Speed of spacecraft (gravitational force)

In summary, an unmanned spacecraft in a circular orbit around the moon experienced an electrical fault that caused an on-board thruster to fire, decreasing its speed by 20.0 m/s. Without any corrective action, the spacecraft will crash into the lunar surface with a speed that can be calculated using the gravitational constant, mass and radius of the moon. The process involves balancing the centripetal and centrifugal forces, finding the initial kinetic energy, and the energy due to falling to determine the final speed upon impact.
  • #1
whitetiger
22
0
An unmanned spacecraft is in a circular orbit around the moon, observing the lunar surface from an altitude of 43.0 km (see Appendix F). To the dismay of scientists on earth, an electrical fault causes an on-board thruster to fire, decreasing the speed of the spacecraft by 20.0 m/s.

If nothing is done to correct its orbit, with what speed (in km/h) will the spacecraft crash into the lunar surface?
Take the gravitational constant to be 6.673 x 10^-11\cdot {\rm m}^{2}/{\rm kg}^{2}, the mass of the Moon to be 7.35 x 10^22\:{\rm kg}, and the radius of the Moon to be 1.74 x 10^{6}\:{\rm m}.

We can use equation v = sqrt(Gme)/r))
 
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  • #2
Show some work or some reasoning or something that tells us you gave it some thought. Then we can advice you where you may be misunderstanding something.
 
  • #3
KoGs said:
Show some work or some reasoning or something that tells us you gave it some thought. Then we can advice you where you may be misunderstanding something.


Thank you KoGs for replying to my question. I have finally figure our how to solve the problem. First I have to balance the centripetal force and the centrifugal forces.

After finding the initial kinetic energy and the energy due to falling I was able to find the speed at which it hits the planet

Again thank for your help
 

Related to Speed of spacecraft (gravitational force)

What is the speed of a spacecraft in the presence of gravitational force?

The speed of a spacecraft in the presence of gravitational force depends on the gravitational force exerted by the celestial body it is orbiting. The spacecraft will accelerate to a certain speed as it falls towards the body, and this speed is known as the orbital velocity.

How is the speed of a spacecraft affected by different gravitational forces?

The speed of a spacecraft is directly affected by the strength of the gravitational force exerted by the celestial body it is orbiting. The stronger the force, the faster the spacecraft will travel in its orbit.

What factors influence the speed of a spacecraft in a gravitational field?

The speed of a spacecraft in a gravitational field is primarily influenced by the mass of the celestial body it is orbiting and the distance between the spacecraft and the body. The closer the spacecraft is to the body, the faster it will travel.

Can the speed of a spacecraft be altered while in the presence of gravitational force?

Yes, the speed of a spacecraft can be altered while in the presence of gravitational force. This can be achieved by using thrusters to change the spacecraft's velocity or by using the gravitational force of other celestial bodies to perform a gravitational slingshot maneuver.

How is the speed of a spacecraft calculated in a gravitational field?

The speed of a spacecraft in a gravitational field can be calculated using the formula v = √(GM/r), where v is the orbital velocity, G is the universal gravitational constant, M is the mass of the celestial body, and r is the distance between the spacecraft and the body.

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