|Astronomy 110||PRINT Name   __________________________|
|Fall 2005   Section 006|
Homework 4 : Orbits
(Due Thursday, Oct 6, 2005)
Start by writing down the parameters of the Moon's orbit --- its average size and its period. These are your known quantities. You can find these in the textbook (try the appendices). The quantities you want are the distance of the Moon from the center of its orbit (the center of the Earth) and the period of its orbit.
Write these in here :   (Remember the UNITS!)
Size of orbit  (dmoon)   :   ___________________     Period   (Pmoon)   :   ___________________
Is this the sidereal period or the synodic period? _______________
Low Earth Orbit (Space Shuttle)     The first thing you'll calculate is the period of a satellite, such as the Space Shuttle, that (usually for reasons of economy) is in an orbit quite close to the surface of the Earth. Assume the average height of the satellite is 300 km above the surface of the Earth. Remember that it's distance from the center of the Earth that's important, however, so you'll need to add the 300 km to the radius of the Earth to get the size of the satellite orbit. This is also one of the known (or assumed) quantities.
Write this in here :   (Remember to use the SAME UNITS as for the Moon!)
Size   (dshuttle) = 300 km + radius of Earth   :   ___________________     Period   (Pshuttle)   :   unknown
To solve for Pshuttle,the method is to write down Kepler's third law, as an equality, twice, once for the Moon and once for the shuttle :
The trick is to divide one equation by the other so that
you end up with one equation for what you want to know (the period of
the space shuttle's orbit) in terms of the other three known
quantities. Do that here:
Notice that the constant K goes away so you don't need to worry about its value.
Use this equation to solve for the value of Pshuttle .
You will need a calulator that calculates square roots. Remember the
What is the answer in minutes? ________________________________
Notice that this is less than a day. A satellite in an orbit with a period of one day is called a geostationary satellite. Such a satellite stays over the same spot on Earth all the time.
Do you expect that a geostationary satellite will orbit closer to
the Earth than the low-Earth satellite you just calculated,
or further away? _______________
Will it be closer than the orbit of the Moon? _______________
Consider a satellite in a very low orbit, one just grazing the
surface of the Earth (you'd have to clear away mountains and tall
buildings). Explain why such a satellite doesn't orbit once
in 24 hours, even though the ground just underneath it rotates once
round in 24 hours.
Can you use your equation to calculate the properties of the orbit
of, say, Mars? that is, can you directly compare in this way
the orbit of the Moon and the orbit of Mars?