Kepler's 3rd law: ratios don't fit data2019 Community Moderator Election Announcing the arrival of Valued Associate #679: Cesar Manara Planned maintenance scheduled April 23, 2019 at 23:30 UTC (7:30pm US/Eastern) 2019 Moderator Election Q&A - Question CollectionKepler's third law doesn't give earth's orbital period! Why?Only gravitation and Newton's $2^mathrmnd$ law needed to derive Kepler's laws?Newton's gravity formulas for ellipsesAngular Momentum and Kepler's Second LawCan the constant $k$ from Kepler's third law be independent of the mass of the planet?Kepler's law and my problemKepler's 3rd law applied to binary systems: How can the two orbits have different semi-major axes?Which Kepler laws might change with the Universal Gravitational Constant?Why does angular momentum being constant prove Kepler's first law?Kepler's third law is unintuitive
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Kepler's 3rd law: ratios don't fit data
2019 Community Moderator Election
Announcing the arrival of Valued Associate #679: Cesar Manara
Planned maintenance scheduled April 23, 2019 at 23:30 UTC (7:30pm US/Eastern)
2019 Moderator Election Q&A - Question CollectionKepler's third law doesn't give earth's orbital period! Why?Only gravitation and Newton's $2^mathrmnd$ law needed to derive Kepler's laws?Newton's gravity formulas for ellipsesAngular Momentum and Kepler's Second LawCan the constant $k$ from Kepler's third law be independent of the mass of the planet?Kepler's law and my problemKepler's 3rd law applied to binary systems: How can the two orbits have different semi-major axes?Which Kepler laws might change with the Universal Gravitational Constant?Why does angular momentum being constant prove Kepler's first law?Kepler's third law is unintuitive
$begingroup$
I have been looking at satellite orbits around the earth, or any object around any planet in fact, and am trying to find the orbital radius, or semi major length of a given satellite.
Kepler's third law gives the equation $P^2 = a^3$ where $P$ is the period of orbit and $a$ the distance.
I have a table of satellites currently orbiting the earth, as well as their altitude in the sky on their geosynchronous trajectory. One in particular is 99.9 and has an altitude of 705.
By solving the equation for $a$, I get $a = (P^2)^1/3$.
When I plug in the numbers, they don't correspond.
So my questions are:
- Are there unit standards I need for both $P$ and $a$? Currently $P$ is in minutes, $a$ in kilometres.
- Am I missing something, like Newton's universal gravitational constant? I get a page deriving Kepler's third law using this constant.
newtonian-mechanics newtonian-gravity orbital-motion celestial-mechanics satellites
edited 5 hours ago
Qmechanic♦
108k122001253
asked 6 hours ago
triple7triple7
133
New contributor
triple7 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
$endgroup$
add a comment |
$begingroup$
I have been looking at satellite orbits around the earth, or any object around any planet in fact, and am trying to find the orbital radius, or semi major length of a given satellite.
Kepler's third law gives the equation $P^2 = a^3$ where $P$ is the period of orbit and $a$ the distance.
I have a table of satellites currently orbiting the earth, as well as their altitude in the sky on their geosynchronous trajectory. One in particular is 99.9 and has an altitude of 705.
By solving the equation for $a$, I get $a = (P^2)^1/3$.
When I plug in the numbers, they don't correspond.
So my questions are:
- Are there unit standards I need for both $P$ and $a$? Currently $P$ is in minutes, $a$ in kilometres.
- Am I missing something, like Newton's universal gravitational constant? I get a page deriving Kepler's third law using this constant.
newtonian-mechanics newtonian-gravity orbital-motion celestial-mechanics satellites
edited 5 hours ago
Qmechanic♦
108k122001253
asked 6 hours ago
triple7triple7
133
New contributor
triple7 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
$endgroup$
$begingroup$
hyperphysics.phy-astr.gsu.edu/hbase/kepler.html#c6
$endgroup$
– Kyle Kanos
6 hours ago
$begingroup$
The equality only holds in certain units since its dimensionally inhomogeneous. In particular, if you use Earth years and the Earth-Sun distance (i.e. 1a.u.) then it's true, so it must be true in those specific units.
$endgroup$
– jacob1729
3 hours ago
$begingroup$
BTW, do you understand that $a$ is not altitude but rather distance from the center of the Earth?
$endgroup$
– G. Smith
12 mins ago
add a comment |
$begingroup$
I have been looking at satellite orbits around the earth, or any object around any planet in fact, and am trying to find the orbital radius, or semi major length of a given satellite.
Kepler's third law gives the equation $P^2 = a^3$ where $P$ is the period of orbit and $a$ the distance.
I have a table of satellites currently orbiting the earth, as well as their altitude in the sky on their geosynchronous trajectory. One in particular is 99.9 and has an altitude of 705.
By solving the equation for $a$, I get $a = (P^2)^1/3$.
When I plug in the numbers, they don't correspond.
So my questions are:
- Are there unit standards I need for both $P$ and $a$? Currently $P$ is in minutes, $a$ in kilometres.
- Am I missing something, like Newton's universal gravitational constant? I get a page deriving Kepler's third law using this constant.
newtonian-mechanics newtonian-gravity orbital-motion celestial-mechanics satellites
edited 5 hours ago
Qmechanic♦
108k122001253
asked 6 hours ago
triple7triple7
133
New contributor
triple7 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
$endgroup$
I have been looking at satellite orbits around the earth, or any object around any planet in fact, and am trying to find the orbital radius, or semi major length of a given satellite.
Kepler's third law gives the equation $P^2 = a^3$ where $P$ is the period of orbit and $a$ the distance.
I have a table of satellites currently orbiting the earth, as well as their altitude in the sky on their geosynchronous trajectory. One in particular is 99.9 and has an altitude of 705.
By solving the equation for $a$, I get $a = (P^2)^1/3$.
When I plug in the numbers, they don't correspond.
So my questions are:
- Are there unit standards I need for both $P$ and $a$? Currently $P$ is in minutes, $a$ in kilometres.
- Am I missing something, like Newton's universal gravitational constant? I get a page deriving Kepler's third law using this constant.
newtonian-mechanics newtonian-gravity orbital-motion celestial-mechanics satellites
newtonian-mechanics newtonian-gravity orbital-motion celestial-mechanics satellites
edited 5 hours ago
Qmechanic♦
108k122001253
asked 6 hours ago
triple7triple7
133
New contributor
triple7 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
edited 5 hours ago
Qmechanic♦
108k122001253
asked 6 hours ago
triple7triple7
133
New contributor
triple7 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
edited 5 hours ago
Qmechanic♦
108k122001253
edited 5 hours ago
Qmechanic♦
108k122001253
edited 5 hours ago
Qmechanic♦
108k122001253
108k122001253
asked 6 hours ago
triple7triple7
133
New contributor
triple7 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked 6 hours ago
triple7triple7
133
asked 6 hours ago
triple7triple7
133
133
New contributor
triple7 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
New contributor
triple7 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
triple7 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
$begingroup$
hyperphysics.phy-astr.gsu.edu/hbase/kepler.html#c6
$endgroup$
– Kyle Kanos
6 hours ago
$begingroup$
The equality only holds in certain units since its dimensionally inhomogeneous. In particular, if you use Earth years and the Earth-Sun distance (i.e. 1a.u.) then it's true, so it must be true in those specific units.
$endgroup$
– jacob1729
3 hours ago
$begingroup$
BTW, do you understand that $a$ is not altitude but rather distance from the center of the Earth?
$endgroup$
– G. Smith
12 mins ago
add a comment |
$begingroup$
hyperphysics.phy-astr.gsu.edu/hbase/kepler.html#c6
$endgroup$
– Kyle Kanos
6 hours ago
$begingroup$
The equality only holds in certain units since its dimensionally inhomogeneous. In particular, if you use Earth years and the Earth-Sun distance (i.e. 1a.u.) then it's true, so it must be true in those specific units.
$endgroup$
– jacob1729
3 hours ago
$begingroup$
BTW, do you understand that $a$ is not altitude but rather distance from the center of the Earth?
$endgroup$
– G. Smith
12 mins ago
$begingroup$
hyperphysics.phy-astr.gsu.edu/hbase/kepler.html#c6
$endgroup$
– Kyle Kanos
6 hours ago
$begingroup$
hyperphysics.phy-astr.gsu.edu/hbase/kepler.html#c6
$endgroup$
– Kyle Kanos
6 hours ago
$begingroup$
The equality only holds in certain units since its dimensionally inhomogeneous. In particular, if you use Earth years and the Earth-Sun distance (i.e. 1a.u.) then it's true, so it must be true in those specific units.
$endgroup$
– jacob1729
3 hours ago
$begingroup$
The equality only holds in certain units since its dimensionally inhomogeneous. In particular, if you use Earth years and the Earth-Sun distance (i.e. 1a.u.) then it's true, so it must be true in those specific units.
$endgroup$
– jacob1729
3 hours ago
$begingroup$
BTW, do you understand that $a$ is not altitude but rather distance from the center of the Earth?
$endgroup$
– G. Smith
12 mins ago
$begingroup$
BTW, do you understand that $a$ is not altitude but rather distance from the center of the Earth?
$endgroup$
– G. Smith
12 mins ago
add a comment |
3 Answers
3
active
oldest
votes
$begingroup$
that equality should be a proportional to sign. In particular, in SI, the squared period has units of seconds squared, and the semi-major radius of of the orbit cubed is in meters cubed, so they can't be equal.
Instead, I'd be checking whether $T^2/a^3$ is constant for different satellites orbiting the same object (Like the ISS and the moon, for example)
answered 6 hours ago
Jerry SchirmerJerry Schirmer
31.7k257107
$endgroup$
5
$begingroup$
Ok, as I'm blind and use a screenreader, I didn't realise it was a proportion sign. And most sites only show images for formulas, which are inaccessible too. Also, I am assuming you use latec or math jacks for the symbols here, which also make the screen reader hang In a cycle. Could you give me a simple ASCII form of the distance given a period?
$endgroup$
– triple7
6 hours ago
$begingroup$
@triple7: Keplers law says that the square of the period divided by the cube of the distance is equal to a constant for every central body. so, t squared divided by a cubed should be the same for the ISS and for the moon. After Kepler, Newton was able to come up with a theoretical formula to predict what this constant should be, which is 4 * pi squared / (G * M), where G is Newton's constant, and M is the mass of the central body.
$endgroup$
– Jerry Schirmer
6 hours ago
1
$begingroup$
Yep, finally found it. Thanks
$endgroup$
– triple7
5 hours ago
add a comment |
$begingroup$
The general form of Kepler's period law is $T^2 = frac4pi^2G(M+m)a^3$. Often, we make the simplifying assumption that $M>>m$, so that $M+m approx M$.
Kepler's period law only takes the form $T^2 = a^3$ (forgetting about the units) when you use certain quantities- in this case, $M$ being solar mass, $T$ being an Earth year, and $a$ being an astronomical unit.
Try plugging into the equation for the mass of earth (and don't bother with the satellite mass) and use units of meters and seconds. See if you get the right result!
answered 6 hours ago
swickrotationswickrotation
615
$endgroup$
add a comment |
$begingroup$
Kepler's third law claims that $p^2 propto a^3$. The equality sign you use is incorrect.
answered 6 hours ago
my2ctsmy2cts
5,9492719
$endgroup$
add a comment |
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3 Answers
3
active
oldest
votes
3 Answers
3
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
that equality should be a proportional to sign. In particular, in SI, the squared period has units of seconds squared, and the semi-major radius of of the orbit cubed is in meters cubed, so they can't be equal.
Instead, I'd be checking whether $T^2/a^3$ is constant for different satellites orbiting the same object (Like the ISS and the moon, for example)
answered 6 hours ago
Jerry SchirmerJerry Schirmer
31.7k257107
$endgroup$
5
$begingroup$
Ok, as I'm blind and use a screenreader, I didn't realise it was a proportion sign. And most sites only show images for formulas, which are inaccessible too. Also, I am assuming you use latec or math jacks for the symbols here, which also make the screen reader hang In a cycle. Could you give me a simple ASCII form of the distance given a period?
$endgroup$
– triple7
6 hours ago
$begingroup$
@triple7: Keplers law says that the square of the period divided by the cube of the distance is equal to a constant for every central body. so, t squared divided by a cubed should be the same for the ISS and for the moon. After Kepler, Newton was able to come up with a theoretical formula to predict what this constant should be, which is 4 * pi squared / (G * M), where G is Newton's constant, and M is the mass of the central body.
$endgroup$
– Jerry Schirmer
6 hours ago
1
$begingroup$
Yep, finally found it. Thanks
$endgroup$
– triple7
5 hours ago
add a comment |
$begingroup$
that equality should be a proportional to sign. In particular, in SI, the squared period has units of seconds squared, and the semi-major radius of of the orbit cubed is in meters cubed, so they can't be equal.
Instead, I'd be checking whether $T^2/a^3$ is constant for different satellites orbiting the same object (Like the ISS and the moon, for example)
answered 6 hours ago
Jerry SchirmerJerry Schirmer
31.7k257107
$endgroup$
5
$begingroup$
Ok, as I'm blind and use a screenreader, I didn't realise it was a proportion sign. And most sites only show images for formulas, which are inaccessible too. Also, I am assuming you use latec or math jacks for the symbols here, which also make the screen reader hang In a cycle. Could you give me a simple ASCII form of the distance given a period?
$endgroup$
– triple7
6 hours ago
$begingroup$
@triple7: Keplers law says that the square of the period divided by the cube of the distance is equal to a constant for every central body. so, t squared divided by a cubed should be the same for the ISS and for the moon. After Kepler, Newton was able to come up with a theoretical formula to predict what this constant should be, which is 4 * pi squared / (G * M), where G is Newton's constant, and M is the mass of the central body.
$endgroup$
– Jerry Schirmer
6 hours ago
1
$begingroup$
Yep, finally found it. Thanks
$endgroup$
– triple7
5 hours ago
add a comment |
$begingroup$
that equality should be a proportional to sign. In particular, in SI, the squared period has units of seconds squared, and the semi-major radius of of the orbit cubed is in meters cubed, so they can't be equal.
Instead, I'd be checking whether $T^2/a^3$ is constant for different satellites orbiting the same object (Like the ISS and the moon, for example)
answered 6 hours ago
Jerry SchirmerJerry Schirmer
31.7k257107
$endgroup$
that equality should be a proportional to sign. In particular, in SI, the squared period has units of seconds squared, and the semi-major radius of of the orbit cubed is in meters cubed, so they can't be equal.
Instead, I'd be checking whether $T^2/a^3$ is constant for different satellites orbiting the same object (Like the ISS and the moon, for example)
answered 6 hours ago
Jerry SchirmerJerry Schirmer
31.7k257107
edited 5 hours ago
answered 6 hours ago
Jerry SchirmerJerry Schirmer
31.7k257107
answered 6 hours ago
Jerry SchirmerJerry Schirmer
31.7k257107
answered 6 hours ago
Jerry SchirmerJerry Schirmer
31.7k257107
31.7k257107
5
$begingroup$
Ok, as I'm blind and use a screenreader, I didn't realise it was a proportion sign. And most sites only show images for formulas, which are inaccessible too. Also, I am assuming you use latec or math jacks for the symbols here, which also make the screen reader hang In a cycle. Could you give me a simple ASCII form of the distance given a period?
$endgroup$
– triple7
6 hours ago
$begingroup$
@triple7: Keplers law says that the square of the period divided by the cube of the distance is equal to a constant for every central body. so, t squared divided by a cubed should be the same for the ISS and for the moon. After Kepler, Newton was able to come up with a theoretical formula to predict what this constant should be, which is 4 * pi squared / (G * M), where G is Newton's constant, and M is the mass of the central body.
$endgroup$
– Jerry Schirmer
6 hours ago
1
$begingroup$
Yep, finally found it. Thanks
$endgroup$
– triple7
5 hours ago
add a comment |
5
$begingroup$
Ok, as I'm blind and use a screenreader, I didn't realise it was a proportion sign. And most sites only show images for formulas, which are inaccessible too. Also, I am assuming you use latec or math jacks for the symbols here, which also make the screen reader hang In a cycle. Could you give me a simple ASCII form of the distance given a period?
$endgroup$
– triple7
6 hours ago
$begingroup$
@triple7: Keplers law says that the square of the period divided by the cube of the distance is equal to a constant for every central body. so, t squared divided by a cubed should be the same for the ISS and for the moon. After Kepler, Newton was able to come up with a theoretical formula to predict what this constant should be, which is 4 * pi squared / (G * M), where G is Newton's constant, and M is the mass of the central body.
$endgroup$
– Jerry Schirmer
6 hours ago
1
$begingroup$
Yep, finally found it. Thanks
$endgroup$
– triple7
5 hours ago
5
5
$begingroup$
Ok, as I'm blind and use a screenreader, I didn't realise it was a proportion sign. And most sites only show images for formulas, which are inaccessible too. Also, I am assuming you use latec or math jacks for the symbols here, which also make the screen reader hang In a cycle. Could you give me a simple ASCII form of the distance given a period?
$endgroup$
– triple7
6 hours ago
$begingroup$
Ok, as I'm blind and use a screenreader, I didn't realise it was a proportion sign. And most sites only show images for formulas, which are inaccessible too. Also, I am assuming you use latec or math jacks for the symbols here, which also make the screen reader hang In a cycle. Could you give me a simple ASCII form of the distance given a period?
$endgroup$
– triple7
6 hours ago
$begingroup$
@triple7: Keplers law says that the square of the period divided by the cube of the distance is equal to a constant for every central body. so, t squared divided by a cubed should be the same for the ISS and for the moon. After Kepler, Newton was able to come up with a theoretical formula to predict what this constant should be, which is 4 * pi squared / (G * M), where G is Newton's constant, and M is the mass of the central body.
$endgroup$
– Jerry Schirmer
6 hours ago
$begingroup$
@triple7: Keplers law says that the square of the period divided by the cube of the distance is equal to a constant for every central body. so, t squared divided by a cubed should be the same for the ISS and for the moon. After Kepler, Newton was able to come up with a theoretical formula to predict what this constant should be, which is 4 * pi squared / (G * M), where G is Newton's constant, and M is the mass of the central body.
$endgroup$
– Jerry Schirmer
6 hours ago
1
1
$begingroup$
Yep, finally found it. Thanks
$endgroup$
– triple7
5 hours ago
$begingroup$
Yep, finally found it. Thanks
$endgroup$
– triple7
5 hours ago
add a comment |
$begingroup$
The general form of Kepler's period law is $T^2 = frac4pi^2G(M+m)a^3$. Often, we make the simplifying assumption that $M>>m$, so that $M+m approx M$.
Kepler's period law only takes the form $T^2 = a^3$ (forgetting about the units) when you use certain quantities- in this case, $M$ being solar mass, $T$ being an Earth year, and $a$ being an astronomical unit.
Try plugging into the equation for the mass of earth (and don't bother with the satellite mass) and use units of meters and seconds. See if you get the right result!
answered 6 hours ago
swickrotationswickrotation
615
$endgroup$
add a comment |
$begingroup$
The general form of Kepler's period law is $T^2 = frac4pi^2G(M+m)a^3$. Often, we make the simplifying assumption that $M>>m$, so that $M+m approx M$.
Kepler's period law only takes the form $T^2 = a^3$ (forgetting about the units) when you use certain quantities- in this case, $M$ being solar mass, $T$ being an Earth year, and $a$ being an astronomical unit.
Try plugging into the equation for the mass of earth (and don't bother with the satellite mass) and use units of meters and seconds. See if you get the right result!
answered 6 hours ago
swickrotationswickrotation
615
$endgroup$
add a comment |
$begingroup$
The general form of Kepler's period law is $T^2 = frac4pi^2G(M+m)a^3$. Often, we make the simplifying assumption that $M>>m$, so that $M+m approx M$.
Kepler's period law only takes the form $T^2 = a^3$ (forgetting about the units) when you use certain quantities- in this case, $M$ being solar mass, $T$ being an Earth year, and $a$ being an astronomical unit.
Try plugging into the equation for the mass of earth (and don't bother with the satellite mass) and use units of meters and seconds. See if you get the right result!
answered 6 hours ago
swickrotationswickrotation
615
$endgroup$
The general form of Kepler's period law is $T^2 = frac4pi^2G(M+m)a^3$. Often, we make the simplifying assumption that $M>>m$, so that $M+m approx M$.
Kepler's period law only takes the form $T^2 = a^3$ (forgetting about the units) when you use certain quantities- in this case, $M$ being solar mass, $T$ being an Earth year, and $a$ being an astronomical unit.
Try plugging into the equation for the mass of earth (and don't bother with the satellite mass) and use units of meters and seconds. See if you get the right result!
answered 6 hours ago
swickrotationswickrotation
615
edited 5 hours ago
answered 6 hours ago
swickrotationswickrotation
615
answered 6 hours ago
swickrotationswickrotation
615
answered 6 hours ago
swickrotationswickrotation
615
615
add a comment |
add a comment |
$begingroup$
Kepler's third law claims that $p^2 propto a^3$. The equality sign you use is incorrect.
answered 6 hours ago
my2ctsmy2cts
5,9492719
$endgroup$
add a comment |
$begingroup$
Kepler's third law claims that $p^2 propto a^3$. The equality sign you use is incorrect.
answered 6 hours ago
my2ctsmy2cts
5,9492719
$endgroup$
add a comment |
$begingroup$
Kepler's third law claims that $p^2 propto a^3$. The equality sign you use is incorrect.
answered 6 hours ago
my2ctsmy2cts
5,9492719
$endgroup$
Kepler's third law claims that $p^2 propto a^3$. The equality sign you use is incorrect.
answered 6 hours ago
my2ctsmy2cts
5,9492719
answered 6 hours ago
my2ctsmy2cts
5,9492719
answered 6 hours ago
my2ctsmy2cts
5,9492719
answered 6 hours ago
my2ctsmy2cts
5,9492719
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$begingroup$
hyperphysics.phy-astr.gsu.edu/hbase/kepler.html#c6
$endgroup$
– Kyle Kanos
6 hours ago
$begingroup$
The equality only holds in certain units since its dimensionally inhomogeneous. In particular, if you use Earth years and the Earth-Sun distance (i.e. 1a.u.) then it's true, so it must be true in those specific units.
$endgroup$
– jacob1729
3 hours ago
$begingroup$
BTW, do you understand that $a$ is not altitude but rather distance from the center of the Earth?
$endgroup$
– G. Smith
12 mins ago