spaceflight

what is the Hohmann transfer

The minimum-energy, two-impulse transfer orbit between two coplanar circular orbits.

t consists of:

1. First impulse to enter an elliptical transfer orbit.

2. Second impulse at the destination to circularise.

Key features:

• Transfer orbit is tangent to both initial and final circular orbits.

• It is the most fuel-efficient transfer (but not the fastest).

• Used extensively in interplanetary missions.

comment on viability of the Hohmann of earth and another planet

Key points:

• Very high ΔV requirement (~9–10 km/s) just to circularise at Mercury.

• Mercury’s deep gravity well makes capture extremely expensive.

• Large inclination change is required because Mercury’s orbit is tilted (~7°) relative to Earth.

• Strong solar gravity near perihelion → high velocities → difficult braking.

• Thermal environment near the Sun is severe.

1(a) How is the principal direction defined in Orbital Mechanics? [5]

The direction from the central body (focus of the orbit) to the periapsis of the orbit.

More formally:

• It is the direction of the eccentricity vector.

• It lies in the orbital plane.

• It points toward periapsis (perigee/perihelion).

• It defines the reference direction for measuring true anomaly θ.

• True anomaly is measured from the principal direction.

Key examiner phrases to include:

• “Direction to periapsis”

• “Along the eccentricity vector”

• “Reference direction in the orbital plane”

• “Used to define true anomaly”

What are ecliptic and equatorial coordinates?

Equatorial coordinates are defined with respect to:

• Earth’s equatorial plane

• Earth’s rotation axis

They use:

• Right Ascension (RA) – like longitude, measured in the equatorial plane

• Declination (Dec) – like latitude, measured north/south of the equator

• Used mainly for Earth-based observations and satellite tracking.

Ecliptic coordinates are defined with respect to:

• The plane of Earth’s orbit around the Sun (the ecliptic plane)

They use:

• Ecliptic longitude

• Ecliptic latitude

• Used mainly for solar system dynamics and interplanetary motion.

What are Keplerian Orbital Elements and how are they used?

these enable the precise size, shape and location of a Keplerian orbit to be defined in 3 dimensions and for the satellite to be located.

Six parameters that uniquely define the size, shape, orientation, and position of an orbit in space. Keplerian elements define the geometry and orientation of an orbit and locate the spacecraft on that orbit at any time.

They are:

1. Semi-major axis (a) – size of the orbit

2. Eccentricity (e) – shape of the orbit

3. Inclination (i) – tilt of the orbit relative to reference plane

4. Right Ascension of Ascending Node (Ω) – orientation of the line of nodes

5. Argument of Periapsis (ω) – orientation of periapsis in the orbital plane

6. True anomaly (θ) – position of the spacecraft on the orbit

They are used to:

• Completely describe an orbit

• Predict spacecraft position and velocity

• Design and analyse trajectories

• Propagate orbits in time

ballistic coefficient BC

It is a measure of the capacity of an aerospace vehicle or projectile to “punch through” the atmosphere with minimal loss of speed

An object with a high BC will be slowed down less during its passage through a gas than will an object with a low BC; a feather, for example, will have a much lower BC than a pebble of the same mass. (Imagine trying to throw a feather).

rocket motor thrust coefficient

characteristics velocity definition

specific impulse definitions

It is a measure of the overall propulsion system performance and has

dimensions of time. Specific Impulse is numerically equal to the time in seconds for which a given

quantity of propellant mixture would produce its own weight in thrust.

types of propellant combination

what is staging and why is it used

mass reduction means better performance

• Rockets are extremely sensitive to mass. Carrying empty tanks and dead engines hurts efficiency. By dropping spent stages, the remaining vehicle is lighter, so:

  • It accelerates more easily

  • It can reach higher speed (∆v) for the same fuel

Optimizing engines for different flight regimes

• Different parts of flight have different needs:

  • First stage: high thrust, works in dense atmosphere

  • Upper stages: lower thrust, high efficiency in vacuum

  Staging lets you use the best engine type for each phase instead of compromising with one design.

Structural and thermal limits

• Lower stages are built strong to handle:

  • High loads

  • Atmospheric pressure

  • Heating

  Upper stages can be lighter and more delicate because they operate in near-vacuum.

types of staging

Types of staging

• Serial (stacked) staging: one on top of another (most common)

• Parallel staging: boosters burn alongside the core (e.g., Falcon Heavy, Space Shuttle)

• Air-launch staging: first “stage” is an airplane (e.g., Pegasus)

Key considerations in controlled atmospheric entry

1. Thermal loads (heating)

• Aerodynamic heating due to compression and friction

• Must keep heat flux and total heat within TPS limits

2. Deceleration (g-loads)

• High drag → high deceleration

• Must keep within human / structural tolerance

3. Trajectory & flight path angle

• Too steep → excessive heating and g

• Too shallow → skip-out or excessive range

4. Vehicle stability & control

• Must maintain correct attitude

• Avoid tumbling / loss of control

5. Landing accuracy & footprint

• Entry corridor must place spacecraft near target

• Important for recovery and safety

6. Atmospheric uncertainty

• Density variations, winds, weather
  
  

The design of controlled entry is governed by thermal protection limits, allowable deceleration, trajectory shaping to avoid skip-out or burn-up, vehicle stability and control, and landing footprint accuracy under atmospheric uncertainty

Deceleration vs altitude for ballistic capsule

Explanation:

• At high altitude:

  • density is very low → drag small → low deceleration

• As altitude decreases:

  • density rises exponentially → drag increases rapidly → deceleration rises sharply

• Near lower atmosphere:

  • speed drops → drag reduces → deceleration peaks then falls

so deceleration peaks at intermediate altitude

parameter that influence deceleration

• Ballistic coefficient β=mCDA\beta = \frac{m}{C_D A}β=CD​Am​

  • high β → deeper penetration, higher peak g

  • low β → earlier decel, lower peak g

• Entry velocity

• Atmospheric density profile

• Drag coefficient CDC_DCD​

• Entry angle

Cryogenic and hypergolic propellants

cryogenic = propellants stored at extremely low temperatures (liquid hydrogen and liquid oxygen

Features:

• Very high performance (high Isp)

• Complex storage, boil-off issues

hypergolic = fuel and oxidizer ignite spontaneously on contact (MMH + N204)

Features:

• Very high performance (high Isp)

• Complex storage, boil-off issues

How launch to LEO proceeds

1. Vertical lift-off

2. Pitch-over manoeuvre

3. Gravity turn

4. First stage burnout and separation

5. Upper stage burn to reach orbital velocity

6. Circularisation burn

why staging is used

because Dead mass severely reduces performance (rocket equation).

Staging:

• discards empty structure

• increases mass ratio

• improves efficiency