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Every time you read about Chandrayaan or a PSLV launch, you are looking at the result of a decision made in the early 1970s: India would learn to build its own satellites. The scientist given that job was Udupi Ramachandra Rao. This post covers who he was, how his team built Aryabhata, a worked example on its orbit that you can do with Class 11 gravitation, and what his way of working teaches.
Who was U. R. Rao?
ISRO's page on Prof. U. R. Rao gives the outline. He was born on 10 March 1932 in Adamaru, Udupi. He took a BSc from Madras University in 1951, an MS from Banaras Hindu University in 1953 and a PhD from Gujarat University in 1960. He then worked as a faculty member at MIT and as an assistant professor at the University of Texas at Dallas, where he was an experimenter on several Pioneer and Explorer spacecraft. He returned to India in 1966 as a professor at the Physical Research Laboratory in Ahmedabad.
In 1972 he took responsibility for building satellite technology in India. ISRO credits him with guiding more than 18 satellites, starting with Aryabhata in 1975. He directed the ISRO Satellite Centre in Bengaluru from 1975 to 1984 and chaired ISRO from 1984 to 1994, a period in which the ASLV and the PSLV were launched and GSLV and cryogenic engine work began (1991). ISRO lists the Padma Bhushan (1976), the Padma Vibhushan (2017), and his induction into the Satellite Hall of Fame in Washington on 19 March 2013.
How was Aryabhata built?
A radio talk by Satish Dhawan, recorded on 16 January 1975 and reprinted in Resonance (2003), describes the project from the inside. In 1972 the USSR Academy of Sciences offered to launch an Indian-made satellite on a Soviet rocket. India's scientists judged that they could build a satellite sooner than the large rockets needed to launch one, so they accepted. The task went to Rao, who gathered young engineers and worked with electronics and aircraft establishments in Bengaluru.
The satellite took shape in a clean room at the Peenya industrial estate: a 26-faced body about one and a half metres across. Dhawan lists the problems the team had to solve:
Heat and cold. In orbit the spacecraft swings between full sunlight and Earth's shadow. The team used passive thermal control: special paints chosen for how they absorb and emit radiation.
Power. About 18,500 silicon solar cells on the outside, with nickel-cadmium batteries for the time in Earth's shadow.
Testing. Some test facilities did not exist in India, so the team built them alongside the satellite. They made separate mechanical and electrical prototypes, and flew the electrical one under a helicopter at Sriharikota to check radio links with the ground station.
Science. Three Indian-built experiments, one of them in X-ray astronomy led by Rao himself.
ISRO's Aryabhata mission page records the outcome. The 360 kg satellite, "completely designed and fabricated in India", was launched by a Soviet Kosmos-3M rocket from Kapustin Yar on 19 April 1975 into a 563 by 619 km orbit inclined at 50.7 degrees. It carried 46 W of power, was spin-stabilised, had a nominal mission life of six months, kept its mainframe active until March 1981, and re-entered the atmosphere on 10 February 1992.
Worked example: how long did one orbit take?
Kepler's third law for a satellite around Earth is T = 2π √(a³/GM), where a is the semi-major axis measured from Earth's centre. For GM of Earth, use the nominal value from IAU 2015 Resolution B3: 3.986004 × 10¹⁴ m³ s⁻², and its nominal equatorial radius of 6378.1 km.
Find a. For an ellipse, a is the average of the closest and farthest distances from Earth's centre: a = 6378.1 + (563 + 619)/2 = 6378.1 + 591 = 6969.1 km = 6.9691 × 10⁶ m.
Cube it. a³ = (6.9691 × 10⁶)³ ≈ 3.3847 × 10²⁰ m³.
Divide by GM. 3.3847 × 10²⁰ / 3.986004 × 10¹⁴ ≈ 8.4914 × 10⁵ s².
Square root, times 2π. √(8.4914 × 10⁵) ≈ 921.5 s, and 2π × 921.5 ≈ 5790 s.
So one orbit took about 96.5 minutes, or roughly 15 orbits a day (1440/96.5 ≈ 14.9).
Common mistakes:
Using the height above the ground as a. If you put a = 591 km, you get about 2.4 minutes, which is impossible. Orbits are measured from Earth's centre.
Mixing km and m. GM is in m³ s⁻², so a must be in metres.
Forgetting the square root. Without it you get a number in s², not seconds.
For more practice, our guide to satellite problems in gravitation works through orbital speed and energy as well.
What can a student take from Rao's way of working?
Scientists can build things. Rao was a cosmic-ray physicist who became a satellite builder. Depth in one subject made it possible to learn another.
Prototype before the real thing. Each of Aryabhata's prototypes tested one question: shape, electronics or radio links. Breaking a big task into tests is a habit that works for a project file as well as a satellite.
Make your own tools when you have to. The team built test equipment India did not yet have.
Do the science too. Rao ran his own X-ray astronomy experiment on the satellite he was building.
You can read more of this story in our posts on Satish Dhawan and Vikram Sarabhai. If orbits are hard to picture, the Fermi Simulation Lab has interactive simulations for ideas that are easier to see than read, so you can watch how changing the radius changes the period.
Try this today: use the same steps to find the period of a satellite at 400 km, then check whether your answer is shorter than Aryabhata's, as Kepler's law says it should be.
