Infer a surface history without equating craters with age

1. Define the planetary evidence

An impact crater record reflects production and preservation. Volcanic resurfacing, erosion, burial and later impacts can remove or obscure older craters. Comparing surfaces therefore requires common counting criteria, area, size range and a calibrated production history; a larger raw count is not automatically an older surface.

2. Connect mechanism and inference

The original expected density satisfies dN/dt=p−0.2N from N=0. Its solution N(t)=p(1−exp(−0.2t))/0.2 approaches a balance between production and loss. The counts are continuous expectations per area, not fractional observed craters. The constant loss approximation is not a physical model of every erasure mechanism.

At observation time six, 60% of the area retains that full history while a 40% patch was completely reset at supplied time b. The patch’s elapsed time is 6−b. Area weighting combines the two expected densities; the correct weight is patch area, not the count fraction or the age itself.

An analyst who forces this mixed record into one unreset history obtains −ln(1−0.2N_mix/p)/0.2. That effective age is not the formation time, the reset time or necessarily the area-weighted mean age. Actual planetary surface chronology requires mapped relations and independent calibration; this original comparison supplies no real date for Venus, the Moon or Mars.

3. Work the supplied case

For p=2, the unreset six-time-unit surface has density 10(1−e^−1.2)≈6.98806. A patch reset at time four has density 10(1−e^−0.4)≈3.29680. The 60:40 mixture is≈5.51155, lower than the unreset surface without changing the body’s formation time.

4. Predict and investigate

Does one mixed crater density imply one unique surface age?

Keep production, loss, observation time and patch reset separate. Compare the mixed density with both component densities and state why a single-age inversion hides geological history.

Source and boundaries

Primary source. Checked 31 October 2026. Original diagrams and supplied model records are not actual planetary observations. No direct solar viewing, instrument operation or physical experiment is requested.