Numerical Problems - Natural and Artificial Satellites

1. Earth’s Moon

• Radius: 1738 km
• Mass: 7.35E22 kg
• Distance from Earth: 384,400 km
• Orbital Period: 27.3 days

Key Facts:

• The Moon’s radius is about one-fourth of Earth’s radius.
• It has a mass of about 1/81 of Earth’s mass.
• The distance from Earth to the Moon is about 30 Earth’s diameters.

2. International Space Station(ISS)

• Radius: 3096 m
• Mass: 419725 kg
• Distance from Earth: 400,160 km
• Orbital Period: 92.6 minutes

Key Facts:

• ISS orbits Earth every 92 mins, travelling at a speed of about 28,000 km/h (17,000 mph).
• The distance btwn Earth and ISS varies from 340 to 420 kms at different points of its orbit.
• Astronauts onboard experience weightlessness due to continuously falling towards Earth in a state of “free fall”.

3. Galileo Satellites(Europe’s GPS)

• Number of Satellites: 30 (27 Active + 3 spare)
• Radius: 2.95 m
• Mass: 718 kg
• Distance from Earth: 23,222 km (Medium Earth Orbit)
• Orbital Period: 14 hours 21 minutes

Key Facts:

• A constellation of 30 satellites that enable precise positioning with an accuracy up to a few meters or less.
• Medium Earth Orbit (MEO) is btwn 2,000 and 35,786 kms above Earth’s surface.
• Signals are transmitted from the satellites, allowing devices on Earth to determine their position.

4. GPS Satellites(U.S. Global Positioning System)

• Number of Satellites: 31
• Radius: 0.6-1.7 m
• Mass: 780-1520 kg
• Distance from Earth: 20,180 km (Medium Earth Orbit)
• Orbital Period: 11 hours 58 minutes

Key Facts:

• GPS uses a network of 31 operational satellites that provide navigation and location info worldwide.
• Medium Earth Orbit (MEO) is between 2,000 and 35,786 kms above Earth’s surface.
• GPS devices receive signals from multiple satellites, allowing for accurate positioning and navigation.

5. Hubble Space Telescope(HST)

• Radius: 4.2 x 3.6 m
• Mass: 11 tonnes
• Distance from Earth: 547 km (Low Earth Orbit)
• Orbital Period: 97 minutes

Key Facts:

• Launched in 1990, HST revolutionised astronomy by providing stunning observations of the cosmos.
• Low Earth Orbit (LEO) is typically below 2,000 kilometres.
• Orbiting Earth at a speed of about 7.66 kms per second, HST completes nearly 15 orbits per day.

**6. Sputnik: World’s 1st Artificial Satellite **

• Launch Date: October 4 1957
• Radius: 58 cm in diameter
• Mass: 83.60 g
• Apogee - Perigee: 215 miles/142 miles
• Orbital period: 96.2 minutes

Key Facts:

• Sputnik 1 opened the space age, marking a significant milestone in space exploration.
• It travelled at an average speed of about 29,000 km/h (18,000 mph) in an elliptical orbit.
• Sputnik’s launch had a profound impact on the world, sparking the space race between the US and the Soviet Union.

7. James Webb Space Telescope (JWST) - Biggest, Powerful Space Telescope.

• Radius = 6.5 meter - The diameter of the primary mirror.
• Mass = 6200 kg. (approximated value) - Distance from Earth: approximately 1.5 million kilometers.

Key Facts:

• Launched on December 25, 2021.
• Equipped with a 6.5-meter gold-plated mirror, the largest ever launched into space, for unprecedented infrared observations.
• JWST is positioned at the Lagrange point L2, which is about 1.5 million kms away from Earth.
• Aims to study the earliest objects in the universe, including the first galaxies that formed just a few hundred million years after the Big Bang.