A space craft's speed due to gravitaitonal force

In summary, the conversation discusses a question on a practice test regarding the energy principle. A spacecraft is heading towards Mars and the question asks for the speed of the spacecraft when it is 4000 km from the center of Mars. The conversation also mentions the importance of precision and using the correct units in calculations. The final answer is 4.3e3 m/s, as stated in the key for the practice test.
  • #1
chrishobo
2
0
I have this question on a practice test I am using to study. Thanks for any assistance.

I believe it is a Energy Principle question

Homework Statement


A spacecraft is coasting towards mars. The mass of Mars is 6.4e^23 kg and its radius is 3400km. When the spacecraft is 7000km from the center of mars, the spacecraft s speed is 3000 m/s. Later, when the spacecraft is 4000 km from the center of mars, what is its speed?

(i think the following is unimportant, but here it is anyways:)
Assume that the effects of Mars two tiny moons, the other planets, and the sun are negligible. Precision is required to land on mars, so make an accurate calculation, not a rough, approximate calculation. Start from a fundamental principle.


Homework Equations



Energy Initial = Energy Final + work (both the spacecraft and planet are in the system, so work is 0)

Kinetic Energy = .5*mass*velocity^2

Potential energy = -G*mass1*MASS2/radius


The Attempt at a Solution



Ksi+KMi+Ui+mc2+Mc2=Ksf+KMf+Uf+mc2+Mc2

Mc2 cancels
mc2 cancels
KM has a near zero change, so it cancels

Leaving

Ksi+Ui=Ksf+Uf

Plugging in I get

.5*m*(3000)2+(-6.7e-11)*(m*(6.4e23)/(7000)=.5*m*(v)2+(-6.7e-11)*(m*(6.4e23)/(4000)

The m's (mass of craft) should cancel out on both sides,

and solving for v i get 95904 m/s



The key for the practice test (which doesn't give any work) states 4.3e3 m/s
 
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  • #2
You've got a unit problem because you used m/s for v but km for r. Be sure to use only meters (you can't only use kilometers because 6.7e-11 has units of m^3/(kgs^2).
 
  • #3
Also, it's unnecessary to include the rest mass energy or the kinetic energy change of the planet when doing problems like this. Just write Ki+Ui=Kf+Uf and everyone will understand what you mean.
 
  • #4
sweet. i feel silly for overlooking that

glad i did that now and not on the test.

Thanks!
 

What is a space craft's speed due to gravitational force?

A space craft's speed due to gravitational force refers to the speed at which it is moving under the influence of a gravitational field. This can be calculated using the equation v=√(GM/r), where G is the universal gravitational constant, M is the mass of the larger object (such as a planet or star), and r is the distance between the two objects.

How does gravitational force affect a space craft's speed?

Gravitational force acts as an acceleration on a space craft, causing it to constantly increase in speed as it gets closer to a larger object. The farther away the space craft is, the weaker the gravitational force and the slower its speed. This is due to the inverse square law, which states that the force of gravity decreases with the square of the distance between two objects.

Can a space craft's speed due to gravitational force be changed?

Yes, a space craft's speed due to gravitational force can be changed. This can be achieved through various methods such as using a gravitational slingshot maneuver, which involves using the gravitational pull of a larger object to increase the speed of the space craft, or by using propulsion systems to accelerate the space craft.

What is the relationship between a space craft's mass and its speed due to gravitational force?

The mass of a space craft does not directly affect its speed due to gravitational force. However, the more massive an object is, the stronger its gravitational pull will be, and therefore the greater the effect on the speed of the space craft. This is why larger objects, such as planets, have a more significant influence on the speed of a space craft compared to smaller objects like asteroids.

How does the speed of a space craft due to gravitational force impact its trajectory?

The speed of a space craft due to gravitational force plays a crucial role in determining its trajectory. The faster the space craft is moving, the greater its kinetic energy and the more likely it is to escape the gravitational pull of a larger object. This can lead to a change in the spacecraft's trajectory, causing it to either orbit the larger object or continue on a path into deep space.

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