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Satellite motion

Difference with ballistic motion (chatgpt)

Ballistic motion and satellite motion are related but distinct concepts in physics.

Ballistic Motion

Ballistic motion refers to the trajectory of an object that is launched into the air and follows a curved path under the influence of gravity and initial launch velocity. This type of motion is commonly seen with projectiles, like a thrown ball or a bullet, which typically have a parabolic trajectory. Once a projectile is launched, its motion is determined by:

Initial velocity: The speed and direction with which it was launched.
Gravity: Which pulls it downwards, causing a curved path.
No propulsion: After being launched, it is not propelled; it moves solely due to the initial force and gravity.

A ballistic object eventually falls back to Earth once its initial momentum is overcome by gravity.

Satellite Motion

Satellite motion, on the other hand, refers to the continuous orbit of an object around a planet, like Earth, due to the gravitational pull of the planet. A satellite, whether natural (like the Moon) or artificial, has:

High tangential velocity: This is fast enough that, as it “falls” towards Earth due to gravity, Earth’s curved surface “falls away” beneath it, allowing it to stay in continuous orbit.
Orbiting path: Instead of following a parabolic trajectory and returning to Earth, a satellite’s path is elliptical or circular, meaning it continually travels around the Earth.
Balanced gravitational force: In orbit, the gravitational force pulling it toward Earth is balanced by its tangential velocity, keeping it in stable orbit.

Key Differences

Path: Ballistic motion is typically a curved trajectory that ends when the object lands, while satellite motion forms an orbit, continuously circling the Earth.
Velocity: A satellite requires a much higher velocity to achieve and maintain orbit compared to an object in ballistic motion.
Continuous vs. finite: Ballistic motion is finite, ending when the object returns to the ground. Satellite motion is continuous and does not “end” unless influenced by external factors (e.g., atmospheric drag).

Summary

While ballistic motion and satellite motion both involve gravity, only satellite motion involves a balance of gravitational force and tangential velocity that keeps the object in orbit around Earth or another celestial body.

Velocity of an earth’s satellite

To compute the speed of an Earth satellite using Kepler’s Third Law, you can follow these steps:

1. Kepler’s Third Law Basics:

Kepler’s Third Law relates the orbital period (\(T\)) of a satellite to its semi-major axis (\(a\)):

\[ T^2 \propto a^3 \]
For satellites around the Earth, this can be rewritten as:

\[ T^2 = \frac{4 \pi^2 a^3}{GM} \]

Where:

\(T\) = Orbital period (time to complete one full orbit)
\(a\) = Semi-major axis of the orbit (which is approximately the radius of the orbit for a circular orbit)
\(G\) = Gravitational constant (\(6.674 \times 10^{-11} \, \text{m}^3 \text{kg}^{-1} \text{s}^{-2}\))
\(M\) = Mass of the Earth (\(5.972 \times 10^{24} \, \text{kg}\))

2. Relating the Orbital Period to Orbital Radius:

Rearranging the formula:

\[ T = 2\pi \sqrt{\frac{a^3}{GM}} \]

For circular orbits, \(a\) is simply the radius of the orbit (distance from the center of the Earth to the satellite).

3. Computing Orbital Speed:

The orbital speed \(v\) of a satellite in a circular orbit is related to the radius \(r\) (which is the semi-major axis \(a\)) and the gravitational force. It can be expressed as:

\[ v = \sqrt{\frac{GM}{r}} \]

Where:

\(v\) = Orbital speed of the satellite
\(r\) = Radius of the orbit (distance from the Earth’s center)

4. Steps to Compute the Speed:

Determine the radius of the orbit \(r\), which is the distance from the Earth’s center to the satellite. This is typically the Earth’s radius (\(\approx 6.371 \times 10^6 \, \text{m}\)) plus the satellite’s altitude above the Earth’s surface.
Use the formula for the orbital speed:

\[ v = \sqrt{\frac{GM}{r}} \]

Where \(G = 6.674 \times 10^{-11} \, \text{m}^3 \text{kg}^{-1} \text{s}^{-2}\) and \(M = 5.972 \times 10^{24} \, \text{kg}\).

Example:

If a satellite orbits at an altitude of 400 km above the Earth’s surface, the radius \(r\) would be:

\[ r = 6.371 \times 10^6 \, \text{m} + 400 \times 10^3 \, \text{m} = 6.771 \times 10^6 \, \text{m} \]

Now, using the formula:

\[ v = \sqrt{\frac{(6.674 \times 10^{-11}) \times (5.972 \times 10^{24})}{6.771 \times 10^6}} \approx 7.67 \, \text{km/s} \]

So, the speed of the satellite is approximately 7.67 km/s.

Parameters of some earth satellite

Here are orbital details of a few active satellites orbiting the Earth, covering different types of orbits (Low Earth Orbit, Medium Earth Orbit, and Geostationary Orbit):

1. International Space Station (ISS)

Type: Low Earth Orbit (LEO)
Altitude: ~400 km
Orbital Period: ~90 minutes (1.5 hours)
Orbital Speed: ~28,000 km/h (7.66 km/s)
Inclination: 51.6° (relative to the equator)
Purpose: Research, international cooperation, microgravity experiments

2. Hubble Space Telescope

Type: Low Earth Orbit (LEO)
Altitude: ~547 km
Orbital Period: ~95 minutes
Orbital Speed: ~27,300 km/h (7.58 km/s)
Inclination: 28.5°
Purpose: Space observations and astrophysics research

3. GPS Satellites (e.g., GPS Block IIR-M)

Type: Medium Earth Orbit (MEO)
Altitude: ~20,200 km
Orbital Period: ~12 hours
Orbital Speed: ~14,000 km/h (3.88 km/s)
Inclination: 55°
Purpose: Global Positioning System (GPS) for navigation and timing

4. GOES-16 (Geostationary Operational Environmental Satellite)

Type: Geostationary Orbit (GEO)
Altitude: ~35,786 km
Orbital Period: 24 hours (synchronous with Earth’s rotation)
Orbital Speed: ~3.07 km/s
Inclination: 0° (equatorial orbit)
Purpose: Weather monitoring and environmental data collection

5. Sentinel-1A (Earth Observation)

Type: Sun-Synchronous Orbit (a type of Low Earth Orbit)
Altitude: ~693 km
Orbital Period: ~98 minutes
Orbital Speed: ~27,000 km/h (7.5 km/s)
Inclination: 98.18°
Purpose: Radar imaging for environmental monitoring and disaster management

6. Iridium NEXT Constellation

Type: Low Earth Orbit (LEO)
Altitude: ~780 km
Orbital Period: ~100 minutes
Orbital Speed: ~26,800 km/h (7.45 km/s)
Inclination: 86.4°
Purpose: Global satellite communication

These satellites serve a variety of purposes, from research and earth observation to communication and navigation, and their orbits are chosen based on the mission requirements.

Orbital maneuvers

Yes, satellites change orbits by firing thrusters, which are small rocket engines that generate thrust. This process is known as an orbital maneuver. Here’s how it works:

1. The Basics of Orbital Change:

Thrust changes the satellite’s velocity (speed and direction), which in turn affects its orbit due to the relationship between velocity and orbital parameters.
Changing an orbit typically involves increasing or decreasing the satellite’s velocity (delta-v), which modifies the shape or altitude of its orbit.

2. Types of Orbital Maneuvers:

There are several common types of orbital maneuvers, depending on the goal:

a. Hohmann Transfer Orbit:

Used to change a satellite’s altitude (e.g., from a lower to a higher orbit).
It involves two main burns:
1. First burn: The satellite fires its thrusters at the perigee (lowest point in orbit) to increase its velocity and move into an elliptical transfer orbit.
2. Second burn: Once the satellite reaches the apogee (highest point), it fires the thrusters again to circularize the new, higher orbit.

b. Plane Change:

Used to change the inclination of the satellite’s orbit (its angle relative to the equator).
A plane change is more costly in terms of fuel because it requires a velocity change that’s not just along the satellite’s flight path, but also sideways to its motion.
Thrusters are fired perpendicular to the satellite’s orbital velocity to adjust its angle relative to Earth’s equator.

c. Geostationary Transfer Orbit (GTO) to GEO:

To move a satellite from a Geostationary Transfer Orbit (GTO) to a Geostationary Orbit (GEO), thrusters are fired at apogee to increase velocity and circularize the orbit at about 35,786 km.

3. Thrusters Used in Satellites:

Satellites are equipped with small propulsion systems to conduct these maneuvers. There are different types of thrusters depending on the satellite’s size and mission:

a. Chemical Thrusters:

These are the traditional rocket engines that use chemical propellants (like hydrazine).
They provide high thrust over short durations, making them effective for large orbital changes.

b. Electric/Ion Thrusters:

These use electricity (usually from solar panels) to accelerate ions, providing very efficient but low-thrust propulsion.
They are often used for smaller, long-duration adjustments (e.g., maintaining position in a geostationary orbit).

4. Examples of Orbit Changes:

Altitude Adjustment: A satellite may fire its thrusters at the perigee of its orbit to increase velocity and raise the apogee (raising the overall orbit).
Deorbiting: Satellites at the end of their mission may fire retrograde (opposite to their motion) to slow down, which lowers the orbit until they re-enter the atmosphere and burn up.

5. Fuel Limitations:

Since satellites carry a limited amount of fuel, the number of orbital changes they can perform is constrained. Efficient fuel management is crucial for extending the satellite’s operational lifetime.

In summary, satellites fire thrusters to change their velocity, which alters their orbit. The type and direction of the thrust depend on the nature of the orbit change (e.g., altitude increase, plane change, or deorbiting).