Question

1.Carlos becomes an Aerospace Engineer for NASA and needs to send a 5,000 kg rocket containing astronauts and supplies to the International Space Station (ISS) which orbits Earth at an altitude of 254 miles (408.8 km). What speed must Carlos give the rocket so that it orbits Earth at that altitude?

2.Jennifer joins NASA as an astronaut, but instead of being sent to somewhere cool like Mars she is stuck in a 12,000 kg spacecraft orbiting Venus. If Jennifer's spacecraft is orbiting Venus with a speed of 9,000 m/s, what is the radius of Jennifer's orbit? [Hint: you're looking for "r"]

B.Violet also joins NASA as an astronaut, and does get to go to Mars. What is the acceleration due to gravity that Violet feels when she gets there? If Violet throws a Mars rock straight up with a speed of 25 m/s, how high will it go?

Answer 1

24 GA Rth GM 7 V2 24 a = 4.01 x 10 m 6 1. Mass of earth, Mz 6x10 kg Radius of earth, R = 6.4 x10°m height of the orbit, h= 4.088x10 m = 0.4058 x 10 m Orbital speed of Carlos, U=U 16.67x10 x 6X1024 (6.4 +0. 4088) x 100 Speed, Vo = 7.67X10 3 m/s Orbiting speed of Tennifer, Vo - 9000 m/s Mass of Venus, M= 4.87 x10*7 kg Orbital speed, Vo = / =) orbital radius, 8= GM GM 6-67X10" x 4.87X10 (9000) 2 Radius of the orbit, 8=4-01 X10 om Mass of Mars, M = 6.42 x10 ²3 kg Radius of Mars, R = 3.40 x1 om GM on Mars, g = R2 Acceleration due to gravily 6.67 X10 g= = 3.70 m/s2 (3:40x1082 Acceleration due to gravity, g = 3.70 m/s² initial speed of throw, u = 25 mls. using the equation, v²= uhtaas ; voo at the highest point O=u²_agh h= 42 252 =84.5m 29 Height, h=84.5m 3. 23 x 6. 42x10 - 2x3-7