A spacecraft first circles Earth and raises its orbit step by step, then a final burn sends it to the Moon, where braking burns let the Moon's gravity capture it.
The Moon is about 384,400 km from Earth on average. Getting there is less about raw distance and more about speed. ISRO's Chandrayaan-3 mission in 2023 shows each step.
The Moon is also moving: it goes round Earth once every 27.3 days. So the final departure burn has to be timed so that the spacecraft reaches the far end of its orbit just as the Moon gets there.
An LVM3 rocket launched Chandrayaan-3 from Sriharikota on 14 July 2023. It dropped the spacecraft into an elliptic parking orbit of about 170 × 36,500 km.
Over the next two weeks the spacecraft's own engine fired near its low point several times, each burn pushing the high point farther out: to 41,762 km, then 71,351 km.
On 1 August 2023 the trans-lunar injection burn stretched the orbit to 288 × 369,328 km. Now the far end of the orbit reached out to where the Moon would be.
Arriving near the Moon, a spacecraft is moving too fast to stay. It must fire its engine to slow down so the Moon's gravity can hold it. Chandrayaan-3 did this on 5 August 2023, entering a 164 × 18,074 km lunar orbit.
More braking burns made the orbit smaller and rounder: 170 × 4,313 km on 6 August, 174 × 1,437 km on 9 August, 153 × 163 km on 16 August. The lander then separated from its propulsion-module, lowered itself to 25 × 134 km on 20 August, and soft-landed on 23 August 2023, 40 days after launch. ISRO's prime landing site was at about 69.4° south on the Moon.
ISRO's plan had the propulsion module carry the lander to a circular polar orbit about 100 km above the Moon before the two parted. Each braking burn moved the spacecraft one step closer to that target.
Chandrayaan-3's propulsion module is now in a very high Earth orbit, listed at about 125,000 × 308,000 km; the tracker shows its estimated position far beyond ordinary satellites. Track Chandrayaan-3
A Moon transfer is close to a Hohmann-style ellipse: perigee near Earth, apogee at the Moon's distance. Its travel time is half the ellipse's period.
Worked numbers for Chandrayaan-3's trans-lunar orbit (R = 6,378 km, GM = 398,600 km³/s²):
So the trans-lunar orbit is just short of escape — about 0.1 km/s below. The spacecraft is still bound to Earth, but it climbs so far that the Moon's gravity takes over near apogee. The region where the Moon's pull dominates is its sphere-of-influence.
The 4.8-day estimate fits the record: injection on 1 August, lunar orbit insertion on 5 August.
Arriving, the spacecraft comes in on a fast path relative to the Moon. A braking burn near the closest point (perilune) lowers its speed below the Moon's local escape speed and closes the orbit. Each later burn at perilune lowers the apolune, and vice versa, the same rule as orbit-raising run in reverse. ISRO's planned final orbit before descent was a roughly 100 km circular polar orbit.
Its launcher placed it in an Earth orbit with a high point of about 36,500 km. The spacecraft then used its own engine near perigee several times, each burn raising the far end, until the 1 August 2023 burn sent it towards the Moon.
A braking burn near the Moon that slows the spacecraft enough for the Moon's gravity to capture it into lunar orbit. For Chandrayaan-3 it happened on 5 August 2023.
About five days. Half the period of a 288 × 369,328 km orbit is about 4.8 days.