = [tex]\frac{2\pi *357643*10^3}{2358720}[/tex]  

orbital speed of the moon v  = 9.5 × 10² m/s

oladayoademosu

We know that the centripetal force on the moon, F equals the gravitational force of attraction between the earth and moon, F'

F = mv²/r where

  • m = mass of moon,
  • v = orbital speed of moon and
  • r = radius of orbit.

Also, F' = GMm/r² where G = 6.67 × 10⁻¹¹ Nm²/kg², M = mass of earth = 5.972 × 10²⁴ kg, m = mass of moon and r = radius of orbit

Since F = F', we have

mv²/r = GMm/r²

v² = GM/r

v = √(GM/r)

Orbital speed at apogee

The orbital speed at apogee is 990 m/s

Now, when r = radius at apogee = 406395 km = 406395000 m = 4.06395 × 10⁸ m

v = √(GM/r)

v = √(6.67 × 10⁻¹¹ Nm²/kg² × 5.972 × 10²⁴ kg/4.06395 × 10⁸ m)

v = √(39.83324 × 10¹³ Nm²/kg/4.06395 × 10⁸ m)

v = √(9.802 × 10⁵ Nm/kg)

v = √(98.02 × 10⁴ Nm/kg)

v = 9.9 × 10² m/s

v = 990 m/s

The orbital speed at apogee is 990 m/s

Orbital speed at perigee

The orbital speed at perigee is 1.06 km/s

Also, when r = radius at perigee = 357,643 km = 357643000 m = 3.57643 × 10⁸ m

v = √(GM/r)

v = √(6.67 × 10⁻¹¹ Nm²/kg² × 5.972 × 10²⁴ kg/3.57643 × 10⁸ m)

v = √(39.83324 × 10¹³ Nm²/kg/3.57643 × 10⁸ m)

v = √(11.138 × 10⁵ Nm/kg)

v = √(111.38 × 10⁴ Nm/kg)

v = 10.554 × 10² m/s

v = 1.0554 × 10³ m/s

v = 1.0554 km/s

v ≅ 1.06 km/s

The orbital speed at perigee is 1.06 km/s

Learn more about orbital speed of the moon here:

https://brainly.com/question/4346822

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