Compute radius knowing period and Gaussian constant

Problem:

If I now that a celestial body has a period T about a center, can I
compute the distance from that center using
Gauss constant?

Thanks

Skeu wrote:
Problem:

If I now that a celestial body has a period T about a center, can I
compute the distance from that center using
Gauss constant?

Yes.

In article
,
Skeu wrote:

Problem:

If I now that a celestial body has a period T about a center, can I
compute the distance from that center using
Gauss constant?

The mean distance, yes, assuming that the central body is the Sun or
that you also know its mass (in solar-mass units).

--
Odysseus

On 3 Mag, 22:52, Odysseus wrote:
In article
,

*Skeu wrote:
Problem:

If I now that a celestial body has a period T about a center, can I
compute the distance from that center using
Gauss constant?

The mean distance, yes, assuming that the central body is the Sun or
that you also know its mass (in solar-mass units).

--
Odysseus

No, I mean a new central body with unknown mass.
For example, Earth has a period around that cantral body of 25.000
years.
So it is possible to compute radius and mass of that center ?
I know that Gaussian constant is valid for all celestial bodies.
Clearly the ratio between a certain path in this new orbit and the
time necessary to it
is constant.

Thanks.

"Skeu" wrote in message
...
Problem:

If I now that a celestial body has a period T about a center, can I
compute the distance from that center using
Gauss constant?

Thanks


The Gauss constant has within it the implicit assumption that you are
dealing with a body orbiting the Sun (one solar mass). So the answer is yes
if you are in our solar system orbiting the Sun, and no if you are dealing
with a body orbiting an unknown mass (or one of the planets).

The general-case orbit would be an ellipse so you would be trying to
determine the semi-major axis.

You would need to determine the mass of the central object. Usually what is
done is to determine the orbit (period and semi-major axis), which tells you
the mass via the general form of Kepler's third law.

--
Mike Dworetsky

(Remove pants sp*mbl*ck to reply)

On 4 Mag, 10:44, "Mike Dworetsky"
wrote:
"Skeu" wrote in message

...

Problem:

If I now that a celestial body has a period T about a center, can I
compute the distance from that center using
Gauss constant?

Thanks

The Gauss constant has within it the implicit assumption that you are
dealing with a body orbiting the Sun (one solar mass). *So the answer is yes
if you are in our solar system orbiting the Sun, and no if you are dealing
with a body orbiting an unknown mass (or one of the planets).

The general-case orbit would be an ellipse so you would be trying to
determine the semi-major axis.

You would need to determine the mass of the central object. *Usually what is
done is to determine the orbit (period and semi-major axis), which tells you
the mass via the general form of Kepler's third law.

--
Mike Dworetsky

(Remove pants sp*mbl*ck to reply)

0,017 is an universal constant!
Or not? Gauss explains in De motu.... that its value must be
indipendent from bodies used to compute it!
You are telling : "The Gauss constant has within it the implicit
assumption that you are
dealing with a body orbiting the Sun (one solar mass). " . Something
is wrong!

jesko wrote:
On 4 Mag, 10:44, "Mike Dworetsky"
wrote:
"Skeu" wrote in message

...

Problem:

If I now that a celestial body has a period T about a center, can I
compute the distance from that center using
Gauss constant?

Thanks

The Gauss constant has within it the implicit assumption that you are
dealing with a body orbiting the Sun (one solar mass). So the answer is
yes
if you are in our solar system orbiting the Sun, and no if you are
dealing
with a body orbiting an unknown mass (or one of the planets).

The general-case orbit would be an ellipse so you would be trying to
determine the semi-major axis.

You would need to determine the mass of the central object. Usually what
is
done is to determine the orbit (period and semi-major axis), which tells
you
the mass via the general form of Kepler's third law.

--
Mike Dworetsky

(Remove pants sp*mbl*ck to reply)

0,017 is an universal constant!
Or not? Gauss explains in De motu.... that its value must be
indipendent from bodies used to compute it!
You are telling : "The Gauss constant has within it the implicit
assumption that you are
dealing with a body orbiting the Sun (one solar mass). " . Something
is wrong!

Nothing's wrong. The value for Gauss' constant *for our solar system*
is specified. It would be different for different systems.

The utility of Gauss' constant lies in the way it relates the period
to the mean distance (semimajor axis) for bodies in orbit about the
Sun. Note that this is just Kepler's Third Law with the constant of
proportionality penciled in.

On 4 Mag, 13:16, "Greg Neill" wrote:
jesko wrote:
On 4 Mag, 10:44, "Mike Dworetsky"
wrote:
"Skeu" wrote in message

....

Problem:

If I now that a celestial body has a period T about a center, can I
compute the distance from that center using
Gauss constant?

Thanks

The Gauss constant has within it the implicit assumption that you are
dealing with a body orbiting the Sun (one solar mass). So the answer is
yes
if you are in our solar system orbiting the Sun, and no if you are
dealing
with a body orbiting an unknown mass (or one of the planets).

The general-case orbit would be an ellipse so you would be trying to
determine the semi-major axis.

You would need to determine the mass of the central object. Usually what
is
done is to determine the orbit (period and semi-major axis), which tells
you
the mass via the general form of Kepler's third law.

--
Mike Dworetsky

(Remove pants sp*mbl*ck to reply)

0,017 is an universal constant!
Or not? Gauss explains in De motu.... that its value must be
indipendent from bodies used to compute it!
You are telling : "The Gauss constant has within it the implicit
assumption that you are
dealing with a body orbiting the Sun (one solar mass). *" . Something
is wrong!

Nothing's wrong. *The value for Gauss' constant *for our solar system*
is specified. *It would be different for different systems.

The utility of Gauss' constant lies in the way it relates the period
to the mean distance (semimajor axis) for bodies in orbit about the
Sun. *Note that this is just Kepler's Third Law with the constant of
proportionality penciled in.- Nascondi testo citato

- Mostra testo citato -

Ok! R = (0.017*T)/2Pi = R in AU.

if T = 25000 years then 9125000 days

so R = (0.017*9125000 )/2Pi == 24701,433121019108280254777070064
AU.

So the mean distnce from that center is
24701,433121019108280254777070064 AU.

Is this correct?

Thanks for your help and patience.

jesko wrote:
On 4 Mag, 13:16, "Greg Neill" wrote:
jesko wrote:
On 4 Mag, 10:44, "Mike Dworetsky"
wrote:
"Skeu" wrote in message


...

Problem:

If I now that a celestial body has a period T about a center, can I
compute the distance from that center using
Gauss constant?

Thanks

The Gauss constant has within it the implicit assumption that you are
dealing with a body orbiting the Sun (one solar mass). So the answer is
yes
if you are in our solar system orbiting the Sun, and no if you are
dealing
with a body orbiting an unknown mass (or one of the planets).

The general-case orbit would be an ellipse so you would be trying to
determine the semi-major axis.

You would need to determine the mass of the central object. Usually
what is
done is to determine the orbit (period and semi-major axis), which
tells you
the mass via the general form of Kepler's third law.

--
Mike Dworetsky

(Remove pants sp*mbl*ck to reply)

0,017 is an universal constant!
Or not? Gauss explains in De motu.... that its value must be
indipendent from bodies used to compute it!
You are telling : "The Gauss constant has within it the implicit
assumption that you are
dealing with a body orbiting the Sun (one solar mass). " . Something
is wrong!

Nothing's wrong. The value for Gauss' constant *for our solar system*
is specified. It would be different for different systems.

The utility of Gauss' constant lies in the way it relates the period
to the mean distance (semimajor axis) for bodies in orbit about the
Sun. Note that this is just Kepler's Third Law with the constant of
proportionality penciled in.- Nascondi testo citato

- Mostra testo citato -

Ok! R = (0.017*T)/2Pi = R in AU.

if T = 25000 years then 9125000 days

so R = (0.017*9125000 )/2Pi == 24701,433121019108280254777070064
AU.

So the mean distnce from that center is
24701,433121019108280254777070064 AU.

Is this correct?

No, you haven't used Kepler's Third Law. Also, you've got
the Gaussian constant to three decimal places; you can't
have a result with more accuracy than you start with. So all
those decimal places in your result are unwarranted.

Kepler's Third says that T^2 ~ R^3

so that

R ~ T^(2/3)

The expression you're looking for using the Gaussian constant
will look something like:

R = (k*T/(2*pi))^(2/3)

with T in days and the result in AU.

Using k = 0.0172 AU^(3/2) * Msun^(-1/2) * day^-1
and setting T = 25000 * 365.256 (sidereal years)

R = (k*T/(2*pi))^(2/3) = 854.9 AU

On 4 Mag, 16:32, "Greg Neill" wrote:
jesko wrote:
On 4 Mag, 13:16, "Greg Neill" wrote:
jesko wrote:
On 4 Mag, 10:44, "Mike Dworetsky"
wrote:
"Skeu" wrote in message

...







Problem:

If I now that a celestial body has a period T about a center, can I
compute the distance from that center using
Gauss constant?

Thanks

The Gauss constant has within it the implicit assumption that you are
dealing with a body orbiting the Sun (one solar mass). So the answer is
yes
if you are in our solar system orbiting the Sun, and no if you are
dealing
with a body orbiting an unknown mass (or one of the planets).

The general-case orbit would be an ellipse so you would be trying to
determine the semi-major axis.

You would need to determine the mass of the central object. Usually
what is
done is to determine the orbit (period and semi-major axis), which
tells you
the mass via the general form of Kepler's third law.

--
Mike Dworetsky

(Remove pants sp*mbl*ck to reply)

0,017 is an universal constant!
Or not? Gauss explains in De motu.... that its value must be
indipendent from bodies used to compute it!
You are telling : "The Gauss constant has within it the implicit
assumption that you are
dealing with a body orbiting the Sun (one solar mass). " . Something
is wrong!

Nothing's wrong. The value for Gauss' constant *for our solar system*
is specified. It would be different for different systems.

The utility of Gauss' constant lies in the way it relates the period
to the mean distance (semimajor axis) for bodies in orbit about the
Sun. Note that this is just Kepler's Third Law with the constant of
proportionality penciled in.- Nascondi testo citato

- Mostra testo citato -

Ok! * * *R = *(0.017*T)/2Pi *= * R in AU.

if T = 25000 years then *9125000 days

so * R = *(0.017*9125000 )/2Pi *== 24701,433121019108280254777070064
AU.

So the mean distnce from that center is
24701,433121019108280254777070064 *AU.

Is this correct?

No, you haven't used Kepler's Third Law. *Also, you've got
the Gaussian constant to three decimal places; you can't
have a result with more accuracy than you start with. *So all
those decimal places in your result are unwarranted.

Kepler's Third says that *T^2 ~ R^3

so that

R ~ T^(2/3)

The expression you're looking for using the Gaussian constant
will look something like:

R = (k*T/(2*pi))^(2/3)

with T in days and the result in AU.

Using k = 0.0172 AU^(3/2) * Msun^(-1/2) * day^-1
and setting T = 25000 * 365.256 * * * (sidereal years)

R = (k*T/(2*pi))^(2/3) = 854.9 AU- Nascondi testo citato

- Mostra testo citato -

No perchè la costante ha già semplificato il cubo e il quadrato.
Mi sembra ad esempio che A^3 / B^2 = A / Sqrt[b]