Question 1.

Fill in the blanks and explain the statements with reasoning:

a. If the height of the orbit of a satellite from the earth’s surface is increased, the tangential velocity of the satellite will ………………

Answer:

If the height of the orbit of a satellite from the earth’s surface, is increased, the tangential velocity of the satellite will decrease.

Explanation. The gravitational force exerted by the Earth on the satellite decreases as the orbit height of the satellite from the Earth’s surface increases, resulting in a decrease in the satellite’s tangential velocity.

b. The initial velocity (during launching) of the Mangalyaan must be greater than ………… from the earth.

Answer:

The initial velocity (during launching) of the Mangalyaan must be greater than the escape velocity from the earth.

Explanation: The velocity of the satellite should be more than the escape velocity of the earth than only the satellite can travel beyond the gravitational pull of the earth.

Question 2.State with reasons whether the following statements are true or false.

a. If a spacecraft has to be sent away from the influence of the earth’s gravitational field, its velocity must be less than the escape velocity.

False.

The minimum velocity needed to project a body from Earth’s surface to escape the gravitational field is known as escape velocity. This indicates that the statement provided is incorrect.

b. The escape velocity on the moon is less than that on the earth.

Answer.

c. A satellite needs a specific velocity to revolve in a specific orbit.

True

Explanation.

The centripetal force on the satellite at velocity v^2c/R+h equals the gravitational force exerted by the earth on the satellite GMm/(R+h)^2, where m represents the mass of the satellite, υc stands for the critical velocity of the satellite, h denotes the height of the satellite from the surface of the earth, M represents the mass of the earth, R is the radius of the earth, and G is the gravitational constant. Therefore, v/2c=GM/R+h and v/c=√GM/R+h. Consequently, if the value of h changes, the value of υc also changes. This implies that a satellite must be given a specific velocity (in the tangential direction) to maintain its orbit.

Orbit of an artificial satellite

According to the formula υc = √GM/R+h, when the value of h goes up, the value of υc goes down. Therefore, as the satellite’s distance from the earth’s surface increases, its velocity decreases..

Question 3.

Answer the following questions:

a. What is meant by an artificial satellite? How are the satellites classified based on their functions?

Answer : An artificial satellite is a manmade object that orbits the Earth or another planet. These satellites operate using solar energy, with photovoltaic panels resembling wings attached on both sides. Equipped with transmitters and other tools, satellites facilitate signal transmission between Earth and themselves. Satellites are categorized based on their functions:

1. Weather satellites: These satellites gather data on weather conditions, including temperature, air pressure, wind direction, humidity, and cloud cover. The information is relayed to Earth’s space research stations for weather forecasting.

2. Communication satellites: These satellites enable communication via mobile phones or the internet between different locations on Earth. Placed strategically in Earth’s orbit, they ensure seamless communication in various forms like voicemail, email, photos, and audio messages.

3. Broadcasting satellites: Used to transmit radio, television, and live programs globally, broadcasting satellites provide access to real-time information, events, sports, and programs from any location.

4. Navigational satellites: These satellites support surface, water, and air transportation by providing live maps and real-time traffic updates, helping to coordinate busy schedules effectively.

5. Military satellites: Essential for monitoring borders and tracking movements of neighboring or enemy nations, military satellites play a crucial role in guiding missile systems.

6. Earth observation satellites: These satellites offer real-time information on Earth’s resources, natural phenomena, and environmental changes, aiding in resource management and continuous monitoring.

 7. Other satellites: Beyond the aforementioned categories, specialized satellites like EDUSAT for education, CARTOSAT for surveys, and telescopic satellites such as the Hubble Telescope serve diverse purposes. The International Space Station (ISS) serves as a temporary residence for astronauts to conduct research and study space activities, showcasing the broad spectrum of satellite functions.

b. What is meant by the orbit of a satellite? On what basis and how are the orbits of artificial satellites classified?

Answer:

The orbit of a satellite refers to its path around the Earth. Artificial satellites can be classified based on various criteria:

 1. On the angle of the orbital plane: The orbital plane of a satellite may align with the Earth’s equatorial plane or be positioned at an angle to it.

2. On the nature of the orbit: The orbital path can be circular or elliptical in shape.

3. On the height of the satellite: Satellites can be categorized as High Earth Orbit (HEO), Medium Earth Orbit (MEO), or Low Earth Orbit (LEO).

(i) High Earth Orbit (HEO) satellite: Satellites orbiting at a height equal to or greater than 35780 km above the Earth’s surface fall under this category. A satellite in HEO has a critical velocity (υc) of 3.08 km/s, completing one revolution around the Earth in approximately 23 hours and 54 minutes. Positioned in the Earth’s equatorial plane, a geostationary or geosynchronous satellite appears stationary relative to a point on the Earth.

(ii) Medium Earth Orbit (MEO) satellite: Satellites orbiting at a height between 2000 km and 35780 km above the Earth’s surface are known as Medium Earth Orbit satellites. Their orbital paths are typically elliptical, passing through the North and South polar regions. These satellites take around 12 hours to complete one revolution.

(3)A Low Earth Orbit (LEO) satellite is a satellite that orbits at a height ranging from 180 km to 2000 km above the Earth’s surface. Typically, these satellites complete one revolution around the Earth in 90 minutes. Examples of LEO satellites include weather satellites, space telescopes, and the International Space Station.

Orbit of satellite

c. Why are geostationary satellites not useful for studies of polar regions? 

Answer. Geostationary satellites have two unique features: They are HEO satellites positioned 35780 km above the earth’s surface.

Orbit of Geostationary satellites

Geostationary satellites orbit the Earth’s equatorial plane, making them unable to pass over the polar regions. As a result, geostationary satellites are not beneficial for researching the polar regions.

d. What is meant by a satellite launch vehicle? Explain the satellite launch vehicle developed by ISRO with the help of a schematic diagram.

A launch vehicle is a rocket that carries an artificial satellite to a specific height above the earth’s surface and propels it with the correct velocity to establish the desired orbit around the earth.

To achieve this, the launch vehicle must possess the necessary velocity and thrust based on the satellite’s weight and orbital height.

The design of the launch vehicle is determined by these factors, as well as the weight of the fuel which significantly impacts the total weight of the vehicle. To optimize fuel usage, multi-stage launch vehicles have been developed and implemented. An example of such a launch vehicle is the Polar Satellite Launch Vehicle (PSLV) created by ISRO, which is illustrated in the schematic diagram below.

e. Why is it beneficial to use a satellite j launch vehicle made up of more than one stage?
Answer:Earlier, Satellite Launch Vehicles (SLV) used to consist of single-stage vehicles, which were heavy and costly in terms of fuel consumption. As a solution, SLVs with multiple stages were developed. In multi-stage SLVs, as the launch vehicle progresses in its journey and reaches a specific velocity and height, the first stage’s fuel is depleted. At this point, the empty fuel tank detaches from the main body of the vehicle and falls back into the sea or unpopulated land. With the first stage depleted of fuel, the engine in the second stage ignites. The reduced weight of the launch vehicle enables it to achieve higher velocity, resulting in fuel savings. Therefore, utilizing a multi-stage satellite launch vehicle is advantageous.

Question 5.

Solve the following problems:

a. If the mass of a planet is eight times the mass of the earth and its radius is twice the radius of the earth, what will be the escape velocity for that planet?

Answer:

1. The planet’s mass is 8 times that of Earth, equivalent to 8 × 6 × 10^24 kg.
2. Its radius is twice that of Earth, equal to 2 × 6.4 × 10^6 km.
3. The gravitational constant is 6.67 × 10^-11 N·m^2/kg^2. Determine the escape velocity of this planet.

b. How much time would a satellite in an orbit at a height of 35780 km above the earth’s surface take to complete one revolution around the earth, if the mass of the earth were four times its original mass?

Answer:
Given: R (Earth) = 6400 km = 6.4 × 10⁶ m,
M (Earth) = 6 × 10²⁴ kg
∴ M’ = 4M = 4 × 6 × 10²⁴ kg
h = 35780 km = 3.578 × 10⁷ m = 35.78 × 10⁶ m,
G = 6.67 × 10^-11 N·m²/kg², T = ?
The time that the satellite would take to complete one revolution around the earth,

= Approx 4.303 × 10⁴ s
= Approx 11.95 h
or 11 hours 57 minutes 10 seconds.

c. If the height of a satellite completing one revolution around the earth in T seconds is h1 meters, then what would be the height of a satellite taking 22–√ T seconds for one revolution? Answer:
Given:
(1) Time: T seconds
(2) Height: h₁
Let us assume the height of the satellite completing one revolution in 22–√ T seconds as h₂.

∴ R + h₂ = 2R + 2h₁
∴ h₂ = R + 2h₁