Your starship, the Aimless Wanderer, lands on the mysterious planet Mongo. As chief scientist-engineer, you make the following measurements:

Question

Your starship, the Aimless Wanderer, lands on the mysterious planet Mongo. As chief scientist-engineer, you make the following measurements: A 2.50 kg stone thrown upward from the ground at 13.0 m/s returns to the ground in 4.50 s; the circumference of Mongo at the equator is 2.00×10^5km; and there is no appreciable atmosphere on Mongo. The starship commander, Captain Confusion, asks for the following information:

a. What is the mass of Mongo?
b. If the Aimless Wanderer goes into a circular orbit 30,000 km above the surface of Mongo, how many hours will it take the ship to complete one orbit?

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Sapo 3 years 2021-07-16T00:09:04+00:00 1 Answers 312 views 0

Answers ( )

    1
    2021-07-16T00:10:36+00:00

    Given Information:  

    Initial speed = v₁ = 13 m/s

    time = t = 4.50 sec

    Circumference of Mongo = C = 2.0×10⁵ km = 2.0×10⁸ m

    Altitude = h = 30,000 km = 3×10⁷ m

    Required Information:  

    a) mass of Mongo = M = ?

    b) time in hours = t = ?

    Answer:  

    a) mass of Mongo = M =  8.778×10²⁵ kg

    b) time in hours = t = 11.08 h

    Explanation:  

    We know from the equations of kinematics,

    v₂ = v₁t – ½gt²

    0 = 13*4.50 – ½g(4.50)²

    58.5 = 10.125g

    g = 58.5/10.125

    g = 5.78 m/s²

    Newton’s law of gravitation is given by

    M = gC²/4π²G

    Where C is the circumference of the planet Mongo, G is the gravitational constant, g is the acceleration of planet of Mongo and M is the mass of planet Mongo.

    M = 5.78*(2.0×10⁸)²/(4π²*6.672×10⁻¹¹)

    M = 8.778×10²⁵ kg

    Therefore, the mass of planet Mongo is 8.778×10²⁵ kg

    b) From the Kepler’s third law,

    T = 2π*(R + h)^3/2/(G*M)^1/2

    Where R = C/2π

    T = 2π*(C/2π + h)^3/2/(G*M)^1/2

    T = 2π*((2.0×10⁸/2π) + 3×10⁷)^3/2/(6.672×10⁻¹¹*8.778×10²⁵)^1/2

    T = 39917.5 sec

    Convert to hours

    T = 39917.5/60*60

    T = 11.08 hours

    Therefore, it will take 11.08 hours for the ship to complete one orbit.

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