Orbital Mechanic Question

[Der Anfang]

Hello! First and foremost, I am hoping that I've posted this in the right topic. Alright... so I am beginning to learn a few things here and there about some astrophysics related things. At least the very basic stuff, or so I presume. For [near] circular orbits, I have learned how to calculate orbital velocity and from that I am also able to calculate the time it would take for said object to orbit based on the parametres given. However.... I am not sure I understand how to calculate an object's semi major axis (in a circular orbit) based on orbital time. For instance... if an object is in a circular orbit around the Earth, we know it has an orbital period of ~2 hours... but what is it's SMA? I don't know how to do the calculations for that. I do know that Orbital Velocity = Sqrt of GM/R (where R is the semi-major axis of the object) and that Orbital Time = (R2*3.14)/V...

[K^2]

Lets start with a perfect circle. Distance around orbit is 2ÀR. Velocity is Sqrt(µ/R). (Where µ = GM is gravitational parameter.) So T = 2ÀR/Sqrt(µ/R). This simplifies to T = 2À * Sqrt(R³/µ).

Now, the cool thing about Kepler's Laws is that they tell you that period depends on semi-major axis only. Not on eccentricity. So the general formula is identical T = 2À * Sqrt(a³/µ), regardless of whether it's a circular orbit or not.

To work out semi-major axis from period, just solve that for a. Square both sides, find a³, and take the cube root of that.

[Der Anfang]

Lets start with a perfect circle. Distance around orbit is 2ÀR. Velocity is Sqrt(µ/R). (Where µ = GM is gravitational parameter.) So T = 2ÀR/Sqrt(µ/R). This simplifies to T = 2À * Sqrt(R³/µ).

Now, the cool thing about Kepler's Laws is that they tell you that period depends on semi-major axis only. Not on eccentricity. So the general formula is identical T = 2À * Sqrt(a³/µ), regardless of whether it's a circular orbit or not.

To work out semi-major axis from period, just solve that for a. Square both sides, find a³, and take the cube root of that.

I am still a little confused... what is a?

Could you give me a sample problem with numbers?

[Brotoro]

The semi-major axis (a) is half of the long axis of the ellipse. For a circular orbit, it's just the radius. For a satellite orbiting the Earth in a circular orbit, it's just the distance from the center of the Earth to the orbit.

[Der Anfang]

The semi-major axis (a) is half of the long axis of the ellipse. For a circular orbit, it's just the radius. For a satellite orbiting the Earth in a circular orbit, it's just the distance from the center of the Earth to the orbit.

And I am trying to figure out how to calculate for a based on the period...

[ZetaX]

And I am trying to figure out how to calculate for a based on the period...

K^2 gave you a formula and even how to turn that into a formula for a. There is also no need for numbers because all that adds is less clarity (you don't see what really happens, and all that simple short letters get replaced by long ugly numbers).

So you only have to solve for a. After that, plugging in numbers is fine, but the formula will just be "multiply stuff, take third root".

[Der Anfang]

K^2 gave you a formula and even how to turn that into a formula for a. There is also no need for numbers because all that adds is less clarity (you don't see what really happens, and all that simple short letters get replaced by long ugly numbers).

So you only have to solve for a. After that, plugging in numbers is fine, but the formula will just be "multiply stuff, take third root".

Oh, okay. Thank you! I get it now.