Scientists want to place a 2800 kg satellite in orbit around Mars. They plan to

Question

Scientists want to place a 2800 kg satellite in orbit around Mars. They plan to have the satellite orbit a distance equal to 2.4 times the radius of Mars above the surface of the planet. Here is some information that will help solve this problem:

mass mars = 6.4191 x 10^23 kg

radius mars = 3.397 x 10^6 m

G = 6.67428 x 10^-11 N-m2/kg2

1)What speed should the satellite have to be in a perfectly circular orbit?

2)How much time does it take the satellite to complete one revolution? hrs

3)What should the radius of the orbit be (measured from the center of Mars), if we want the satellite to take 8 times longer to complete one full revolution of its orbit?

Thank you in advance!

Explanation / Answer

In orbit

Fc = Fg

m*V^2/(R+h) = G*Mm*m/(R+h)^2

v = sqrt(G*Mm/(R+h))

h = 2.4 R

v = sqrt((6.67*10^-11*6.4191*10^23)/(3.4*3.397*10^6))

v = 1925.4 m/s   <<<<<<----------------answer

+++++++++

2)

T = 2*pi*(R+h)/V = 2*pi*(R+h)/sqrt(G*Mm/(R+h))

T = 2*pi*(R+h)^(3/2)/sqrt(G*Mm)

T = (2*pi*(3.4*3.397*10^6)^(3/2))/sqrt((6.67*10^-11*6.4191*10^23)

T = 37691.4 s

T = 37691.4/(60*60)   = 10.4698 hrs

_____________________

3)

T2 / T1 = (r2/r1)^(3/2)

T2 = 8*T1

r2 = R + h2

r1 = r + h1

8 = ((3.397*10^6+h)/(3.4*3.397*10^6))^(3/2)

h = 42802200 m <----------answer

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