Celestial Mechanics: Calc Mass & Velocity of Proton

In summary, the question asks to calculate the mass of a proton with half its kinetic energy being equal to its total energy. The answer is 3.34 * 10^-27 kg. The question also asks for the proton's velocity, which is 0.87 times the speed of light.
  • #1
a.a
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Homework Statement


a) Calculate the mas of a proton ( ms = 1.67 * 10^-27 kg) whose kenetic energy is half its toral energy. (ANS. 3.34 * 10^ -27 kg)
b) How fast is it travelling? ( ANS. 0.87c) c- speed of light


Homework Equations



E(kenetic) = Gm(1)m(2) all over R^2

E(total) = -0.5Gm(1)m(2) all over R

V(orbit) = sqrt. GM/r, where M is the mass of planetary object

E = mc^2


The Attempt at a Solution



The most I can come up with is that there is no gravitational potential energy because
1/2E(k) = E(total)
 
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  • #2
a.a said:
a) Calculate the mas of a proton ( ms = 1.67 * 10^-27 kg) whose kenetic energy is half its toral energy. (ANS. 3.34 * 10^ -27 kg)
I believe the question is asking for the proton's relativistic mass.
 
  • #3

FAQ: Celestial Mechanics: Calc Mass & Velocity of Proton

1. How is the mass of a proton calculated?

The mass of a proton is calculated using a unit called atomic mass units (amu). One amu is equal to 1/12th the mass of a carbon-12 atom. The mass of a proton is approximately 1.007 amu.

2. What is the velocity of a proton?

The velocity of a proton can vary depending on its energy and the conditions it is under. In a particle accelerator, protons can reach velocities close to the speed of light, which is approximately 299,792,458 meters per second.

3. How does the mass of a proton affect its behavior in celestial mechanics?

The mass of a proton is a crucial factor in celestial mechanics as it determines the strength of the proton's gravitational pull and its interaction with other celestial bodies. The mass of a proton also affects its acceleration and trajectory in orbit around a larger body.

4. Can the mass and velocity of a proton change?

Yes, the mass and velocity of a proton can change depending on its energy and the environment it is in. For example, a proton can gain energy and increase its velocity when accelerated in a particle accelerator.

5. How do scientists measure the mass and velocity of a proton?

The mass and velocity of a proton can be measured using various techniques such as mass spectrometry, which measures the mass of a proton based on its deflection in a magnetic field, and particle accelerators, which can measure the velocity of a proton by tracking its trajectory and energy. Protons can also be observed using detectors and sensors in space missions.

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