Orbits and satellites Knowledge-Based Practice

Questions

1. 1.

   A satellite moves in a circular orbit at an altitude equal to Earth's radius, $R$. If the gravitational acceleration at Earth's surface is $g$, what is the gravitational acceleration of the satellite at this orbital altitude?

   • A) $g/4$
   • B) $g/2$
   • C) $g$
   • D) 0
2. 2.

   A satellite travels in a circular orbit around a planet with an orbital speed $v$. What is the minimum speed the satellite must attain at its current location to completely escape the gravitational pull of the planet?

   • A) $\frac{v}{\sqrt{2}}$
   • B) $v$
   • C) $\sqrt{2}v$
   • D) $2v$
3. 3.

   A satellite of mass $m$ moves at a constant speed in a circular orbit of radius $r$ around a planet of mass $M$. How much work is done by the gravitational force on the satellite during one complete orbit?

   • A) $-\frac{GMm}{r}$
   • B) $\frac{2\pi GMm}{r}$
   • C) $\frac{GMm}{2r}$
   • D) 0
4. 4.

   A satellite travels in an elliptical orbit around a planet. As the satellite moves from its closest point to the planet (perigee) toward its farthest point (apogee), how do its orbital speed and its angular momentum about the planet's center change?

   • A) The orbital speed increases, and the angular momentum remains constant.
   • B) The orbital speed decreases, and the angular momentum remains constant.
   • C) The orbital speed decreases, and the angular momentum decreases.
   • D) The orbital speed remains constant, and the angular momentum decreases.
5. 5.

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

   • A) It must orbit over Earth's poles from north to south with an orbital period of 12 hours.
   • B) It must orbit in Earth's equatorial plane from west to east with an orbital period of 24 hours.
   • C) It must orbit at an arbitrary inclination angle from east to west with an orbital period of 24 hours.
   • D) It must orbit along a fixed line of longitude from north to south with an orbital period of 48 hours.
6. 6.

   An astronaut aboard a spacecraft in a circular orbit around Earth experiences apparent weightlessness. Which statement correctly explains why the astronaut floats freely inside the spacecraft?

   • A) Earth's gravitational force is completely shielded by the hull of the spacecraft.
   • B) Both the astronaut and the spacecraft are in continuous free fall toward Earth with the same acceleration.
   • C) The spacecraft orbits at an altitude where Earth's gravitational pull has dropped to zero.
   • D) The high forward speed of the spacecraft exactly cancels the downward pull of gravity.
7. 7.

   Two artificial satellites, A and B, orbit the same planet in identical circular orbits. If satellite B has three times the mass of satellite A, which statement correctly compares their orbital speeds?

   • A) Satellite B travels with three times the orbital speed of satellite A.
   • B) Satellite B travels with one-third the orbital speed of satellite A.
   • C) Satellite B travels with $\sqrt{3}$ times the orbital speed of satellite A.
   • D) Satellite B travels with the same orbital speed as satellite A.
8. 8.

   A satellite of mass $m$ orbits a planet of mass $M$ in a stable circular path of radius $r$. What is the ratio of the satellite's kinetic energy to the magnitude of its gravitational potential energy, $\frac{K}{|U|}$?

   • A) $\frac{1}{2}$
   • B) $1$
   • C) $2$
   • D) $\frac{1}{4}$
9. 9.

   A satellite moves in a stable circular orbit of radius $r$ around a planet of mass $M$ with an orbital period $T$. If the satellite's orbital radius is increased to $4r$, what is its new orbital period in terms of $T$?

   • A) $2T$
   • B) $4T$
   • C) $8T$
   • D) $16T$
10. 10.

    Two artificial satellites, X and Y, orbit Earth in concentric circular paths of radii $r$ and $4r$, respectively. If satellite X moves with an orbital speed $v$, what is the orbital speed of satellite Y?

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

Answers and step-by-step solutions appear after you finish the test.