7.3 - Orbits of Planets & Satellites

Question 1

What is the equation for the linear speed of a mass in orbit? (considering Fg = Fcentripetal)

Answer 1

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)

Question 2

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?

Answer 2

Neither. If they have the same orbital radius they will travel at the same speed.

Question 3

prove T² is directly proportional to r³

Answer 3

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

Question 4

What is Kepler’s third law?

Answer 4

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)

Question 5

Why does a log graph of T against r not go through the origin?

Answer 5

It has a negative y-intercept

Question 6

What is the total energy of an orbiting satellite?

Answer 6

Total energy = kinetic energy + gravitational potential energy

Question 7

What happens to the energy of a satellite if its orbital radius decreases?

Answer 7

It’s kinetic energy increases and GPE decreases.

Question 8

What happens to the energy of a satellite if its orbital radius increases?

Answer 8

Kinetic energy decreases and GPE increases.

Question 9

Why does the kinetic energy of a satellite increase when the orbital radius smaller?

Answer 9

When orbiting closer to a planet, it experiences a greater gravitational pull and orbits faster.
Ek ∝ v²

Question 10

What is the definition of escape velocity?

Answer 10

The minimum speed that will allow an object to escape a gravitational field with no further energy input.

Question 11

When does an object reach the escape velocity of a planet?

Answer 11

When all its kinetic energy has transferred to gravitational potential energy.

Question 12

What is the equation to calculate escape velocity?

Answer 12

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

Question 13

Why do rockets not need to reach Earth’s escape velocity to leave Earth’s atmosphere?

Answer 13

• 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.

Question 14

What is a synchronous orbit?

Answer 14

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.

Question 15

What is a geosynchronous/geostationary orbit?

Answer 15

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

Question 16

What are geostationary satellites mainly used for?

Answer 16

Telecommunication transmissions (like radio and tv broadcast).

Question 17

How do geostationary satellites send TV signals?

Answer 17

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.

Question 18

What is a polar orbit?

Answer 18

The satellite orbits around the north and south pole of the Earth.

Question 19

What is an example of a low orbit?

Answer 19

A polar orbit.

Question 20

Why are low orbits useful?

Answer 20

Good for taking high-quality photographs of Earth’s surface - good for weather and military applications.

Question 21

How would you compare the time period and orbital radius of 2 planets?

Answer 21

1T²/1r³ = 2T²/2r³
use ratio of proportional relationship to find the unknown