Question

A satellite has a mass of 6154 kg and is in a circular orbit 4.01 x 10⁵ m above the surface of a planet. The period of the orbit is 1.9 hours. The radius of the planet is 4.76 x 10⁶ m. What would be the true weight of the satellite if it were at rest on the planet's surface?

Answer 1

5.55 x 10^5 N.

Step-by-step explanation:

The true weight of the satellite on the planet's surface would be 6154 kg multiplied by the acceleration due to gravity on the planet's surface. The acceleration due to gravity can be calculated using the following equation:

g = (GM/R2)

where G is the universal gravitational constant (6.67 x 10-11 Nm2/kg2), M is the mass of the planet (4.76 x 10^24 kg), and R is the radius of the planet (4.76 x 10^6 m).

Therefore, the true weight of the satellite would be 6154 kg x (6.67 x 10-11 Nm2/kg2) x (4.76 x 10^24 kg)/(4.76 x 10^6 m)2 = 5.55 x 10^5 N.