Std 10 Science Part 1 · Chapter 10

10. Space Missions

Complete solutions to the Exercise, with diagrams and step-by-step numericals. Maharashtra State Board (Balbharati), Std 10 Science and Technology Part 1.

Exercise

1Fill in the blanks and explain the statements with reasoning.

(a) If the height of the orbit of a satellite from the earth surface is increased, the tangential velocity of the satellite will …

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

Reason: The critical velocity of a satellite is v_c = √GM/(R + h). G, M and R are constant, so v_c is inversely proportional to √(R + h). As the height h increases, v_c decreases.

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

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

Reason: Mangalyaan had to leave the earth’s gravitational field and travel to Mars. Only an object whose initial velocity is greater than the escape velocity (11.2 km/s) can overcome the earth’s gravity and go into outer space.

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

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

False. To escape the earth’s gravitational field, the velocity of a spacecraft must be greater than or equal to the escape velocity (11.2 km/s).

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

True. Escape velocity is v_esc = √2GM/R. The mass of the moon is much smaller than that of the earth, so its escape velocity (about 2.4 km/s) is less than the earth’s (11.2 km/s).

(d) A satellite needs a specific velocity to revolve in a specific orbit.

True. A satellite revolves in an orbit only when it is given a specific tangential velocity, the critical velocity v_c = √GM/(R + h), which depends on the height of that orbit.

(e) If the height of the orbit of a satellite increases, its velocity must also increase.

False. From v_c = √GM/(R + h), the velocity of a satellite decreases as the height of its orbit increases.

The textbook numbers these (a), (b), (d), (e); there is no (c).

3Answer the following questions.

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

Artificial satellite: A man-made object that revolves around the earth or any other planet in a fixed orbit is called an artificial satellite. The first artificial satellite, Sputnik, was sent into space by the Soviet Union in 1957.

Classification based on functions:

Type of satellite	Function
Weather satellite	Study and prediction of weather
Communication satellite	Communication between different places in the world using specific waves
Broadcast satellite	Telecasting of television programmes
Navigational satellite	Fixing the location of any place on the earth in terms of its precise latitude and longitude
Military satellite	Collecting information for security
Earth observation satellite	Study of forests, deserts, oceans and polar ice; management of natural resources; guidance during floods and earthquakes

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

Orbit: The fixed path along which a satellite revolves around the earth is called its orbit. The function of the satellite decides the height of its orbit, its shape (circular or elliptical) and whether it is parallel to the equator or at an angle to it.

Basis: Orbits are classified on the basis of their height above the earth’s surface.

Orbits classified by height above the earth’s surface. (Not to scale)

Orbit	Height above earth’s surface	Features and uses
High Earth Orbit	35780 km or more	Takes about 24 hours for one revolution, so the satellite appears stationary (geosynchronous). Used for weather, telephone, TV and radio signals.
Medium Earth Orbit	2000 km to 35780 km	One revolution in 2 to 24 hours. Includes polar orbits and orbits of global positioning satellites (about 20,200 km).
Low Earth Orbit	180 km to 2000 km	One revolution in about 90 minutes. Used for scientific experiments and atmospheric studies; the International Space Station and Hubble telescope are here.

Geostationary satellites revolve in orbits above the equator, parallel to it.
They remain stationary with respect to the earth, so they continuously observe only a fixed part of the earth near the equator.
The polar regions are not in their view. So they are not useful for studying polar regions. Elliptical polar orbits passing over the poles are used for this.

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

Satellite launch vehicle: The vehicle used to carry a satellite to a specific height and place it in its orbit is called a satellite launch vehicle. It works on Newton’s third law of motion: hot gases from burning fuel are forcefully expelled through nozzles at the rear, and the reaction thrust drives the vehicle upward.

Schematic diagram of the Polar Satellite Launch Vehicle (PSLV) of ISRO. (Not to scale)

PSLV (Polar Satellite Launch Vehicle) of ISRO:

It is a four-stage launch vehicle. Solid fuel boosters (strap-on engines) around the first stage provide the initial thrust.
The first stage uses solid fuel, the second stage liquid fuel, the third stage solid fuel and the fourth stage liquid fuel.
The satellite is placed at the top of the vehicle.
As the fuel of each stage is used up, its empty tank and engine separate and fall into the sea or on unpopulated land. The next stage is then ignited.
The vehicle becomes lighter step by step, gains higher speed, and finally places the satellite in its orbit.

(e) Why it is beneficial to use satellite launch vehicles made of more than one stage?

The fuel forms a major part of the weight of a launch vehicle, so the vehicle has to carry a very large weight.
In a multi-stage vehicle, when the fuel in one stage is exhausted, that stage (empty tank and engine) is detached.
The weight of the vehicle is reduced step by step after launching, so the remaining stages can move with higher speed using less fuel.
This makes it possible to take the satellite to its orbit efficiently.

4Complete the following table.

Satellite series	Type / function	Launch vehicle
IRNSS	Navigational satellite (fixing precise latitude and longitude)	PSLV
INSAT / GSAT	Weather study and prediction	GSLV
IRS	Earth’s observation	PSLV

5Solve the following problems.

(a) If 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?

Given: M_p = 8M, R_p = 2R, escape velocity of the earth v_e = 11.2 km/s. To find: v_p

v_e = √2GM/R
v_p = √2G(8M)/(2R) = √4 × 2GM/R = 2 × √2GM/R = 2v_e
v_p = 2 × 11.2 = 22.4 km/s

The escape velocity for that planet is 22.4 km/s.

(b) How much time a satellite in an orbit at height 35780 km above earth’s surface would take, if the mass of the earth would have been four times its original mass?

Given: h = 35780 km. With the actual mass M, the satellite takes T = 23.89 h ≈ 24 h (solved example). New mass = 4M. To find: new period T₂

v = √GM/(R + h) ⇒ v₂ = √G(4M)/(R + h) = 2v
T = 2π(R + h)v ⇒ T₂ = 2π(R + h)2v = T2
T₂ = 23.892 = 11.95 h ≈ 12 hours

The satellite would take about 12 hours for one revolution.

(c) If the height of a satellite completing one revolution around the earth in T seconds is h₁ meter, then what would be the height of a satellite taking 2√2 T seconds for one revolution?

Given: height h₁, period T₁ = T; period T₂ = 2√2 T. To find: h₂

By Kepler’s third law, T² ∝ r³, where r = R + h
T₂²T₁² = (R + h₂)³(R + h₁)³
(2√2 T)²T² = 8 = (R + h₂)³(R + h₁)³
Taking cube roots: R + h₂R + h₁ = 2 ⇒ R + h₂ = 2R + 2h₁
h₂ = R + 2h₁

The height of the second satellite would be R + 2h₁ metres, where R is the radius of the earth.

★Project: 1. Collect information about the space missions undertaken by Sunita Williams. 2. Assume that you are interviewing Sunita Williams. Prepare a questionnaire and also the answers.

1. Space missions of Sunita Williams

Mission	Details
2006–2007	Travelled to the International Space Station in space shuttle Discovery. Worked as flight engineer and completed four spacewalks (about 29 hours). Stayed for a record period for a woman at that time.
2012	127-day mission launched from Baikonur, Kazakhstan. Became commander of the space station (Expedition 33) and completed three spacewalks.
2024–2025	Flew on the first crewed test flight of Boeing Starliner in June 2024. The short trip turned into a 286-day stay; she commanded the station and returned in March 2025.

In all, she spent 608 days in space and 62 hours on nine spacewalks, the most spacewalk time by any woman. She retired from NASA in December 2025.

2. Sample interview

Q: What inspired you to become an astronaut?
A: I was a navy test pilot. A visit to NASA’s Johnson Space Center made me want to fly in space.
Q: How does it feel to see the earth from space?
A: It is beautiful. There are no borders; the whole earth looks like one home.
Q: How do astronauts eat and sleep without gravity?
A: Food comes in packets, and we sleep in sleeping bags tied to the wall so that we do not float away.
Q: What is a spacewalk like?
A: We wear a special suit and work outside the station, tied with safety tethers. It needs a lot of practice and care.
Q: What was the most difficult moment?
A: When my 2024 mission was extended by many months. We stayed calm, kept working and trusted our teams on the ground.
Q: What is your message for students?
A: Study hard, be curious, stay fit and never give up on your dreams.

The interview answers are imagined, based on her known life and missions. Students may add their own questions.

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