Step-by-step solution
We start by determining the satellite’s orbital radius. Careful: this is not the satellite’s height above the surface of the Earth, but its distance
from the center of the planet.
Now we apply the equation for orbital speed.
Step Reason
1. r = rE + h equation for satellite’s orbital radius
2. r = 6.38×10^6 m + 5.00×10^5 m enter values
3. r = 6.88×10^6 m add
Step Reason
4. orbital speed equation
5. enter values
6. v = 7610 m/s evaluate
12.11 - Interactive problem: intercept the orbiting satellite
In this simulation, your mission is to send up a rocket to intercept a rogue satellite
broadcasting endless Barney® reruns. You can accomplish this by putting the
rocket into an orbit with the same radius and speed as that of the satellite, but
traveling in the opposite direction. The resulting collision will destroy the satellite
(and your rocket, but that is a small price to pay to save the world’s sanity).
The rogue satellite is moving in a counterclockwise circular orbit 40,000 kilometers
(4.00×10^7 m) above the center of the Earth. Your rocket will automatically move to
the same radius and will move in the correct direction.
You must do a calculation to determine the proper speed to achieve a circular orbit
at that radius. You will need to know the mass of the Earth, which is 5.97×10^24 kg.
Enter the speed (to the nearest 10 m/s) in the control panel and press GO. Your
rocket will rise from the surface of the Earth to the same orbital radius as the
satellite, and then go into orbit with the speed specified. You do not have to worry
about how the rocket gets to the orbit; you just need to set the speed once the
rocket is at the radius of the satellite. If you fail to destroy the satellite, check your
calculations, press RESET and try a new value.
12.12 - Interactive problem: dock with an orbiting space station
In this simulation, you are the pilot of an orbiting spacecraft, and your mission is to
dock with a space station. As shown in the diagram to the right, your ship is initially
orbiting in the same circular orbit as the space station. However, it is on the far side
of the Earth from the space station.
In order to dock, your ship must be in the same orbit as the space station, and it
must touch the space station. To dock, your speed and radius must be very close to
that of the space station. A high speed collision does not equate to docking!
You have two buttons to control your ship. The “Forward thrust” button fires rockets
out the back of the ship, accelerating your spacecraft in the direction of its current
motion. The other button, labeled “Reverse thrust,” fires retrorockets in the opposite
direction. To use more “professional” terms, the forward thrust is called prograde
and the reverse thrust is called retrograde.
Using these two controls, can you figure out how to dock with the space station?
To assist in your efforts, the current orbital paths for both ships are drawn on the
screen. Your rocket’s path is drawn in yellow, and the space station’s is drawn in
white.
This simulation requires no direct mathematical calculations, but some thought and experimentation are necessary. If you get too far off track,
you may want to press RESET and try again from the beginning.