Question

n order better to map the surface features of the Moon, a 361 kg361 kg imaging satellite is put into circular orbit around the Moon at an altitude of 147 km.147 km. Calculate the satellite's kinetic energy K,K, gravitational potential energy ????,U, and total orbital energy E.E. The radius and mass of the Moon are 1740 km1740 km and 7.36×1022 kg.

Answer 1

Step-by-step explanation:

Mass of satellite

M_s = 361 kg

Distance of satellite from moon

h = 147 km = 147,000m

Radius of the moon is

R_m = 1740 km = 1740,000m

Mass of the moon is

M_m = 7.36 × 10²² kg.

The kinetic energy is equal to the potential energy of the body to the surface of the moon from the conservation of energy.

K.E = P.E = mgh

Gravity on moon is g = 1.62 m/s²

K.E = 361 × 1.62 × 147,000

K.E = 8.597 × 10^7 J.

B. The gravitational potential energy can be calculated using

U = G•M_s × M_m (1/R_s - 1 / R)

R is the total distance from the centre of the moon to the satellite

R = h + R_m = 147 + 1740 = 1887km

R = 1,887,000 m

U = 6.67 × 10^-11 × 361 × 7.36 × 10²² (1/1,740,000 - 1/1,887,000)

U = 6.67 × 10^-11 × 361 × 7.36 × 10²² × 4.48 × 10^-8

U = 7.93 × 10^7 J

Then,

The total energy becomes

E = K.E + U

E= 8.597 × 10^7 + 7.93 × 10^7 J

E = 1.653 × 10^8 J