Is it possible to find orbital velocity depending on time?

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SUMMARY

The discussion centers on calculating orbital velocity and period using gravitational constants and the mass of Earth. It is established that without knowing the radius of the orbit, one cannot determine the orbital period solely from the gravitational constant (G) and the mass of Earth (M). According to Kepler's Law, the relationship between the orbital period and radius is defined by the equation T²/R³ = 4π²/GM. Additionally, when calculating the mass of Earth using the moon's orbit, it is necessary to subtract the moon's mass for accuracy, resulting in a corrected mass of approximately 5.99E+24 kg.

PREREQUISITES
  • Understanding of Kepler's Laws of planetary motion
  • Familiarity with gravitational constants (G) and mass of Earth (M)
  • Basic knowledge of orbital mechanics
  • Ability to perform calculations involving scientific notation
NEXT STEPS
  • Study Kepler's Third Law in detail
  • Learn about gravitational force calculations and their applications
  • Research methods for calculating orbital parameters using satellite data
  • Explore the impact of celestial body masses on gravitational calculations
USEFUL FOR

Astronomy students, astrophysicists, and anyone involved in orbital mechanics or satellite calculations will benefit from this discussion.

hmvince
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A satellite is in orbit around earth,
(you know G, mass of earth, etc. but NOT the radius)
is it possible to find orbital period?
 
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hmvince said:
A satellite is in orbit around earth,
(you know G, mass of earth, etc. but NOT the radius)
is it possible to find orbital period?

If only G and mass are all that is known, then No. According to Kepler's Law you must know the radius to get the orbital period, (or vice versa). All you can determine with only G and M is the ratio of the orbital period squared to the radius cubed...which is equal to 4(pi)^2 / GM.

Creator
 
Sorry about the late reply, but thankyou very much.
If it's not too much trouble, when calculating the mass of the Earth using the moon as a reference and Kepler's 3rd Law, is it correct to subtract the moon's mass after completing the sum:

Code: 
m[SUB]e[/SUB] = (4*(pi)[SUP]2[/SUP]*r[SUP]3[/SUP]) / (G*t[SUP]2[/SUP])

m[SUB]e[/SUB] = (4*(pi)[SUP]2[/SUP]*385000000[SUP]3[/SUP]) / (G*2358720[SUP]2[/SUP])

m[SUB]e[/SUB] = 6.07[SUB]E[/SUB]+24

Should I be subtracting the moons mass to get:

Code: 
m[SUB]e[/SUB] = 6.07[SUB]E[/SUB]+24 - 7.36[SUB]e[/SUB]+22  =   5.99[SUB]E[/SUB]+24

I know its not a big difference but I would like to be doing this correctly.
Thanks very much
 

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