A satellite of mass 190 kg is placed into Earth orbit at a height of 800 km abov

Question

A satellite of mass 190 kg is placed into Earth orbit at a height of 800 km above the surface.
(a) Assuming a circular orbit, how long does the satellite take to complete one orbit?

28.64 h

Incorrect: Your answer is incorrect.

It may be easiest to answer part (b) (find the speed of the satellite) first. h

(b) What is the satellite's speed?

438.5 m/s

Incorrect: Your answer is incorrect.

You appear to have correctly calculated the speed using your incorrect value from part (a). m/s

(c) Starting from the satellite on the Earth's surface, what is the minimum energy input necessary to place this satellite in orbit? Ignore air resistance but include the effect of the planet's daily rotation.

-10.54E9 J

Incorrect: Your answer is incorrect.

The satellite has some initial kinetic energy on the surface of the Earth because of the Earth's rotation. What is the total energy of the satellite when it is orbit? J

Explanation / Answer

Solution:

a)

Using Newtons 2nd law of motion:

GMm/r^2 = m*v^2/r

=> GMm/r^2 = m*4^2*r/T^2

=> T = sqrt(4^2*r^3/GM)

=> T = sqrt(4^2*(6.37x10^6+ 800x10^3)^3/(6.67x10^-11*5.98x10^24)

=> T = 6040.325 sec

or 1.6778 hours

b)

Here;

v = sqrt(GM/r) (r= R + h)

=> v = 7455.527 m/s

c)

Using conservation of energy :

K + U)earth = K+U)orbit where U = -GMm/r

=> K = U orbit - U earth + K orbit

=> - GMm/r -(-GMm/R) + 1/2*m*v^2

=> GMm*(1/R - 1/r) + 1/2*m*v^2

=> K = 6.6 * 109 J

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