Using Orbital Energy to Calculate Velocity

In summary: The only thing I can think of is the potential energy changes in the problem statement are wrong.In summary, the conversation was about calculating initial and final potential energies and determining the change in kinetic energy. The final velocity was also calculated, but it was found to be significantly higher than the correct answer. The mistake was determined to be in the calculation of the change in potential energy, which was 103 times too high, suggesting that there may be an error in the problem statement. Specifically, the potential energy changes may be incorrect, which could explain the inconsistency between the obtained perigee speed and conservation of angular momentum.
  • #1
JoeyBob
256
29
Homework Statement
See attached picture
Relevant Equations
change Ek + change Ep =0, Ek=1/2mv^2, Ep=-GMm/r
So what I did first was calculate the initial and final potential energies with Epi=-9.433*10^11 m and Epf = -1.503*10^12 m.

Then I found change in potential energy, -5.597*10^11 m.

Using this I determined the change in kinetic energy, 5.597*10^11. I then added this change to the initial kinetic energy I calculated (103.68 m) to get a final Ek of 5.597*10^11 m.

Then I calculated the final velocity, Ekm=v^2*0.5, finding that v=1058017, which is obviously way higher than the right answer.

Where am I going wrong here? Is there some non conservative work or something?
 

Attachments

  • Question.PNG
    Question.PNG
    10.7 KB · Views: 103
Physics news on Phys.org
  • #2
JoeyBob said:
Homework Statement:: See attached picture
Relevant Equations:: change Ek + change Ep =0, Ek=1/2mv^2, Ep=-GMm/r

So what I did first was calculate the initial and final potential energies with Epi=-9.433*10^11 m and Epf = -1.503*10^12 m.

Then I found change in potential energy, -5.597*10^11 m.

Using this I determined the change in kinetic energy, 5.597*10^11. I then added this change to the initial kinetic energy I calculated (103.68 m) to get a final Ek of 5.597*10^11 m.

Then I calculated the final velocity, Ekm=v^2*0.5, finding that v=1058017, which is obviously way higher than the right answer.

Where am I going wrong here? Is there some non conservative work or something?
Please post all your working, just as algebra, no plugged in values. This will make it much easier to see where the mistake is, unless it is purely arithmetic, which is unlikely.
 
  • #3
Your units are all over the place. Plugging in r in km and v in km/s means you get ΔEp = -5.597*1011m mJ and Eki = 103.68m MJ. (I haven't checked the calculations, but the numbers look in the right ballpark.) It is much better to convert everything to SI units (and back at the end if necessary), and INCLUDE THE UNITS AT EACH STAGE OF THE CALCULATION. Can never stress too much the importance of units.
 
  • #4
JoeyBob said:
Homework Statement:: See attached picture
Relevant Equations:: change Ek + change Ep =0, Ek=1/2mv^2, Ep=-GMm/r

Where am I going wrong here? Is there some non conservative work or something?
Your change in potential energy is 103 times too high. What does this suggest to you?

On edit: I am questioning the validity of this problem. The perigee speed ##v_p##, obtained from the given parameters using energy conservation, is inconsistent with conservation of angular momentum. Angular momentum conservation (per unit mass) requires that ##v_1 r_1\sin\theta=v_p r_p##. Solving for ##\sin\theta## returns a value greater than 1 which is impossible if my calculation is correct.
 
Last edited:
  • Like
Likes pai535

1. How is orbital energy related to velocity?

Orbital energy is the sum of an object's kinetic and potential energy while in orbit. This energy is directly related to the object's velocity, as an increase in velocity leads to an increase in kinetic energy and a decrease in potential energy.

2. What is the formula for calculating velocity using orbital energy?

The formula for calculating velocity using orbital energy is v = √(2E/m), where v is velocity, E is orbital energy, and m is the mass of the object.

3. How does the distance from the central body affect orbital energy and velocity?

The distance from the central body affects both orbital energy and velocity. As the distance increases, the potential energy decreases and the kinetic energy increases, resulting in a higher orbital energy and a higher velocity.

4. Can orbital energy be used to calculate the velocity of any object in orbit?

Yes, orbital energy can be used to calculate the velocity of any object in orbit, as long as the mass and distance from the central body are known.

5. How is orbital energy used in space missions?

Orbital energy is used in space missions to determine the necessary velocity for a spacecraft to enter and maintain a stable orbit around a planet or other celestial body. It is also used to calculate the amount of fuel needed for a spacecraft to reach a certain velocity and maintain its orbit.

Similar threads

  • Introductory Physics Homework Help
Replies
1
Views
708
  • Introductory Physics Homework Help
Replies
5
Views
1K
  • Introductory Physics Homework Help
Replies
29
Views
887
  • Introductory Physics Homework Help
Replies
7
Views
1K
  • Introductory Physics Homework Help
Replies
7
Views
1K
  • Introductory Physics Homework Help
Replies
7
Views
796
  • Introductory Physics Homework Help
Replies
21
Views
599
  • Introductory Physics Homework Help
2
Replies
55
Views
2K
  • Introductory Physics Homework Help
Replies
15
Views
325
  • Introductory Physics Homework Help
Replies
8
Views
1K
Back
Top