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Landing softly is harder than reaching the Moon. A spacecraft in lunar orbit is moving fast and must end up touching the ground at walking pace, on a surface with no air to slow it down. This post explains what Chandrayaan-3 was designed to do, what its instruments found near the lunar south pole, and the kinematics behind its touchdown limits, using equations from your JEE and board syllabus.
What was Chandrayaan-3 built to do?
ISRO's Chandrayaan-3 details page describes it as a follow-on to Chandrayaan-2 to demonstrate end-to-end capability in safe landing and roving on the Moon. Its three objectives were a safe and soft landing, a rover moving on the surface, and experiments carried out on the spot. It had a propulsion module of 2,148 kg and a lander module of 1,752 kg that included a 26 kg rover, for a total of 3,900 kg. The prime landing site was 4 km by 2.4 km, centred at 69.367621° S, 32.348126° E, and the planned life of the lander and rover was one lunar day, about 14 Earth days.
How did it get from Earth to the Moon?
ISRO's mission updates give the sequence. LVM3 M4 launched the spacecraft on 14 July 2023. Engine burns raised its Earth orbit in steps until a translunar injection on 1 August put it on a 288 km by 369,328 km path. It entered lunar orbit on 5 August, was lowered to about 153 km by 163 km, and the lander separated on 17 August. Two de-boost burns brought the lander to a 25 km by 134 km orbit, and it soft-landed on 23 August 2023.
Worked example 1: what does a 2 m/s touchdown mean?
The details page sets the touchdown limits: vertical velocity no more than 2 m/s, horizontal velocity no more than 0.5 m/s, and a slope no steeper than 12°. NASA's Moon fact sheet gives the Moon's surface gravity as 1.62 m/s².
Step 1: equivalent drop height. From rest, v² = 2gh, so h = v² ÷ 2g = (2)² ÷ (2 × 1.62) = 4 ÷ 3.24 = 1.23 m. Hitting the ground at 2 m/s on the Moon is like falling freely from about 1.2 m.
Step 2: compare with Earth. With g = 9.80 m/s², h = 4 ÷ 19.6 = 0.20 m. The same speed on Earth is a 20 cm drop. Weak lunar gravity makes the limit easier to meet, but only if the lander has already removed almost all its speed.
Step 3: time to fall. t = v ÷ g = 2 ÷ 1.62 = 1.23 s. If the engines cut out more than about a metre up, the lander would exceed the limit within little more than a second.
Worked example 2: could the engines hold the lander up?
The details page lists four 800 N throttleable engines on the lander, so the maximum thrust is 4 × 800 = 3,200 N.
Lander weight on the Moon at its full listed mass: 1,752 × 1.62 = 2,838 N. Thrust exceeds weight, with a ratio of 3,200 ÷ 2,838 = 1.13, so the engines can slow the lander and even hover. By landing, propellant had been used, so the real margin was larger.
The same lander on Earth: 1,752 × 9.8 = 17,170 N. The engines could not lift it at all.
This uses only F = ma: to slow a descent, the net force must point up, so thrust must be greater than weight.
The 12° slope. On a 12° slope, gravity's component along the surface is g sin 12° = 1.62 × 0.208 = 0.34 m/s². To stay put without sliding, the legs need a friction coefficient of at least tan 12° = 0.21.
What did the instruments find?
On 28 August 2023, ISRO reported that the rover's laser-induced breakdown spectroscope (LIBS) had made the first in-situ measurements of elemental composition near the south pole and confirmed sulphur, which orbiters had not been able to do. It also detected aluminium, calcium, iron, chromium and titanium, and then manganese, silicon and oxygen. LIBS works by firing a laser pulse at the soil, making a hot plasma, and reading the wavelengths of light each element emits.
The lander's ChaSTE probe pushed 10 temperature sensors up to 10 cm into the soil, giving what ISRO calls the first temperature profile for the lunar south pole.
What mistakes do students make with landing problems?
Using Earth's g. See the callout.
Setting thrust equal to weight to slow down. Equal thrust and weight give constant velocity. Deceleration needs T − mg = ma with T larger.
Misreading orbit sizes. "25 km by 134 km" gives the lowest and highest altitudes of the orbit, not a radius.
Forgetting horizontal speed. The lander also had to cut its sideways motion to 0.5 m/s.
Our guide to vertical motion under gravity covers the kinematics in more depth.
What can a student take from the mission?
ISRO's details page lists the tests the team ran on Earth before flight: sensors flown on a helicopter, closed-loop tests from a tower crane, and landing-leg tests on a bed of simulated lunar soil. They checked each part under conditions they could control first.
You can do the same with a solution: test it in a simple case before trusting it on the hard one. When you get stuck setting up a force or kinematics problem, the Fermi Problem Library has a step-by-step solver that explains the reasoning, so you can compare your set-up with a worked one.
Now redo worked example 1 for Mars, where NASA's Mars fact sheet gives a mean surface gravity of 3.73 m/s², and compare the drop heights.
