Naked Science Forum
On the Lighter Side => New Theories => Topic started by: opportunity on 17/12/2018 07:09:32
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Understood that they, the planets, take a different time to travel around the sun given their distance from the sun, and there are some very absurd answers on the web answering a question like this with "no, the further out the planets go, the longer it takes to circle the sun". Wow.
The first question in this topic is therefore, "Does anyone understand the question being asked?".
Is it wrong in thinking that current estimates of the speed of planets around the sun is according to a standardised time, and thus "the same speed". The issue is, if they are not at the same speed, the planets, then relativity issues become apparent. Would it be wrong to suggest that?
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The issue is, if they are not at the same speed, the planets, then relativity issues become apparent. Would it be wrong to suggest that?
The three relativistic effects that you might see are:
1) Time dilation due to the velocity of planets
2) Time dilation due to their position in a gravitational well
3) Radiation of gravitational waves
In our Solar System:
1) The fastest moving planet is Mercury, averaging 50km/s, or about 0.02% of c. Since the relativistic time dilation formula contains a (v/c)2, this has a very small impact on the velocity of the planet. The 21% orbital eccentricity will have a bigger impact on orbital speed.
2) Mercury is deepest in the Sun's gravitational well. This time dilation changes the point where Mercury is closest to the Sun by 43/3600 of 1 degree per century. This does not really affect the orbital velocity. See: https://en.wikipedia.org/wiki/Tests_of_general_relativity#Perihelion_precession_of_Mercury
3) The Earth radiates gravitational waves amounting to around 200W, which is tiny compared to the kinetic energy of the Earth. However, this is detectable with closely orbiting neutron stars, see: https://en.wikipedia.org/wiki/Hulse%E2%80%93Taylor_binary
So, overall, relativistic effects have minimal effect on velocity measurements in our Solar System.
Until we get atomic clocks on space probes (like we do on GPS satellites), temperature variations in our solar system will impact frequency & time measurements more than relativistic effects.
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Well spotted. That was the next question. Data on planets mass and time variations.
Would you consider all the planets travel within a similar speed?
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Does anyone have an explanation as to why mass could change its velocity as a planet as it circles the sun?
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Would you consider all the planets travel within a similar speed?
No, the planets all move at different speeds. We can measure how long it takes for each planet to go around the Sun and we also know the circumference of each planet's orbit. Mercury takes about 88 days to move a distance of almost 364 million kilometers. That's a little over 4.1 million kilometers per day. Venus takes about 225 days to move a complete orbital distance of almost 680 million kilometers. That's a little over 3 million kilometers per day. The Earth completes an orbit of almost 940 million miles in 365 days. That's almost 2.6 million kilometers per day.
Since we are making all of these measurements from the same reference frame (the Earth), relativistic effects like time dilation won't matter.
Does anyone have an explanation as to why mass could change its velocity as a planet as it circles the sun?
More mass would mean a stronger total gravitational force, which in turn would require a higher orbital velocity in order to keep that planet from falling into the Sun.
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Does anyone have an explanation as to why mass could change its velocity as a planet as it circles the sun?
Yes: Conservation of energy.
Planets (and comets) follow an elliptical path around the Sun.
- When they are farthest from the Sun (aphelion), they have a high gravitational potential energy, but reduced kinetic energy = reduced speed.
- When they are closest to the Sun (perihelion), they have a lower gravitational potential energy, but increased kinetic energy = higher speed.
- The total gravitational+kinetic energy remains constant during the orbit (ignoring tiny deviations like the impact of meteorites, solar wind and gravitational waves).
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More mass would mean a stronger total gravitational force, which in turn would require a higher orbital velocity in order to keep that planet from falling into the Sun.
That is almost false. For the same reason a rock falls at the same speed as a feather, a pebble will orbit a planet at the same speed as a much larger rock.
But not much-much larger, to where you start to be a significant percentage of the primary. Earth for instance orbits the barycenter consisting of the center of mass of the Earth, moon, Venus, Mercury, and Sun. If you add one KG of mass to Earth (or to Mercury even), that barycenter moves a tiny bit, and that changes the orbital radius. The new stable radius will depend on how/when that new mass is added.
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That is almost false.
"Almost" being the key word.
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Does anyone have an explanation as to why mass could change its velocity as a planet as it circles the sun?
Yes: Conservation of energy.
Planets (and comets) follow an elliptical path around the Sun.
- When they are farthest from the Sun (aphelion), they have a high gravitational potential energy, but reduced kinetic energy = reduced speed.
- When they are closest to the Sun (perihelion), they have a lower gravitational potential energy, but increased kinetic energy = higher speed.
- The total gravitational+kinetic energy remains constant during the orbit (ignoring tiny deviations like the impact of meteorites, solar wind and gravitational waves).
This is a good answer as "model" of conservation of energy re. gravitational potential and kinetic energy.
The obvious question then is re. comets, which would move at the same speed despite their distance from the sun, right? Or wouldn't they?
Has Voyager 2 slowed down, for instance?
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For Voyager 1 and 2 as they sped through the solar system would be their ping times, to nano seconds. Do we have data on that according to previously calculated projected milestone distances to suggest a change in speed?
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What I just mentioned was one of the reasons of sending the Yoyager probes out there, right?
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Intermission: