Welcome to Technology in Space (SPC)
In this chapter, we are going to explore the physics that keeps satellites running in the harsh environment of space. From the solar cells that provide power to the dc circuits that manage it, this is where fundamental physics meets high-tech engineering. Whether you are aiming for an A* or just trying to get your head around the basics, these notes will help you master the journey.
1. The Basics of Electric Flow
To understand a satellite's power system, we first need to understand how electricity moves.
Electric Current
Electric current is the rate of flow of charged particles (usually electrons in a wire). We measure it in Amperes (A).
The formula is: \( I = \frac{\Delta Q}{\Delta t} \)
Where:
\( I \) = Current (Amperes)
\( \Delta Q \) = Change in charge (Coulombs)
\( \Delta t \) = Time interval (seconds)
Potential Difference (Voltage)
Potential Difference (p.d.) is the energy transferred per unit charge. Think of it as the "push" that gets the charge moving.
The formula is: \( V = \frac{W}{Q} \)
Where:
\( V \) = Potential difference (Volts)
\( W \) = Work done or Energy transferred (Joules)
\( Q \) = Charge (Coulombs)
Resistance and Ohm's Law
Resistance is how much a component "fights" the flow of current. It is defined by the ratio of p.d. to current: \( R = \frac{V}{I} \).
Ohm's Law is a special case. It states that for some conductors, the current is directly proportional to the potential difference, provided the temperature stays constant (\( I \propto V \)).
Quick Review: If you double the voltage across a fixed resistor, the current will double. If you double the resistance, the current will halve!2. Circuit Laws: Keeping the Power Balanced
Satellites use complex circuits. To solve them, we use two very important rules based on the "Conservation Laws."
Kirchhoff’s First Law (Current)
This law states that the total current entering a junction must equal the total current leaving it. This is a consequence of the conservation of charge—charge cannot just disappear!
Kirchhoff’s Second Law (Energy)
In any closed loop of a circuit, the sum of the electromotive forces (e.m.f.) is equal to the sum of the potential differences (p.d.). This is a consequence of the conservation of energy.
Combining Resistances
Satellites often have multiple components. Here is how you calculate their total resistance (\( R_{total} \)):
1. In Series: \( R_{total} = R_1 + R_2 + R_3 ... \)
2. In Parallel: \( \frac{1}{R_{total}} = \frac{1}{R_1} + \frac{1}{R_2} + \frac{1}{R_3} ... \)
3. Power and Energy
Space missions are all about "power budgets." We need to know exactly how much energy we are using.
Power (P) is the rate of doing work, measured in Watts (W).
Equations for Power:
\( P = VI \)
\( P = I^2R \)
\( P = \frac{V^2}{R} \)
To find the total Work (W) or energy used over time, use: \( W = VIt \)
4. Internal Resistance: The "Battery Tax"
Don't worry if this seems tricky at first—most students find it strange! In the real world, batteries (and solar cells) aren't perfect. They have their own internal resistance (\( r \)).
Electromotive Force (e.m.f.) vs. Terminal p.d.
e.m.f. (\( \epsilon \)): The total energy a battery gives to each Coulomb of charge.
Terminal p.d. (V): The voltage actually measured across the battery's terminals when it's working.
The formula is: \( \epsilon = I(R + r) \) or \( V = \epsilon - Ir \)
Where:
\( R \) = External resistance (the satellite's equipment)
\( r \) = Internal resistance (inside the battery/cell)
5. Sensory Physics: LDRs and Thermistors
Satellites need to monitor their surroundings. They use components that change their resistance based on the environment.
Thermistors (Negative Temperature Coefficient - NTC)
As temperature increases, the resistance of an NTC thermistor decreases.
Why? In semi-conductors, more heat energy releases more conduction electrons, making it easier for current to flow. This outweighs the effect of lattice vibrations.
Light Dependent Resistors (LDRs)
As light intensity increases, the resistance of an LDR decreases.
Why? Photons (light particles) hit the material and release more conduction electrons.
6. Solar Power and Intensity
Satellites use solar panels to catch light. The amount of power they get depends on the Intensity of the light.
Intensity (I) is the power per unit area: \( I = \frac{P}{A} \)
Units: \( W m^{-2} \)
7. The Photoelectric Effect: Light as a Particle
This is a groundbreaking concept. Sometimes, light doesn't act like a wave—it acts like a stream of "packets" called photons.
Einstein’s Photoelectric Equation
When a photon hits a metal surface (like a solar cell), it can knock an electron off. This is called the photoelectric effect.
\( hf = \phi + \frac{1}{2}mv_{max}^2 \)
Where:
\( hf \) = Energy of the incoming photon (\( h \) is Planck's constant, \( f \) is frequency)
\( \phi \) (Work Function) = The minimum energy needed to liberate an electron from the surface.
\( \frac{1}{2}mv_{max}^2 \) = The maximum kinetic energy of the escaping electron.
Key Points to Remember:
- Threshold Frequency: The minimum frequency of light required to escape the metal. If the light is below this frequency, no electrons are emitted, no matter how bright the light is!
- The Electronvolt (eV): Because Joules are too big for subatomic particles, we use the eV. \( 1 eV = 1.6 \times 10^{-19} J \).
- Evidence for Particles: The photoelectric effect proves that light acts as a particle (photon), not just a wave.
Quick Review Box
\( I = \Delta Q / \Delta t \) (Current is charge flow)
\( V = \epsilon - Ir \) (Real batteries lose voltage)
\( I \propto 1/R \) (More resistance = less current)
\( hf = \phi + KE_{max} \) (Einstein's light-particle rule)
NTC Thermistor: Hotter = Lower Resistance
LDR: Brighter = Lower Resistance