Scientist want to place a 3100 kg satellite in orbit around Mars They plan to ha

Question

Scientist want to place a 3100 kg satellite in orbit around Mars They plan to have the satellite orbit at a speed of 2563 m/s in a perfectly circular orbit Here is some information that may help solve this problem: M_mass = 6.4191 times 10^23 kg r_mass = 3.397 times 10^6 m c_1 = 6.67428 times 10^-11 N-m^2/kg^2 What radius should the satellite move at in its orbit? (Measured from the center of Mass.) What is the force of attraction between Mars and the satellite? What is the acceleration of the satellite in orbit? Which of the following quantities would change the radius the satellite needs to orbit at? the mass of the satellite the mass of the planet the speed of the satellite What should the speed of the orbit be, if we want the satellite to take 8 times longer to complete one full resolution of its orbit?

Explanation / Answer

Given,

m = 3100 kg ; v = 2563 m/s ;

a)R = GM/v^2

R = 6.67 x 10^-11 x 6.4191 x 10^23/2563^2 = 6.517 x 10^6 m

Hence, R = 6.517 x 10^6 m

b)F = G M m/r^2

R = 6.67 x 10^-11 x 6.4191 x 10^23 x 3100/(6.517 x 10^6)^2 = 3125 N

Hence, F = 3.125 x 10^3 N

c)F = ma =. a = F/m

a = 3125/3100 = 1.01 m/^2

Hence, a = 1.01 m/s^2

d)the speed of the satellite

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