Read Sudden Gravity Changes: Keep Position and Velocity Continuous
When the Sun's mass changes instantaneously, Earth has no time to change its position or velocity. Angular momentum about the Sun therefore remains unchanged at that instant.
Motion and force questions become simpler when direction, starting condition, time and the acting forces are marked first.
Start with the condition
Identify the current point as an apsis, then use energy and angular momentum to find the new ellipse.
Build the governing relation
At the new pericentre, use angular-momentum conservation or vis-viva to obtain the largest speed. Check that the orbit is bound by confirming negative new specific energy.
Finish with a physical check
Check the limiting case before selecting an option: remove the special feature in the diagram or make the relevant parameter very large or very small. The result should reduce to a familiar relation.
OlympIQ exam lens
- ✓State the physical condition before choosing a formula.
- ✓Keep direction, sign and constraint information explicit.
- ✓Test one limiting case before committing to an option.
Applying Kepler's third law to the old circular radius assumes the new orbit remains circular, which it does not.
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