By what formula is this graph predicted? Cumulative Periastron Time Shift

In summary, The predictions on the graph were formed by calculating the cumulative change in time, not in frequency. The formula provided is for the integrated shift in time, not the change in frequency. The paper explains that the first measured orbit was 7.75 hours and subsequent orbits were 67 nanoseconds shorter, resulting in a cumulative shift of 4.3 seconds over 10 years. The parabola on the graph reflects this calculation.
  • #1
Meerio
16
1
B1913+16.gif

I'm confused about how the predictions of this graph were formed.
I have this formula:
Untitled.png

But the change in frequency per second is about : 2x 10^-12 which has a problem because when you multiply this by 10 years you don't even get a change of frequency of 1/1000 of a second and in the graph it says it's around 5 seconds.
Anyone know what I'm doing wrong?

Paper: https://arxiv.org/pdf/1011.0718v1.pdf
 
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  • #2
This is the cumulative change in time, not in frequency. You need the integral or sum.

The first measured orbit was about 7.75 hours, the next was 2.4 * 10-12 * 7.75h = 67ns shorter (integrated shift: 67 ns), the following one was 2*67 ns shorter than the first one (cumulative shift: 67+2*67 = 201 ns) and so on.

In 10 years, there were 11300 orbits, for a cumulative shift of 1/2 * 67 ns * 113002 = 4.3 seconds, in agreement with the parabola shown there.
 
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Likes Meerio
  • #3
Thx so much this was the answer I was looking for !
 

1. What is a cumulative periastron time shift?

A cumulative periastron time shift refers to the change in the time at which a celestial object reaches its closest approach to another object in its orbit. This shift can occur due to various factors such as gravitational interactions, relativistic effects, and observational errors.

2. How is a cumulative periastron time shift measured?

Cumulative periastron time shift is typically measured by observing the orbital parameters of a celestial object over a period of time and comparing the predicted periastron time with the observed periastron time. The difference between the two is the cumulative periastron time shift.

3. What formula is used to predict the periastron time shift?

There is no single formula to predict the periastron time shift as it depends on various factors such as the masses and distances of the objects in orbit, their velocities, and the angle of observation. Different mathematical models and equations are used to calculate the cumulative periastron time shift for different scenarios.

4. Why is it important to predict the cumulative periastron time shift?

Predicting the cumulative periastron time shift is important for accurately understanding the dynamics of celestial objects in orbit. It can also help in making precise predictions and calculations for future astronomical events such as eclipses and planetary transits. Additionally, it can provide valuable insights into the effects of gravitational interactions and relativistic effects on celestial bodies.

5. Can the cumulative periastron time shift be observed directly?

No, the cumulative periastron time shift cannot be observed directly. It can only be inferred by comparing the predicted and observed periastron times of celestial objects in orbit. However, with advancements in technology and space exploration, we may be able to directly measure and observe the cumulative periastron time shift in the future.

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