10. Space Missions

Space Missions Satellite Launch Vehicles Artificial Satellites Classification Orbits Missions Beyond Earth

Quick Navigation: Can you recall? • Need & Importance • Artificial Satellites • Classification • Orbits & Equations • Launch Vehicles • Missions Beyond Earth • India & Space Tech • Inspiring Astronauts • Space Debris

Can you recall?

Space vs Sky: The sky is what we see within Earth’s atmosphere; space lies beyond it where air is negligible.
Solar System Objects: Sun, planets, dwarf planets, moons, asteroids, comets, meteoroids.
Satellite: A body orbiting a planet; can be natural (Moon) or artificial (man-made).
Natural satellites of Earth: One — the Moon.

Space Missions — Need & Importance

Space technology connects the world and supports:

Instant communication (phone/TV/internet).
Weather monitoring, cyclone alerts, disaster early warning.
Resource mapping (forests, minerals, water, coasts, agriculture).
Navigation & precise timing.
Security and strategic reconnaissance.

Historic Firsts

First human in space — Yuri Gagarin (1961)
First Moon landing — Neil Armstrong (1969)
First Indian in space — Rakesh Sharma (1984)
Indian-origin astronauts — Kalpana Chawla, Sunita Williams

Artificial Satellites

An artificial satellite is a man-made object placed in orbit for specific tasks (communication, weather, navigation, Earth observation, science).

Power & Payloads: Solar panels supply energy. Antennas handle uplink/downlink. Sensors & instruments vary by mission.

Sputnik-1 (USSR, 1957) — first artificial satellite. Now, thousands orbit Earth.

Classification of Artificial Satellites (by Function)

Type	Main Functions	Indian Series	Launcher
Weather	Meteorology, cloud images, monsoon tracking, cyclone alerts	INSAT, GSAT	GSLV
Communication	Phone, TV, internet, data links (incl. EDUSAT for education)	INSAT, GSAT	GSLV
Broadcast	Television & radio beaming	INSAT, GSAT	GSLV
Navigation	Precise position, navigation & timing	IRNSS (NavIC)	PSLV
Earth Observation	Resources, land/ocean/ice, disaster management	IRS	PSLV
Military	Security, reconnaissance, secure comms	Various	PSLV/GSLV

Orbits of Artificial Satellites

To place a satellite, a launcher raises it to height \(h\) and gives the required tangential/critical velocity \(v_c\).

Critical Velocity (Derivation)

Equate centripetal and gravitational forces:
\[ \frac{m v_c^2}{R+h}=\frac{GMm}{(R+h)^2} \;\Rightarrow\; v_c=\sqrt{\frac{GM}{R+h}} \] Constants for Earth: \(G=6.67\times10^{-11}\,\text{N·m}^2\!\!/\text{kg}^2\), \(M=6\times10^{24}\,\text{kg}\), \(R=6.4\times10^{6}\,\text{m}\).

Orbit Bands

High Earth Orbit (HEO): \(h \ge 35{,}780\) km — geosynchronous/geostationary, appear fixed over one region (best for weather & comms).
Medium Earth Orbit (MEO): \(2{,}000\text{ km} \le h < 35{,}780\text{ km}\) — includes polar/elliptical; GNSS around ~20,200 km.
Low Earth Orbit (LEO): \(180\text{–}2{,}000\) km — science, Earth observation; ~90–120 min period (ISS, Hubble).

Solved Example 1 — Velocity at Geostationary Height

\[ h = 35{,}780\ \text{km},\quad R+h = 42{,}180\ \text{km} = 4.218\times10^{7}\ \text{m} \] \[ v_c = \sqrt{\frac{GM}{R+h}} \approx \sqrt{\frac{3.986\times10^{14}}{4.218\times10^{7}}} \approx \boxed{3.08\ \text{km/s}} \]

Solved Example 2 — Time Period at Geostationary Height

\[ T=\frac{2\pi(R+h)}{v}\approx \frac{2\pi\times 42{,}180\ \text{km}}{3.08\ \text{km/s}} \approx 8.6\times10^4\ \text{s}\approx \boxed{23\ \text{h }54\ \text{min}} \] (≈ one sidereal day)

Student Satellite “Swayam” (COEP, 2016): ~1 kg nanosatellite launched by ISRO into ~515 km LEO for point-to-point messaging experiments.

Satellite Launch Vehicles

Principle: Newton’s Third Law — high-speed exhaust produces equal & opposite thrust.

Multistage design: Empty stages are jettisoned to reduce mass and reach higher velocity (e.g., PSLV, GSLV).
Fuels: Solid, liquid, cryogenic, or hybrid—chosen per mission and payload.

PSLV (ISRO): Polar Satellite Launch Vehicle — highly reliable for LEO/MEO & Sun-synchronous orbits (mixed solid/liquid stages).

GSLV (ISRO): Geosynchronous Satellite Launch Vehicle — heavier payloads, high-energy orbits; cryogenic upper stage variants.

Reusable systems: Classic rockets are single-use. Space Shuttle (USA) returned for reuse (except external tank). Modern trend favours reusable boosters to cut cost.

Space Missions Away from Earth

Escape Velocity

To leave Earth’s gravitational field: \[ v_{\text{esc}}=\sqrt{\frac{2GM}{R}} \;\Rightarrow\; v_{\text{esc}} \approx \boxed{11.2\ \text{km/s}} \]

How far is the Moon? Light takes ~1.3 s; spacecraft (much slower) take hours–days. A record short transfer took ~8 h 36 min using a special trajectory.

Moon Missions

Luna (USSR): Luna-2 (1959) reached the Moon; later missions studied gravity, radiation; some returned samples.
Apollo (USA): Manned landings (1969–72). Neil Armstrong — first human on the Moon (1969).
Chandrayaan-1 (India, 2008): Orbiter that discovered water on the lunar surface — a landmark result.

Mars Missions

Mars is challenging; many missions have failed worldwide.
Mangalyaan (Mars Orbiter Mission, ISRO): Launched Nov 2013; Mars orbit insertion Sep 2014; valuable surface & atmospheric insights; famed for success on first attempt with modest cost.

Missions to Other Bodies

Flybys, orbiters, landers, and sample-returns have explored planets, asteroids, and comets, sharpening our understanding of Solar System formation and evolution.

India & Space Technology

Launchers: PSLV & GSLV families place payloads into diverse orbits.
INSAT/GSAT: Communication, broadcasting, meteorology; EDUSAT for education.
IRS: Earth observation, resources, disaster management.
IRNSS (NavIC): Regional navigation & timing services.

Launch Centres

Thumba (Thiruvananthapuram)
Sriharikota (Satish Dhawan Space Centre)
Chandipur, Odisha

Key ISRO Centres

Vikram Sarabhai Space Centre (VSSC), Thiruvananthapuram
Satish Dhawan Space Centre (SDSC), Sriharikota
Space Applications Centre (SAC), Ahmedabad

Vikram Sarabhai — Father of India’s space programme; led PRL, INCOSPAR, Thumba range (1963), and paved the way to ISRO and India’s first satellite Aryabhata.

Inspiring Astronauts (Indian Connection)

Rakesh Sharma: First Indian in space (1984), spent ~8 days in orbit in a joint Indo-USSR mission.
Kalpana Chawla: Aeronautical engineer; 336 hours in space; perished in Space Shuttle Columbia accident (2003).
Sunita Williams: Long-duration missions aboard ISS; extensive spacewalk time; record-setting stays.

Space Debris & Its Management

Earth orbit also hosts non-functional satellites, spent stages, and fragments from break-ups — called space debris.

An estimate (2016) suggested ~20 million objects ≥1 cm in orbit. High-speed impacts threaten satellites and crewed spacecraft. Solutions include end-of-life de-orbiting, passivation, debris tracking, and active removal technologies.

Everyday Links

Mobile & TV: Often relayed via geostationary communication satellites.
Weather maps: From meteorological imagers in visible/IR bands.
Maps & navigation apps: Use MEO constellations (GNSS) and regional systems like NavIC.

Chapter 10 — Space Missions : Exercise Answers (With Reasoning)

1) Fill in the blanks (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 decrease.

Reason: For a circular orbit, the required (critical) velocity is \[ v_c=\sqrt{\frac{GM}{R+h}} \] As height \(h\) increases, the denominator \((R+h)\) increases, so \(v_c\) decreases.

b. The initial velocity (during launching) of the Mangalyaan must be greater than the Earth’s escape velocity.

Reason: To depart Earth’s gravitational field and head for Mars transfer, the spacecraft must achieve energy ≥ escape energy: \[ v_{\text{esc}}=\sqrt{\frac{2GM}{R}}\approx 11.2\ \text{km s}^{-1}\ (\text{for Earth}) \]

2) True/False — justify each

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.

It must be at least escape velocity: \(v\ge v_{\text{esc}}=\sqrt{2GM/R}\).

b. “The escape velocity on the Moon is less than that on the Earth.” — True.

Moon has much smaller \(M\) and comparable but smaller \(R\), so \(\sqrt{2GM/R}\) is smaller (~2.38 km/s) than Earth’s (~11.2 km/s).

c. “A satellite needs a specific velocity to revolve in a specific orbit.” — True.

Orbital speed is fixed by radius: \(v_c=\sqrt{\dfrac{GM}{R+h}}\). For each orbit radius \((R+h)\), there is a unique \(v_c\).

d. “If the height of the orbit of a satellite increases, its velocity must also increase.” — False.

From \(v_c=\sqrt{GM/(R+h)}\), increasing \(h\) reduces \(v_c\).

3) Answer the following

a) Artificial satellite & classification by function

An artificial satellite is a man-made object placed into orbit for tasks like communication, weather, navigation, Earth observation, or science. Based on function, satellites are classified as:

Communication Broadcast Weather (Meteorology) Navigation Earth Observation Military/Strategic Scientific

b) Orbit — meaning & classification

An orbit is the path a satellite follows around Earth, usually circular or elliptical. Classification commonly uses:

By height: LEO (180–2000 km), MEO (2000–35780 km), HEO (≥35780 km; geosynchronous/geostationary).
By inclination: Equatorial (inclination ≈ 0°), Polar (≈ 90°), Sun-synchronous, etc.
By shape: Circular vs Elliptical.

c) Why geostationary satellites are not useful for polar studies

Geostationary satellites orbit above the equator (inclination 0°) and “hover” over one longitude. From near-equator vantage, the poles are at very low elevation/visibility, giving poor spatial coverage and geometry—hence not ideal for polar observation. Polar or Sun-synchronous orbits are preferred.

d) Satellite launch vehicles; PSLV schematic (ISRO)

Satellite Launch Vehicles (SLVs) are multistage rockets that provide the thrust (via high-speed exhaust) to place satellites into desired orbits (Newton’s 3rd Law). ISRO’s PSLV (Polar Satellite Launch Vehicle) uses mixed solid/liquid stages:

Payload Fairing — protects satellite during ascent

Fourth Stage (PS4) — Liquid (precision orbit insertion)

Third Stage (PS3) — Solid

Second Stage (PS2) — Liquid (Vikas engine)

First Stage (PS1) — Large Solid + strap-on solid boosters for extra thrust

How it works: Each stage burns then is jettisoned, reducing mass and allowing higher speeds. PSLV excels at LEO/SSO and also multi-satellite deployments.

e) Why use multistage rockets?

Dropping empty stages dramatically reduces mass, improving efficiency and achievable \(\Delta v\). This enables heavier payloads and higher orbits with practical engines/fuels.

4) Complete the table

Type of Satellite	Primary Function	Indian Series	Typical Launcher
Weather	Weather study & prediction	INSAT / GSAT	GSLV
Communication / Broadcast	Telephony, TV, internet, data	INSAT / GSAT	GSLV
Navigation	Positioning, navigation, timing	IRNSS (NavIC)	PSLV
Earth’s Observation	Resource mapping, disasters, land/ocean/ice	IRS	PSLV
Military / Strategic	Reconnaissance, secure comms	Various	PSLV / GSLV

5) Numerical Problems — Worked Solutions

(a) Escape velocity on a different planet

Given: Planet has mass \(M_p=8M_E\), radius \(R_p=2R_E\). Show \(v_{\text{esc}}\approx 22.4\ \text{km/s}\).

\[ v_{\text{esc}}=\sqrt{\frac{2GM}{R}} \;\Rightarrow\; v_{\text{esc},p} =\sqrt{\frac{2G(8M_E)}{2R_E}} =\sqrt{4}\,\sqrt{\frac{2GM_E}{R_E}} =2\,v_{\text{esc},E} \] Since \(v_{\text{esc},E}\approx 11.2\ \text{km/s}\), \[ v_{\text{esc},p}\approx 2\times 11.2 = \boxed{22.4\ \text{km/s}} \]

(b) Geostationary height, but Earth’s mass ×4 — new period?

Given: Same orbital radius \(r=R+h\) where \(h=35780\ \text{km}\), but Earth’s mass becomes \(4M\). Find the new period \(T'\).

Using \(T=2\pi\sqrt{\dfrac{r^3}{GM}}\), at fixed \(r\): \[ T' = 2\pi\sqrt{\frac{r^3}{G(4M)}}=\frac{1}{2}\,2\pi\sqrt{\frac{r^3}{GM}}=\frac{T}{2} \] Original \(T\approx 24\ \text{h}\Rightarrow T'\approx \boxed{12\ \text{h}}\ (\text{≈ }11.97\ \text{h})

(c) Height for a different period

Given: A satellite with period \(T\) has height \(h_1\) (radius \(r_1=R+h_1\)). Find the height for a satellite whose period is a different multiple of \(T\).

From Kepler’s 3rd law for circular orbits: \[ T \propto r^{3/2}\ \Rightarrow\ \left(\frac{T_2}{T_1}\right)=\left(\frac{r_2}{r_1}\right)^{3/2} \ \Rightarrow\ r_2=r_1\left(\frac{T_2}{T_1}\right)^{2/3} \] With \(T_1=T,\ r_1=R+h_1\), and \(T_2=\alpha T\) (any factor \(\alpha>0\)): \[ r_2=(R+h_1)\,\alpha^{2/3} \quad\Rightarrow\quad \boxed{\,h_2=(R+h_1)\,\alpha^{2/3}-R\,} \] Example: If the new period is double (\(\alpha=2\)), then \(h_2=(R+h_1)\,2^{2/3}-R\).

This general form covers any stated multiple (e.g., \(2T,\ 3T,\ 2\sqrt{2}\,T\), etc.). Insert \(\alpha\) accordingly.