Interactive physics simulator
Artificial Satellites
Explore how human-made satellites orbit the Earth. Compare orbit regimes, test signal footprint beam coverage, and perform Hohmann transfer injections.
Artificial Satellites Lab
Analyze LEO, MEO, and GEO altitude properties, observe footprint beams, and execute transfer burns.
Live Telemetry
- Satellite Name
- ISS (LEO)
- Orbit Regime
- LEO
- Altitude (h)
- 400 km
- Orbital Speed (v)
- 7.67 km/s
- Orbital Period (T)
- 92.5 min
- Beam Width (θ)
- N/A
- Earth Coverage
- N/A
- Min Satellites
- N/A
Physics of Artificial Satellites
An artificial satellite is a human-made spacecraft placed into orbit around the Earth. The orbit is sustained by the balance between the outward inertial velocity of the satellite and the inward gravitational attraction of the Earth. According to Newton's laws of motion, a satellite is in a state of perpetual free fall around Earth: it falls toward Earth but travels fast enough horizontally that it constantly misses the Earth's curvature.
Orbit Classifications
Earth satellites are classified into four primary orbital regimes based on their altitude:
- Low Earth Orbit (LEO): Altitudes between 160 km and 2,000 km. Fast speeds (~7.8 km/s) and short periods (~90 minutes). Used for ISS, weather observation, and communication constellations.
- Medium Earth Orbit (MEO): Altitudes between 2,000 km and 35,786 km. Orbital periods typically range from 2 to 24 hours. Primarily used for navigation satellite constellations (like GPS).
- Geostationary Earth Orbit (GEO): Circular orbit at exactly 35,786 km above the equator. The orbital period matches Earth's rotation (23.93 hours), making the satellite appear stationary. Used for telecommunications and TV.
- Highly Elliptical Orbit (HEO): Egg-shaped orbits (e.g., Molniya orbits) that allow satellites to hover over polar regions for extended durations.
Footprint & Coverage
A satellite's signal footprint is the area on Earth's surface that has direct line-of-sight to the satellite:
- LEO Constellations: Small footprints mean hundreds of satellites are required for global coverage.
- GEO Satellites: A single GEO satellite covers up to 42% of Earth's surface. Only three GEO satellites are needed for complete global coverage (excluding poles).
- Coverage Angle: The maximum coverage arc angle φ on Earth's center is related to altitude h by: cos(φ/2) = RE / (RE + h).
Solved Examples
A communication satellite is launched into a circular Low Earth Orbit (LEO) at an altitude of h = 400 km. Calculate its orbital speed v and period T. (Earth radius RE = 6,371 km, GM = 3.986 × 105 km³/s²)
- Identify the given values: altitude h = 400 km, Earth radius RE = 6,371 km, gravitational parameter GM = 3.986 × 105 km³/s².
- Calculate the total orbital radius r: r = RE + h = 6,371 + 400 = 6,771 km.
- Apply the circular orbital velocity formula: v = √(GM / r).
- Substitute the values: v = √(3.986 × 105 / 6,771) = √58.868 ≈ 7.67 km/s.
- Apply the orbital period formula: T = 2π·r / v.
- Substitute values to get period in seconds: T = 2π · 6,771 / 7.67 ≈ 5,547 seconds.
- Convert to minutes: T = 5,547 / 60 ≈ 92.5 minutes.
- The satellite travels at 7.67 km/s and completes one orbit in about 92.5 minutes.
Answer: Orbital Speed v ≈ 7.67 km/s, Period T ≈ 92.5 minutes
Calculate the footprint coverage angle θ of a satellite in GEO at h = 35,786 km above Earth's surface to cover 30% of Earth's circumference. What is the line-of-sight distance? (RE = 6,371 km)
- Note that 30% coverage of Earth's circumference corresponds to a central coverage angle φ from the center of Earth: φ = 0.30 × 360° = 108°.
- State the geometry: The satellite, Earth center, and edge of footprint form a triangle. The central angle is half of φ, so φ/2 = 54°.
- Calculate the footprint coverage half-angle θ/2 from the satellite using trigonometry: tan(θ/2) = RE·sin(φ/2) / (RE + h - RE·cos(φ/2)).
- Substitute RE = 6,371 km and r = RE + h = 42,157 km.
- Numerically evaluate: sin(54°) ≈ 0.8090, cos(54°) ≈ 0.5878.
- Numerator = 6,371 × 0.8090 ≈ 5,154. Denominator = 42,157 - (6,371 × 0.5878) = 42,157 - 3,745 = 38,412.
- tan(θ/2) = 5,154 / 38,412 ≈ 0.1342. Therefore, θ/2 = arctan(0.1342) ≈ 7.64°.
- Double to find the total beam footprint width θ: θ = 2 × 7.64° ≈ 15.28°.
- The satellite needs a transmitter beam angle of about 15.3 degrees to cover 30% of Earth.
Answer: Transmitter beam angle θ ≈ 15.3°
A satellite is being transferred from a circular LEO (r1 = 6,800 km) to a circular MEO (r2 = 20,200 km) via a Hohmann Transfer. Calculate the initial speed kick (Delta-v1) needed to enter the transfer ellipse. (GM = 3.986 × 105 km³/s²)
- Calculate the initial circular velocity in LEO: v1 = √(GM / r1) = √(3.986 × 105 / 6,800) = √58.618 ≈ 7.66 km/s.
- State the semi-major axis of the transfer ellipse: atx = (r1 + r2) / 2 = (6,800 + 20,200) / 2 = 13,500 km.
- Apply the vis-viva equation to find the speed at perigee of the transfer orbit: vp = √(GM · (2/r1 - 1/atx)).
- Substitute values: vp = √(3.986 × 105 · (2/6,800 - 1/13,500)) = √(3.986 × 105 · (0.0002941 - 0.00007407)) = √(3.986 × 105 · 0.0002200) = √87.692 ≈ 9.36 km/s.
- Calculate the first speed increment Delta-v1: Delta-v1 = vp - v1.
- Substitute values: Delta-v1 = 9.36 - 7.66 = 1.70 km/s.
- The satellite must fire its engine to increase its speed by 1.70 km/s to enter the elliptical transfer orbit.
Answer: Initial speed increment Delta-v1 = 1.70 km/s
Common Misconceptions
- Believing satellites require constant thrust to stay in orbit. In the vacuum of space, inertia keeps them moving horizontally, and gravity acts as the centripetal force.
- Assuming satellites are outside Earth's gravity. At LEO altitudes, gravity is still about 90% as strong as it is on Earth's surface. Satellites float because they are in free fall, not because there is no gravity.
- Thinking geostationary orbits can be set at any altitude. They can only exist at exactly 35,786 km altitude because that is the unique radius where the period matches Earth's rotational period.
Hohmann Orbit Transfer
Hohmann transfer is the most fuel-efficient method to move a satellite between two circular orbits:
It uses an elliptical transfer orbit with perihelion at the lower radius r1 and aphelion at the higher radius r2. Burn 1 places the satellite on the ellipse, and Burn 2 circularizes it at r2.
Practice Questions
1. Why are geostationary satellites placed exactly 35,786 km above the equator?
To appear stationary in the sky, a satellite must rotate at the same rate as the Earth (once per day). Kepler's Third Law dictates that there is exactly one unique orbital radius where the period equals 23h 56m 4s. Solving T = 24 hours for Earth's mass yields a radius of 42,164 km, which corresponds to 35,786 km altitude. It must be over the equator so its orbit does not wobble north and south relative to the ground.
2. How does the orbital speed of a LEO satellite compare to a GEO satellite, and why?
LEO satellites are much closer to Earth (e.g., 400 km vs 35,786 km). Because gravitational pull is stronger close to Earth, LEO satellites must travel much faster (approx. 7.67 km/s) to maintain their orbit. GEO satellites travel at a slower speed (approx. 3.07 km/s) due to the weaker gravity at that altitude.
3. Explain how a Hohmann Transfer Orbit utilizes two impulse burns.
To raise an orbit, the first burn (Delta-v1) is performed in the direction of motion while in LEO, which stretches the circular orbit into a long ellipse with apogee at the target height. The satellite coasts along this ellipse. At apogee, a second burn (Delta-v2) is performed to accelerate the satellite to circular velocity at this new altitude, completing the transfer.
4. What is the visual horizon of a satellite, and how does altitude affect signal footprint?
The visual horizon is the point where the line of sight becomes tangent to Earth's sphere. A satellite at low altitude (LEO) can only see a tiny portion of the surface because Earth's curve quickly blocks the signal. A satellite at high altitude (GEO) has a wide view angle, allowing its signal to cover a massive footprint of up to 42% of Earth's surface.
FAQ
Frequently Asked Questions
What is an artificial satellite?
An artificial satellite is a human-made object placed intentionally into orbit around Earth or another celestial body to perform tasks like communication, weather monitoring, scientific research, or navigation.
What is the difference between a natural and artificial satellite?
A natural satellite is a celestial body that orbits a planet, such as the Moon orbiting Earth. An artificial satellite is constructed by humans and launched into space via rockets.
What are the three main types of orbits for Earth satellites?
The three main orbit regimes are: Low Earth Orbit (LEO, 160-2,000 km altitude), Medium Earth Orbit (MEO, 2,000-35,786 km), and Geostationary Earth Orbit (GEO, exactly 35,786 km).
What is a Geostationary Orbit (GEO)?
A Geostationary Orbit is a circular orbit 35,786 km above Earth's equator. Satellites in GEO have an orbital period of exactly 23 hours, 56 minutes, and 4 seconds (matching Earth's rotation), making them appear stationary over a fixed point on the ground.
Why are Low Earth Orbits (LEO) popular?
LEO satellites are close to Earth, which minimizes signal delay (latency) and requires less transmitter power. They are ideal for high-resolution earth imaging, weather observation, and communication constellations like Starlink.
What orbits do GPS satellites use?
GPS (Global Positioning System) satellites orbit in Medium Earth Orbit (MEO) at an altitude of approximately 20,200 km, with orbital periods of exactly 12 hours.
What is a Hohmann Transfer Orbit?
A Hohmann Transfer Orbit is an elliptical trajectory used to transition a satellite between two circular coplanar orbits of different altitudes. It consists of two engine burns (Delta-v): one to enter the elliptical transfer path, and a second to circularize at the final target altitude.
How does altitude affect a satellite's speed?
According to the physics of orbital motion (v = √(GM/r)), speed is inversely proportional to the square root of the orbital radius. Satellites in lower orbits move much faster than satellites in higher orbits (e.g., LEO speed ≈ 7.8 km/s, while GEO speed ≈ 3.07 km/s).
What is a satellite's footprint or signal coverage?
A satellite's footprint is the area on Earth's surface that can receive its signal. The size of the footprint increases with altitude, but the signal strength decreases. A GEO satellite has a massive footprint covering about one-third of the globe.
How many geostationary satellites are needed for global coverage?
Assuming a clear line-of-sight and excluding the extreme polar regions, a minimum of three geostationary satellites spaced 120 degrees apart are sufficient to cover the entire Earth.
Who launched the first artificial satellite?
The Soviet Union launched the first artificial satellite, Sputnik 1, on October 4, 1957, marking the beginning of the space age.
Do satellites require fuel to stay in orbit?
Once in orbit, satellites do not need fuel to maintain their circular velocity because gravity acts as the centripetal force in a vacuum. However, they carry small thrusters and fuel (propellant) for periodic station-keeping to correct orbital decay and orient solar panels.