Orbital Mechanics

Why is orbital mechanics important?

Copernicus (1473-1543) proposed what?

Brahe (1546-1601) did what?

Kepler (1571-1630) worked on what?

What does peri-x and apo-x mean respectively?

What does -gee, -helion, -lune, -apsis mean?

Orbits of planets are what shape around which body and how many foci?

What does orbit mean?

What do the following values of 'e' (eccentricity) mean?
e<1
e>1
e=0
e=1

How do you find the radius of periapsis and apoapsis?

How do you calculate the semi major axis, a, eccentricity, e, location of focal centre, Cp, area of ellipse and semi minor axis,b?

Equation of ellipse?

Where is the altitude of a satellite measured from?

What is significant about the line from the sun to planets sweeping arounds its orbit?

What is K3?

What is a sidereal day?

What is a solar day?

Which day does the Earth rotate 360 degrees?

Which day are satellites are aligned to?

What are Newtons 3 laws?

What is the celestial equator?

What is the plane of orbit around the sun for the Earth?

Which direction does the earth move around the sun?

Which plane is used for interplanetary journeys?

Which plane is used for Earth based missions?

Where is the first point of Aries?

When is the vernal equinox?

How are the vernal equinox and First point of Aries related?

ECI axis (Earth centered Inertial)?

Earth Centered Earth-Fixed (ECEF) axis?

Spherical coordinate system

What is Inclination?

What is the true anomaly, v?

What is the argument of periapsis?

What is the longitude of/right ascension of the ascending node (RAAN)?

What is a ground trace?

What is special about the angle of ground trace?

What is a satellite with inclination of zero degrees?

What is a satellite with an inclination of 90 degrees?

What is a sun-synchronous orbit?

Difference between ascending and descending node?

What is the difference between retrograde and prograde?

What are the rough altitudes of the following satellites:
LEO
MEO
GEO

What issues arise for LEO orbits?

What does the Earth not being completely spherical result in?

How can nodal regression be useful?

What is a Molniya orbit?

What other factors effect orbits?

What is attractive force in space?

What is kinetic energy in space?

What is G.P.E?

So What is total Energy in space?

What is V-escape?

Why are these gravitational equations important?

How are force and radius related in terms of acceleration?

Distance to centre of mass between two masses, Ro?

Why are we interested in centre of mass?

What if M>>m?

What if d(Ro)/dt is constant?

What if d^2(Ro)/dt^2 is zero?

What must we find in order to solve Keplers problems?

What is the conservation of momentum?

Define angular momentum, L

What does h represent?

How does differentiating L= r x mr(dot) using chain rule give us the proof for angular momentum?
Write out for clarity

How can we rewrite h=r x v?
Write out for clarity

For which points is the flight path angle zero?

How does conservation of momentum apply to our last expression?

How can we rewrite specific angular momentum in terms of tangential velocity?

State the steps of the derivation of radial acceleration

Step 1

Step 2

Step 3

What other useful equation is equal to what we have just found?

What do each other terms in our derived equation represent?

What is the significance of angular momentum being conserved?

Use h=r^2*θdot to show angular acceleration is zero

Prove angular momentum is zero using area swept by the radius

Which substitution is used in the first stage of deriving the orbit equation?

Stage 1 of derivation

Stage 2

Stage 3

Final required stage A=e*μ/h^2
and u=1/r

What are the equations for position vector/orbit equation r , for an ellipse and specific energy?

what does h^2/μ equal?

Using the orbit equation for ellipses, find the radii at perigee and apogee

Use area to derive K3, step 1

Step 2

Step 3

Why is velocity important?

Derive the vis visa equation

How does the vis versa equation change for a circular orbit?

When does Vescape occur?

What is the increase factor needed to go from vc to vescape?

How do you calculate hyperbolic orbit speeds?

What is the Kepler equation?

What is mean anomaly?

What is the mean notion?

Describe the launch losses which occur

Earths rotation gives the launch extra delta V. How can this be calculated

Principles of maneuvers

Why is U defined as negative?

Where must burns occur in order to change plane?

Why are plane changes avoided if possible?

IF plane changes are carried out are they done at high or low altitudes?

What is the equation for delta V in a simple plane change?

Describe a Hohmann transfer

What is the connection between time of flight of Hohmann transfer nd period of orbit?

Describe how to obtain the Overall delta V for a Hohmann transfer

What else does a launch into GTO in the Hohmann transfer require?

What are the stages of the a rendezvous maneuver?

How do we change the phase of the orbit?

Which scientist is credited with the collection of the data necessary to support the elliptical motion of planets?

Define the term ‘apohelion’

Explain why a solar day is longer than a sidereal day

If the apogee of a satellite’s orbit is 68000km, what is the altitude of the satellite at this point? Assume the radius of the Earth=6378km.

A satellite in earth orbit has a semi-major axis of 6,700 km and an eccentricity of 0.01. Calculate the satellite's altitude ‘h’ at both perigee and apogee.

‘The ascending node can be defined as where an orbiting spacecraft crosses the semi-major axis going north.’ True or False?

‘A sun-synchronous orbit is never a precessing orbit’. True or False? False

What is the angle between the equator and the ecliptic?

Does inclination change with increase in altitude?

How is RAAN measures?

Is argument of perigee measured clockwise or anti-clockwise?

What is the approximate inclination of Molniya orbits?

If the Moon-Earth distance were to shrink, what would happen to the Moon’s Period? Increase/decrease/stay the same?

In the Phoebe example, does it make sense that the resultant acceleration is along –r axis?

Where will a spacecraft go if it has exactly the escape velocity of the planet?

Is a ‘barycentre’ exactly the same as the centre of mass?

What assumption allows us to use 1 body central force model for the motion of Mercury wrt the Sun?

Why do we use polar coordinates for planetary motion?

Use a simple equation to show which vectors determine the plane of an orbit.

What does

Assuming argument of periapsis is 0, what is the value of true anomaly for the apogee point?

If the argument of periapsis is 150, what value of

Forasatellitewithsemimajoraxis7500000m,e=0.1, AOP=45 degrees, calculate the length of its position vector at the descending node.

An artificial Earth satellite is in an elliptical orbit which has a altitude of 250 km at perigee and an altitude of 500 km at apogee. Use the above result to find the perigee velocity.

After launch, what is the first step for a supply ship to rendezvous with a space station?

Describe how a chaser supply ship catches up with a target space station which is trailing it? What is this manoeuvre called?

Where do you do an inclination burn in an elliptical orbit? Why?