Calculating Final Velocity of a Spacecraft Crashing into the Moon

• PsychonautQQ
In summary, a spacecraft in a circular orbit around the moon, observing the lunar surface from an altitude of 50 km, decreases its speed by 20 m/s using on-board thrusters. The speed at which the spacecraft crashes into the moon is incorrect, with calculations resulting in 9532.44 km/h and 6951.7 km/h, while the desired speed is 6060 km/h. This discrepancy may be caused by using the incorrect formula for calculating velocity or the incorrect value for acceleration due to gravity at 50 km off the moon.
PsychonautQQ

Homework Statement

A spacecraft is in a circular orbit around the moon, observing the lunar surface from an altitude of 50 km. The on board thrusters fire, decreasing the speed of the spacecraft by 20 m/s, What is the speed (in km/h) in which the spacecraft crashes into the moon?

Homework Equations

velocity of circular orbit = (Gm/r)^(1/2)
conservation of energy
v^2/r = a_c
radius of moon = 1.74E6 meters
Mass of moon = 7.35E24 kg

The Attempt at a Solution

so you can solve the the velocity of the circular orbit and it comes out to 1678. If you decrease this by 20 as the problem suggests it becomes 1658. From here I took v = (2gh)^(1/2) to see how much velocity would be added from the decreasing potential energy as it falls towards the moon. This calculation led me to it would gain 989.9 m/s in the direction towards the moon. It would still have 1658 m/s in the direction tangential to it's initial centripetal acceleration. adding the 1658 m/s + 989.9 m/s = 2647.9 m/s which comes out to 9532.44 km/h which his incorrect.

If I take (1658^2 + 989.9^2)^(1/2) I get 1931 m/s which comes out to 6951.7 km / hour which is also wrong.

The back of the book is looking for 6060 km/h, I'm having problems getting this number.

g = 9.8 m/s is the acceleration due to gravity at the surface of the Earth. It has nothing to do with the acceleration due to gravity at 50 km off the Moon.

What is Newtonian Gravity?

Newtonian gravity is a physical theory proposed by Sir Isaac Newton in the 17th century to explain the force of gravity between two objects. It states that any two objects with mass will attract each other with a force that is directly proportional to the product of their masses and inversely proportional to the square of the distance between them.

What is the Newtonian Gravity Problem?

The Newtonian Gravity Problem refers to the inability of Newton's theory of gravity to fully explain the observed motion of celestial bodies in our solar system. This problem led to the development of Albert Einstein's theory of general relativity.

How does Newton's theory of gravity differ from Einstein's theory of general relativity?

Newton's theory of gravity is based on the concept of action at a distance, where the force of gravity is transmitted instantaneously between two objects. On the other hand, Einstein's theory of general relativity explains gravity as the curvature of spacetime caused by the presence of mass and energy.

What is the significance of the Newtonian Gravity Problem?

The Newtonian Gravity Problem was a major catalyst for the development of Einstein's theory of general relativity, which revolutionized our understanding of gravity and led to new predictions and explanations of various astronomical phenomena. It also highlighted the limitations of Newton's theory and the need for a more comprehensive and accurate understanding of gravity.

Is Newtonian gravity still used today?

While Einstein's theory of general relativity is considered more accurate and is used to explain many phenomena, Newtonian gravity is still widely used in many practical applications, such as space travel and satellite navigation. It is also a useful approximation for studying the motion of objects on a smaller scale, such as within our solar system.

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