Earth Satellites and Orbital Velocity - UNSOLVED PRACTICE SET

Q7. Derive the expression for orbital velocity of a satellite at height h above Earth's surface.

Q8. Calculate the orbital velocity of a satellite at a height of 600 km above Earth's surface. (R = 6400 km, g = 9.8 m/s²)

Q9. Explain why a satellite in orbit is in a state of free fall. Why doesn't it crash into Earth?

Q10. In your school, a student asks why astronauts in the International Space Station appear weightless. Is it because there is no gravity in space? Explain.

Q11. Derive the expression for the period of revolution of a satellite in terms of its orbital radius.

Q12. The total energy of a satellite is E = −GMm/2r. Explain the significance of the negative sign and the factor of ½.

Q13. Derive expressions for a satellite in circular orbit around Earth:

(i) Orbital velocity

(ii) Period of revolution

(iii) Kinetic energy

(iv) Potential energy

(v) Total energy

Show that the total energy is negative and equal to half the potential energy. Discuss what each energy term represents physically.

Q14. A 500 kg satellite orbits Earth at a height of 800 km.

(a) Calculate the orbital velocity.

(b) Calculate the period of revolution.

(c) Calculate the kinetic, potential, and total energies.

(d) Calculate the binding energy of the satellite.

(e) What energy is required to move this satellite to an orbit at 1600 km height?

Q15. Discuss the energy changes when a satellite's orbit changes:

(a) From a lower orbit to a higher orbit

(b) From circular to elliptical orbit

(c) During atmospheric re-entry

Explain why moving to a higher orbit requires energy input even though the total energy becomes less negative.

Q16. The Hubble Space Telescope orbits Earth at a height of 600 km.

(a) Calculate its orbital velocity.

(b) Calculate its orbital period.

(c) Calculate how many orbits it completes in one day.

(d) If atmospheric drag causes its orbit to decay slowly, what happens to its speed and period?

(e) Calculate the energy dissipated per orbit if the height decreases by 1 km per year.

Q17. A satellite is to be placed in a circular orbit at a height where its period is 12 hours.

(a) Calculate the required orbital radius.

(b) Calculate the orbital velocity at this height.

(c) Compare this with a geostationary satellite (period = 24 hours).

(d) Calculate the energy required to launch this satellite from Earth's surface into this orbit.

(e) Discuss the advantages of different orbital periods for Earth observation.

Q18. In a school project, students design a model satellite launcher using a spring.

(a) Calculate the spring constant needed to launch a 0.5 kg model to 5 m height.

(b) If the spring is compressed by 10 cm, calculate the launch velocity.

(c) Calculate the maximum height if launched vertically.

(d) Discuss why horizontal launch is needed for orbit, not vertical.

(e) Design a simple demonstration to show the difference between projectile and orbital motion.