3. The lunar surface has been shaped by meteorite bombardment 300,000 craters more than 1 Km wide Example: v = 20 km/s, d = 30 m, ρ = 3 gr/cm 3  volume U = 4πr 3 /3 = 1.4*10 4 m 3  mass m = ρU = 4.2*10 7 Kgr E = mv 2 /2 = 8.4*10 15 J (2 megaton TNT bomb) Such an impact in 1 minute could create a 1km wide, 200m deep crater !!

5. A lunar crater with a height (depth) h and a shadow of length L. The line connecting the top of the crater wall and the end of the shadow determines the position of the sun in the sky of the moon. h = L tan(φ)

6. Syene to Alexandria/ circumference of the Earth = 7.2 o / 360 o Eratosthenes earth circumference measurement

7. earth 1 st quarter 3 rd quarter moon sun

8. h = L tan(φ) sin(φ) = d / R sin(φ)  tan(φ)  φ h  (d / R) L

9. L = k L pix d = k d pix k = (θ arc / 2*10 5 ) D km moon θ pixel telescope uncertainty in h = [(ΔL/L) 2 + (Δd/d) 2 ] 1/2 D km S= θ D km

10. Measure the length of the crater shadow in pixels, L pix Compute k where θ arc =3 arcsec, and D km found using SkyMap Convert L pix to length in kilometers, using the formula derived above (L = k L pix ) Measure the perpendicular distance d pix, from the crater to the Earth-Moon line, in pixels Convert this number in kilometers (d = k d pix ) Finally compute the height of the crater under study using R Km =1.738 Km. Steps to get the answer