Around the World in 90 Minutes - Orbit and Planetary Motion

Some distractions before you check your answers:

First, a ride to space on the Space Shuttle:


The view out of a shuttle window during orbit:


This site lists opportunities to see the International Space Station fly over New York City.

There is one pass tomorrow (Thursday) at 6:23 AM, starting in the south at 11 degrees above the horizon, and ending in the East at 35 degrees above the horizon 3 minutes later. It will peak at almost 45 degrees above the horizon halfway through. You will be looking for a fast moving "star", though this "star" is actually a spacecraft housing two Russian and one America astronauts!

Solutions to Orbit Problems from today:

1. The mass of the Earth as determined from this problem is 5.98 x 10²⁴ kg

2. Since the mass of the orbiting satellite divides out from both sides of the equation, it is not possible to determine the mass of a satellite just from knowing its orbital speed and altitude. The government was concerned about what sort of weapon the Russians might be able to load onto such a satellite that passed over the entire world. This kicked off another chain of events that ultimately led to the US developing its own space program.

3. This problem again asks you to derive an expression for the speed of an orbiting satellite. You should obtain that v = (GMe/R)^1/2 where G is the gravitational constant, Me is the mass of the Earth (see question 1) and R is the radius of the orbit of the satellite. The way to increase the altitude of the satellite involves slowing down (or decreasing the speed) by firing a rocket.

In reality, it isn't quite this simple. What is usually done is there are TWO rocket firings required - a first to change the satellite's speed to get it into a new elliptical orbit that reaches the desired new altitude, and a second that pushes the satellite into a circular orbit at the new altitude. This process is called a Hohmann transfer depicted below.


4. Following the steps from class, the radius of the orbit is twice the radius of Earth. The speed of the satellite is 5,591 m/s, and the period is 239 minutes (14340 seconds).

5. minimum speed is (gR)^1/2 = 14 m/s

6. a = (100N*cos(40) - .32*(196 N - 100 N sin(40))/(20 kg) = 1.723 m/s^2

One last toy to check out: An orbit simulator. Try to put some satellites into orbits, and watch how they move differently in elliptical vs. circular paths.