Ejercicio Exercise 2 · Física II URV 2024

Exercise 2 (10 punts). Gravitation and satellite orbital mechanics

A satellite with a mass of $500\text{ kg}$ travels in orbit around the Earth at an altitude of $350\text{ km}$.

a.

What kind of orbit is described by the satellite around the Earth? [1 point]

b.

Taking the mass of the Earth as $M = 5.97 \times 10^{24}\text{ kg}$ and its radius as $R = 6371\text{ km}$, determine the satellite's orbital speed and period. What is its angular velocity? [3 points]

c.

What minimum kinetic energy must the satellite have to completely escape from its orbit to infinity? [2.5 points]

d.

A second satellite moves around the Earth in an elliptical orbit characterized by an eccentricity of $e = 0.8$. Calculate its speed at the closest point to the Earth (perigee), given that the distance at the farthest point (apogee) is $10^4\text{ km}$ and the angular momentum at that point equals $8 \times 10^{12}\text{ kg}\cdot\text{m}^2/\text{s}$. [3.5 points]