Scientists want to place a 2600 kg satellite in orbit around

Scientists want to place a 2600 kg satellite in orbit around Mars. They plan to have the satellite orbit at a speed of 2438 m/s in a perfectly circular orbit. Here is some information that may help solve this problem: m_mars = 6.4191 times 10^23 kg r_mars = 3.397 times 10^6 m G = 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 Mars.) 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 revolution of its orbit?

Solution

1) We know that

Centripital force (F_c) = m x V²/r

where m = mass of satellite

V= Orbital velocity of satellite

r = orbital radius of satellite

and we also know

Gravitational force of attaraction (F) = G M_mars m / r²

Since the stable orbit require that the two forces should be equal hence

F_c = F

therfore , r = G M_mars / V²

Hence    r = 7.2079 x 10⁶ m

Hence satellite should move at 7.2079 X 10⁶ m from the centre of Mars.

2) F = G M_mars m / r²

^{F = 2144.023 N}

3) Acceleration = v² / r = 0.8246 m / s²

4) Radius of satellite is dependant upon speed of the satellite. Hence speed of the satellite would change the radius of the satellite.