Scientists want to place a 3500 kg satellite in orbit around Mars. They plan to

Question

Scientists want to place a 3500 kg satellite in orbit around Mars. They plan to have the satellite orbit at a speed of 2606 m/s in a perfectly circular orbit. Here is some information that may help solve this problem:

mmars = 6.4191 x 1023 kg
rmars = 3.397 x 106 m
G = 6.67428 x 10-11 N-m2/kg2

1)

What radius should the satellite move at in its orbit? (Measured frrom the center of Mars.)

m

2)

What is the force of attraction between Mars and the satellite?

N

3)

What is the acceleration of the satellite in orbit?

m/s2

4)

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

5)

What should the speed of the orbit be, if we want the satellite to take 8 times longer to complete one full revolution of its orbit?

Explanation / Answer

let the radius of orbit = r

as distances are large so we can plante and satellite as point mass

let mass of setellite = m

force on setellite due to mars = F = G m mmars / r2

so from circular motion of setellite

F = mv2/ r

G m mmars / r2 = mv2/ r

r = G  mmars / v2

r = (6.67428 * 10-11 *6.4191 * 1023 )/ (2606)2

r = 6308552.78 m

(2) so

From    F = G m mmars / r2

F = (6.67428 * 10-11 * 3500* 6.4191 * 1023 ) / (6308552.78)2

F = 3767.8 N

(3) a = v2 /r

a= (2606)2 / (6308552.78)

a = 1.07 m/s2

(4)

as

G m mmars / r2 = mv2/ r

r = G  mmars / v2

i.e. radius of planet depending on

mass of mars and velocity of palnet

(5) if r ----> 8r

then v=?

as we know

G m mmars / r2 = mv2/ r

r = G  mmars / v2

so r is proposional to 1/v2

so if r' ----> 8r then

v' = v / 2sqrt2

=921.36 m/s

answer

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