Question

The ISS orbits the Earth at an altitude of 400 km.

a) Write down Newton’s Universal law of gravitation.

b) Write down the magnitude of the Earth’s gravitational pull at this altitude.

c) Find the orbital speed of the ISS assuming a circular orbit.

d) Find the period of the resulting orbit.

Answer 1

a)

according to newton's law of gravitation, the gravitational force of attaraction between two objects placed some distance "r" apart is directly porpotional to the product of the masses of the two objects and inversly propotional to the square of the distance between the two objects.

F = G m₁ m₂/r²

b)

h = height = 400 km = 0.4 x 10⁶ m

R = radius of earth = 6.4 x 10⁶ m

M = mass of earth = 5.98 x 10²⁴ kg

Gravitational pull is given as

E = GM/(R + h)²

E = (6.67 x 10^-11) (5.98 x 10²⁴)/((6.4 x 10⁶) + (0.4 x 10⁶))²

E = 8.63

c)

orbital speed is given as

V = sqrt(GM/(R + h))

V = sqrt((6.67 x 10^-11) (5.98 x 10²⁴)/((6.4 x 10⁶) + (0.4 x 10⁶)))

V = 7658.77 m/s

d)

Period is given as

T² = 4² (R + h)³/(GM)

T² = 4(3.14)² ((6.4 x 10⁶) + (0.4 x 10⁶))³/((6.67 x 10^-11) (5.98 x 10²⁴))

T = 5575.83 sec