Constants PeriodicTabla In the movie The Martian, the crew of the spaceship Heme
ID: 2034100 • Letter: C
Question
Constants PeriodicTabla In the movie The Martian, the crew of the spaceship Hemes returns to Mars by perfoming a "gravitational slingahot maneuver around the Earth. The Hermes travels toward the Earth (in the oppoaite direction of Earth's motion relative to the Sun). slingshots around the Earth and travels back toward Mars. The Hermes gains speed during this process In the film, Commander Lewis mentions that she needs to check NASA's calculations regarding this slingshot maneuver. As part of her calculations, she would need to determine the speed of the Hermes (relative to the sun) right after the slingshot What speed would she cakculate? Before the slingshot maneuver, the speed of the Hemes relative to the Sun is 4.50x101 kph The radius of Earth's approximately circular orbit around the Sun is 149,597,870 km. A gravitational slingshot is an example of an elastic collision. You may not consider this situation to be a collisicn since the Hermes and the Earth never come in contact with each other. However, the Hemes and the Earth do not have to come into contact to interact with one another. They are already interacting with each other oer a long range through gravity. Therefore, you can think of this as ? ong-range colsion PartA What is the speed of the Hermes relative to the sun right after the slingshot maneuver? Express your answver in kph and use three significant figures.Explanation / Answer
Lat speed of planet earth be u and initial velcoity of hemres be v
we have from equation of collsions,
Mu12 + mv12 = Mu22 + mv22 ( M - mass of earth , m - mass of hermes where m <<< M )
Mu1 - mv1 = Mu2 + mv2
Using above two equations, solve for v2 , we get
v2 = ( 1 - m / M ) v1 + 2u1 / 1 + m/M
as m << M , m/M is almost zero.
we get,
v2 = 2u1 + v1
u1 = 2*pi*r / 365.25*24
putting value of given r, we get
u1 = 107226.92 km/h
so,
v2 = 4.50e4 + 2(107226.92)
v2 = 259453.84 kph