7.3 - Orbits of Planets & Satellites Flashcards
What is the equation for the linear speed of a mass in orbit? (considering Fg = Fcentripetal)
GMm/r² = mv²/r
v² = GM/r
v = linear speed of the mass in orbit (m/s)
G = grav constant
M = mass of the object being orbited (kg)
r = orbital radius (m)
If the satellites A and B are have the same orbital radius around Earth, but A’s mass is far greater, which travels at a greater speed?
Neither. If they have the same orbital radius they will travel at the same speed.
prove T² is directly proportional to r³
v = 2πr/T (since 2πr is the circumference of the orbit)
v² = (2πr/T)² = GM/r
T² = 4π²r³/GM
therefore T² ∝ r³
M = mass of the object being orbited
What is Kepler’s third law?
For planets or satellites in a circular orbit about the same central body, the square of the time is proportional to the cube of the radius of the orbit.
(T² ∝ r³)
Why does a log graph of T against r not go through the origin?
It has a negative y-intercept
What is the total energy of an orbiting satellite?
Total energy = kinetic energy + gravitational potential energy
What happens to the energy of a satellite if its orbital radius decreases?
It’s kinetic energy increases and GPE decreases.
What happens to the energy of a satellite if its orbital radius increases?
Kinetic energy decreases and GPE increases.
Why does the kinetic energy of a satellite increase when the orbital radius smaller?
When orbiting closer to a planet, it experiences a greater gravitational pull and orbits faster.
Ek ∝ v²
What is the definition of escape velocity?
The minimum speed that will allow an object to escape a gravitational field with no further energy input.
When does an object reach the escape velocity of a planet?
When all its kinetic energy has transferred to gravitational potential energy.
What is the equation to calculate escape velocity?
1/2mv² = GMm/r
(EK = F)
m = mass of object in grav field
M = mass of object to be escape from
v = escape velocity of object
r = distance from centre of mass M
Why do rockets not need to reach Earth’s escape velocity to leave Earth’s atmosphere?
- They are continuously given energy through fuel and thrust to help them move
- Less energy is needed to achieve orbit than to escape from Earth’s gravitational field.
What is a synchronous orbit?
When an orbiting body has a time period equal to that of the body being orbited and in the same direction of rotation as that body.
What is a geosynchronous/geostationary orbit?
A type of orbit that remains directly above the equator and always orbits at the same point above Earth’s surface.
Move from West to East (same direction as the Earth spins)
T = 24 hours
What are geostationary satellites mainly used for?
Telecommunication transmissions (like radio and tv broadcast).
How do geostationary satellites send TV signals?
A base station on Earth sends the TV signal up to the satellite where it is amplified and broadcast back to the ground to the desired locations.
Satellite dishes on ground point to satellite in sky to receive it.
What is a polar orbit?
The satellite orbits around the north and south pole of the Earth.
What is an example of a low orbit?
A polar orbit.
Why are low orbits useful?
Good for taking high-quality photographs of Earth’s surface - good for weather and military applications.
How would you compare the time period and orbital radius of 2 planets?
1T²/1r³ = 2T²/2r³
use ratio of proportional relationship to find the unknown
