Orbits and satellites Knowledge-Based Download PDF

Questions

1. 1.

   A satellite of mass $m$ travels in a stable circular orbit of radius $r$ around a planet of mass $M$. Assuming the gravitational potential energy is defined to be zero at infinite separation, what is the total mechanical energy of the satellite?

   • A) $-\frac{G M m}{2r}$
   • B) $-\frac{G M m}{r}$
   • C) $\frac{G M m}{2r}$
   • D) $-\frac{2G M m}{r}$
2. 2.

   A satellite travels in a stable circular orbit around a planet with orbital speed $v$. By what factor must the satellite's speed be multiplied so that it can escape the planet's gravitational pull completely?

   • A) 0.5
   • B) 2
   • C) $\sqrt{2}$
   • D) 4
3. 3.

   A satellite moves around Earth in a stable circular orbit. If the satellite is moved to a new stable circular orbit with a larger radius, how do its orbital speed and orbital period change?

   • A) Its orbital speed increases, and its orbital period decreases.
   • B) Its orbital speed increases, and its orbital period increases.
   • C) Its orbital speed decreases, and its orbital period increases.
   • D) Its orbital speed decreases, and its orbital period decreases.
4. 4.

   A satellite orbits a planet in a circular path of radius $r$. If the planet exerts a gravitational force of magnitude $F$ on the satellite, what is the kinetic energy of the satellite?

   • A) $2Fr$
   • B) $Fr$
   • C) $\frac{1}{2}Fr$
   • D) $\frac{1}{4}Fr$
5. 5.

   Which condition must be met for a satellite to maintain a geostationary orbit around Earth?

   • A) It must orbit over Earth's poles with an orbital period of 12 hours.
   • B) It can orbit at any altitude as long as its orbital plane passes through the poles.
   • C) It must orbit eastward in Earth's equatorial plane with a period equal to Earth's rotational period.
   • D) It must orbit westward along a fixed line of latitude with an orbital period of 48 hours.
6. 6.

   An astronaut aboard a spacecraft in a stable circular orbit around Earth experiences apparent weightlessness. Which statement correctly explains why the astronaut feels weightless?

   • A) Earth's gravitational pull is effectively zero at typical orbital altitudes.
   • B) Both the astronaut and the spacecraft are in free fall toward Earth with the same acceleration.
   • C) An outward centrifugal force exactly cancels the inward gravitational force on the astronaut.
   • D) The spacecraft's engines continuously fire to counteract Earth's gravitational attraction.
7. 7.

   Two artificial satellites, one of mass m and the other of mass 2m, travel in identical circular orbits of radius r around Earth. Which statement correctly compares the orbital speed of the satellite of mass 2m to that of the satellite of mass m?

   • A) Its orbital speed is equal to that of the satellite of mass m.
   • B) Its orbital speed is twice that of the satellite of mass m.
   • C) Its orbital speed is half that of the satellite of mass m.
   • D) Its orbital speed is four times that of the satellite of mass m.
8. 8.

   Two satellites, X and Y, move in circular orbits around a planet with orbital radii of $r$ and $4r$, respectively. If satellite X has an orbital period of $T$, what is the orbital period of satellite Y?

   • A) $2T$
   • B) $8T$
   • C) $16T$
   • D) $64T$
9. 9.

   A satellite moves in a stable circular orbit of radius $r$ around Earth with orbital speed $v$. What is its new orbital speed if it is moved to a circular orbit of radius $4r$?

   • A) $2v$
   • B) $v$
   • C) $\frac{v}{2}$
   • D) $\frac{v}{4}$