Question

1) The first artificial satellite to orbit the Earth was Sputnik I, launched October 4, 1957. The mass of Sputnik I was 83.5 kg, and its distances from the center of the Earth at apogee and perigee were approximately 7380 km and 6630 km, respectively. Find the difference in gravitational potential energy for Sputnik I as it moved from apogee to perigee. (Use a positive sign for an increase, negative sign for a decrease in U.) Answer in Joules.

2) On Apollo Moon missions, the lunar module would blast off from the Moon's surface and dock with the command module in lunar orbit. After docking, the lunar module would be jettisoned and allowed to crash back onto the lunar surface. Seismometers placed on the Moon's surface by the astronauts would then pick up the resulting seismic waves. Find the impact speed of the lunar module, given that it is jettisoned from an orbit 310 km above the lunar surface moving with a speed of 1420 m/s. Answer in km/s.

Answer 1

1) apogee = R = 7380 km
perigee = r = 6650 km
PE at R = -GMm/(R) = -4506877425.4742 J
PE at r = -GM/r = -5001617353.383 J
Change in PE from apogee to preigee = -494739927.909 J
decrerase in PE
2) Initial PE = -GMm/R = -2394161.797m J
Final PE = -Gmm/(R - h) = -2821444.559m J
Initial KE = 0.5*m*1420^2 = 1008200m J
Final KE = 0.5mv^2
from conservatioon of energy
v = 1.6943 km/s