Read before you solve · 3 min

Read Escape-to-the-Midpoint: Compare Total Potential

This short read prepares one exact NSEP pattern: launch between two gravitation sources. Identify the physical condition before calculating.

NSEP · Gravitation · 1 linked question · 100% coverage

Know this first

Motion and force questions become simpler when direction, starting condition, time and the acting forces are marked first.

Distance · Length of the path travelledDisplacement · Straight-line change in positionResultant force · Net force including direction

Study deeper: NCERT Physics · Gravitation

Start with the physical model

Read the configuration once, state the conserved quantity or governing law, and mark any changing geometry, sign convention or limiting condition.

The minimum speed is obtained by just reaching the gravitational potential maximum between the planets, which is at the midpoint.

At launch from the near surface of one planet, distances from the two centres are R and 3R, so Ui/

m = -GM/R - GM/(3R) = -4GM/(3R)

At the midpoint both distances are 2R, so Um/

m = -GM/R

Thus required kinetic energy per unit mass is GM/(3R): v2/2 = GM/(3R), hence v = sqrt(2GM/3R).

Check units, sign and one limiting case. A valid result must still fit the original geometry and stated constraint.

OlympIQ trap

The relevant barrier includes both planets' potentials, not only the planet being launched from.

100% coverage across the linked question.