physics
posted by Anonymous .
Consider a spacecraft that is to be launched from the Earth
to the Moon. Calculate the minimum velocity needed for the
spacecraft to just make it to the Moon’s surface. Ignore air drag
from the Earth’s atmosphere. Hint: The spacecraft will not have
zero velocity when it reaches the Moon

Contrary to popular belief, a spacecraft does not have to reach full escape velocity in order to reach the Moon. The full escape velocity from a 200 mile high circular orbit is 24,400 mph. Assuming the trip starts from a 200 mile high circular orbit, the minimum injection velocity out of this orbit would be ~24,200 miles per hour, ~35,500 feet per second, or ~10.82 km/sec., to place the spacecraft on an elliptical, minimum energy, Hohmann Transfer trajectory to the Moon. Since the spacecraft is already traveling at a speed of 25,306 ft/sec to maintain the 200 mile high orbit, the deltaV, additional velocity, needed out of the circular orbit is ~10,194 ft/sec. This elliptical trajectory, eccentricity = .966, would bring the spacecraft tangent to the lunar orbit in 120 hours. Any less velocity and a spaceship would not get there at all. Any more velocity and the time would be shortened as well as the spacecraft passing in front of the Moon. The Apollo missions typically took about 72 hours to reach the moon. As the spacecraft passed in front of the Moon, the Service Module rocket engine fired, slowing the spacecraft down to a velocity that placed the spacecraft into lunar orbit.
Respond to this Question
Similar Questions

Physics
Calculate the force of gravity on a spacecraft 19200 km (3 earth radii) above the Earth's surface if its mass is 1600 kg. Hint: At three earth radii from the surface of the Earth, the gravity force (weight) of the spacecraft will be … 
physics
can you walk me through this problem At what distance from the Earth will a spacecraft on the way to the Moon esperience zero net force due to these two bodies because the EArth and Mon pull with equal and opposite forces? 
physics help please!
A spacecraft is on a journey to the moon. At what point, as measured from the center of the earth, does the gravitational force exerted on the spacecraft by the earth balance that exerted by the moon? 
physics
magine a straight line connecting the centers of the earth and the moon. At some point along this line the gravitational forces pulling a spacecraft towards the moon and towards the earth exactly balance each other, and the craft could … 
physics
When a spacecraft travels from Earth to the Moon, the gravitational force from Earth initially opposes this journey. Eventually, the spacecraft reaches a point where the Moon's gravitational attraction overcomes the Earth's gravity. … 
Physics
When a spacecraft travels from the Earth to the Moon, both the Earth and the Moon exert a gravitational force on the spacecraft. Eventually, the spacecraft reaches a point where the Moon's gravitational attraction overcomes the Earth's … 
physics
Consider a spacecraft that is to be launched from the Earth to the Moon. Calculate the minimum velocity needed for the spacecraft to just make it to the Moon’s surface. Ignore air drag from the Earth’s atmosphere. Hint: The spacecraft … 
physics
A spacecraft is on a journey to the moon. At what point, as measured from the center of the earth, does the gravitational force exerted on the spacecraft by the earth balance that exerted by the moon? 
Algebra URGENT! Conic sections
A spacecraft is in a circular orbit 150 kilometers above Earth. Once it attains the velocity needed to escape the Earth's gravity, the spacecraft will follow a parabolic path with the center of Earth as focus. Suppose the spacecraft … 
Moon Science
What causes the phases of the moon as observed from the Earth?