The method and the results are on the orbits and escape speed lab. Do the analysis yourself first, then check the answers below.
Quick answer: Gravitational potential energy is U = −GMm/r, with zero at infinity. These answers go with the AP Physics C lab on orbits and escape speed: the graph, the calculations, the uncertainties and the conclusion explained, for all 7 analysis questions.
Here are the orbits and escape speed lab answers for AP Physics C: graph, calculations, uncertainties and conclusion. First do the lab yourself, then compare, and go back to the lesson if needed.
Model answers use the sample data in the table. If you use another data set, expect a straight line through the origin and a mass of the right order of magnitude. State the units of the gradient and quote the mass to three significant figures at most.
Level: AP Physics C (Mechanics and E&M, calculus-based) · Curriculum: AP PC:M Unit 7
Gradient = 4π²/(GM), so M = 4π² / (G × gradient) = 39.48 / (6.67 × 10⁻¹¹ × 3.11 × 10⁻¹⁶) = 1.90 × 10²⁷ kg.
Question 5 Logarithmic test
ln(16.69/1.77) = 2.244 and ln(18.83/4.22) = 1.496. The gradient is 2.244 / 1.496 = 1.50, so T ∝ r^(3/2).
Question 6 Uncertainty
The period uncertainty is about 0.3 %. M ∝ r³/T², so the uncertainty in M is about 3 × (radius error) + 2 × 0.3 %. With radius errors near 0.1 %, M is uncertain by about 1 %.
Question 7 Assumptions
The orbits are assumed circular, and the moons’ masses are assumed negligible compared with the planet. If the orbits are slightly elliptical, the mean radius gives a small bias. Both effects are small here.
