Even if we assume that the central mass is our sun, the question is still insufficient for an answer as just giving the semi-major axis isn't enough. We need to know the minor axis as well to calculate the eccentricity.
T2/R3 = K (from Kepler's 3rd Law)
For the Earth, T = 1 year, R = 1 AU . So K = 1 . According to Kepler,
it's the same K for any other body in solar orbit.
For your asteroid . . . R = 2.8 AU
T2/(2.8)3 = 1
T2 = (2.8)3
T = (2.8)3/2 = 4.685 years
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Note: You said that the asteroid has a semimajor axis of 2.8 AU, but in the
above derivation, I have tacitly assumed that this figure actually describes the
asteroid's orbit.
This can be worked out from Kepler's 3rd Law. I make the answer to be
eight ( Earth) years.
8 Earth years.
You can work that out from Kepler's 3rd Law:
(Orbit Period, in Earth years)2 = (average distance from Sun, in AU)3
Use Kepler's 3rd law. The time is 4^(3/2) years, that is 8 years.
Not at all. The only thing that sets the orbital period is the semimajor axis, which is the average of the maximum and minimum distances from the Sun.
jkjnl
That can be calculated from Kepler's 3rd law which says if the period is T years the semimajor axis must be T2/3 astronomical units. So for a period of 12 years the s/m axis is 5.421 AU or 784 million km.
The major axis is the diameter across the widest part. The semimajor axis is half that, and for a planet it's the average of the maximum and minimum distances from the Sun .
You can find the major axis, 0.5+31.5 or 32 AU. The semimajor axis is half that, 16 AU. Then you can use Keplers 3rd law to calculate the period, which is 161.5 or 64 years.
Not at all. The only thing that sets the orbital period is the semimajor axis, which is the average of the maximum and minimum distances from the Sun.
(I'm going to assume that when you said "first" you meant "fastest," because otherwise the question is nonsense.) Because of Kepler's Third Law. The orbital period for a body is related to the semimajor axis of its orbit. Mercury's orbit has the shortest semimajor axis of all the Solar planets, and therefore it has the shortest orbital period.
the period of revolution is related to the semimajor axis.... :)
jkjnl
One of the parts of an ellipse is the length of its major axis. Half that is called the semimajor axis. Kepler's 3rd law says that the time to do one orbit is proportional to the 3/2 power of the semimajor axis. IF the semimajor axis is one astronomical unit the period is one year (the Earth). For a planet with a semimajor axis of 4 AUs the period would have to be 8 years, by Kepler-3.
One of the parts of an ellipse is the length of its major axis. Half that is called the semimajor axis. Kepler's 3rd law says that the time to do one orbit is proportional to the 3/2 power of the semimajor axis. IF the semimajor axis is one astronomical unit the period is one year (the Earth). For a planet with a semimajor axis of 4 AUs the period would have to be 8 years, by Kepler-3.
That can be calculated from Kepler's 3rd law which says if the period is T years the semimajor axis must be T2/3 astronomical units. So for a period of 12 years the s/m axis is 5.421 AU or 784 million km.
The major axis is the diameter across the widest part. The semimajor axis is half that, and for a planet it's the average of the maximum and minimum distances from the Sun .
You can find the major axis, 0.5+31.5 or 32 AU. The semimajor axis is half that, 16 AU. Then you can use Keplers 3rd law to calculate the period, which is 161.5 or 64 years.
The major and minor axes of a circle are the same - either is any diameter. So a semimajor axis is half the diameter which is 12 cm.
4 years
Orbital information. You need to know the size of the "semi-major axis". Then you can calculate the orbital period, using Kepler's Third Law.