DAY 6 – Homework

 

  1. Jupiter’s moon Io has an orbit with radius 422,000 km and period of 1 day, 18 hours, 28 minutes.  Determine the mass of Jupiter.
  1. A satellite in Geostationary Orbit (click for more information) orbits the Earth once every 24 hours.  This means that the satellite remains above the same place on Earth at all times.  The satellites for systems such as DirecTV use this principle.

    (a) Calculate the orbit radius and the altitude above Earth’s surface required for geostationary orbit.
    (b) Calculate the speed of a satellite in geostationary orbit

 
  1. The International Space Station orbits at an altitude of 170 miles.  A 100 kg satellite is orbiting with the ISS.  What energy would be required to move that satellite into geostationary orbit if the ISS and the satellite both orbit in the same plane?  (Actually the ISS’s orbit is tilted with respect to geostationary orbits, so the problem is more complex.)
  1. Look up the current altitude of the ISS and calculate its speed
    (http://spaceflight.nasa.gov/realdata/tracking/).  Do your calculations agree with the stated speed?  What accounts for the discrepancy if there is any?
  1. If the Sun suddenly collapsed into a black hole (i.e. got much, much smaller is size – no change in mass), describe what would happen to the radius, and period of Earth’s orbit.
  1. Use the formula for gravitational field strength g = GM/r2, and the known mass and radius of Earth to calculate g at the surface of the Earth.  Does that value look familiar?
  1. Using Kinetic and Potential energy, explain why objects in elliptical orbits move fastest when closest to the central mass and slowest when furthest from the central mass?  This fastest-closest/slowest-furthest relationship is another one of the laws of orbital motion discovered by Kepler.

 
  1. The length of an ellipse is called its major axis.  The point of closest approach to the Earth in an elliptical orbit is called the perigee. And its point of further approach is called apogee. 


The Chandra X-ray Observatory is in an elliptical orbit around the Earth.  The major axis of the orbit is 7½ times rp.  The period of Chandra’s orbit is 64 hours.  Estimate how much time do you suppose the Chandra spends close to the Earth vs. far from the Earth?  Make a sketch of what a graph of Chandra’s speed vs. time would look like.

 

  1. Calculate the escape velocity from the Earth’s surface in m/s and mph.
  1. What speed would a spacecraft have to have in order to leave the Solar System from the vicinity of the Earth?  Hint – this will involve escape velocity from the Sun – you’ll need the Sun’s mass and the radius of Earth’s orbit around the Sun.