Elliptical Orbits

Question 1

What is the focus for an ellipse?

Answer 1

Where the centre of mass of the system is

Question 2

What is the major axis and the semi-major axis of an ellipse?

Answer 2

The major axis is the longest axis of an ellipse and the semi-major axis is half of this length

Question 3

What is the major axis and the semi-major axis of an ellipse?

Answer 3

The major axis is the longest axis of an ellipse and the semi-major axis is half of this length

Question 4

What is the minor axis and the semi-minor axis of an ellipse?

Answer 4

The minor axis is the shortest axis of an ellipse and the semi-minor axis is half of this length

Question 5

What is the equation for e (the eccentricity of an ellipse)?

Answer 5

e = (1 - b²/a²)^1/2
where a is the semi-major axis and b is the semi-minor axis

Question 6

What value of eccentricity does a circle have?

Answer 6

For a circle, e = 0
This means that a = b

Question 7

What is the periapsis?

Answer 7

The shortest distance between an orbitting object and the focus

Question 8

What formula gives the periapsis (r_p)?

Answer 8

r_p = a(1-e)
where a is the semi-major axis and e is the eccentricity

Question 9

What is the apoapsis?

Answer 9

The greatest distance between an orbitting object and the focus

Question 10

What formula gives the apoapsis (r_a)?

Answer 10

r_a = a(1+e)

Question 11

What effect does changing the eccentricity but keeping the semi-major axis constant have on the orbit’s period?

Answer 11

All the orbits would have the same period (the objects would take the same amount of time to complete an orbit)

Question 12

What formula is used to calculate the area of an ellipse?

Answer 12

A = πab
where a and b are the semi-major and semi-minor axis

Question 13

Is the total energy in every bound orbit positive or negative?

Answer 13

Negative

Question 14

What is the total energy of objects on a parabolic orbit and why?

Answer 14

Zero
This is because they are travelling at escape velocity

Question 15

What equation is used to calculate total energy in a circular orbit?

Answer 15

E_tot = GPE + KE = -GMm/r + 1/2(mv²) = -GMm/2r
(as v = (GM/r)^1/2)
where G is the graviational constant, r is the orbital radius, m is the mass of the sattelite and M is the mass of the object being orbitted

Question 16

How can a circular orbit become elliptical?

Answer 16

If the speed of the object at a point in the orbit is changed.
If the object speeds up, the point where it accelerated becomes the new periapsis.
If it slows down, the point where it deccelerated becomes the new apoapsis.

Question 17

What equation is used to calculate the total energy of an elliptical orbit?

Answer 17

E_tot = -GMm/2a
where G is the gravitational constant, a is the semi-major axis, m is the mass of the sattelie and M is the mass of the object being orbitted