Escape velocity

Escape velocity looks like a formula to memorise. It is tempting to learn 11.2 km/s for Earth and √(2GM/R) and hope the question matches. The trouble starts when the question changes the planet, gives g instead of the mass, or mentions a satellite.

One relationship between two speeds does most of the work, and it saves you from learning a second formula. Once you see where it comes from, you can cross-check the values for Earth, the Moon and Mars instead of memorising each one.

In a numerical, the final number is the easy part. The marks go on picking the right form, converting kilometres to metres, and not letting the launch angle or the object's mass throw you off.

Below you get the meaning, a five-step routine with a pass or fail test at each step, a worked example, and the confusions that cost marks in HSC (Higher Secondary Certificate) Physics and MHT-CET (Maharashtra Health and Technical Common Entrance Test).

It is really a speed, because direction does not matter, so it is also called escape speed. The formula is v = √(2GM/R), which becomes √(2gR) when you know g and R.

Here G is the gravitational constant, M is the mass of the planet and R is the distance from its centre. Gravity is conservative, so only the start and end points matter, not the path. That is why the angle drops out. The object's mass m cancels from ½mv² = GMm/R.

Escape speed is √2 times the circular orbital speed, the speed that keeps an object circling just above the surface, because escaping needs twice the kinetic energy of circling. A circular orbit comes from mv²/R = GMm/R², giving v_orb = √(GM/R). Escape comes from ½mv² = GMm/R, giving v_esc = √(2GM/R). Divide one by the other and √2 is left.

Circling versus escaping: a √2 speed ratio

The table is calculated from NASA fact sheet values, using v_esc = √(2GM/R), v_orb = √(GM/R) and G = 6.674×10⁻¹¹ N m² kg⁻², with R taken as half of NASA's listed diameter.

The ratio is √2 in every row because of the algebra above, not because of the data. NASA's own table lists escape velocities of 11.2, 2.4, 5.0 and 59.5 km/s for the same four bodies.

Pick the form from what the question gives you, then run five steps built on the formulas above.

1. Name what is asked. "Just escapes" or "never returns" means escape speed; "circular orbit" means circular orbital speed. Pass: you can point to the phrase that tells you.
2. Choose the form from the table. Pass: the quantities you were given are exactly the ones in the formula you picked. Fail: you need a value the question does not give.
3. Convert units. R in metres, g in m/s². Pass: Earth lands near 11,000 m/s. Fail: 11 or 11 million.
4. Size-check. Pass: the answer is within about 10% of the nearest of 11.2 (Earth), 2.4 (Moon) or 5.0 km/s (Mars) for a body of similar size. Fail: it is off by a factor of about 1,000 or by √2.
5. Cross-check with √2. Pass: escape speed divided by circular orbital speed is about 1.414.

Three confusions cost marks: mixing up escape speed with circular orbital speed, with the speed a rocket actually flies, and with the effect of the object's mass or launch angle. Escape speed is for a non-propelled object. A rocket with engines running keeps adding energy, so it can leave Earth without ever touching 11.2 km/s. Circular orbital speed is the speed to circle, which is lower.

A bigger object does not need a bigger speed (m cancels), and a slanted launch does not need more speed (energy does not care about direction). Related terms to know are gravitational potential energy and the binding energy of a satellite.

Escape velocity belongs to Gravitation, a Class 11 topic in the MHT-CET syllabus. As of 30 October 2026, check the State CET Cell syllabus and marking scheme page for the syllabus that applies to MHT-CET 2027; the one released on 21 November 2025 was for academic year 2026-27. Gravitation is a single Class 11 chapter, so escape velocity is likely a small but scoring topic.

Our MHT-CET 2027 Long Term Batch, taught by Rahul Jewaani (RG Sir), covers the full MHT-CET syllabus plus Class 11 Physics basics, with live classes, recordings, notes, PYQs (previous year questions) and mock tests. As of 30 October 2026 it costs ₹1,632. If Class 11 feels shaky, start with our Class 11 catch-up units and keep the HSC formula sheet open. Padhna Aasaan Hai: the rest of our courses are in the store.