A newly discovered asteroid has an orbital period of 5.63 yrs. Mars has an orbital period of 1.8809 yrs...?

Question

A newly discovered asteroid has an orbital period of 5.63 yrs. Mars has an orbital period of 1.8809 yrs. The largest asteroid, Ceres, has an orbital period of 4.603 yrs. Does this new asteroid orbit nearer to Mars or nearer to Ceres? Explain your Answer.

ty for your help!

Answer 1

Relatively simple. The farther away (on average) from the sun, the longer the orbital period. Ceres' period is larger than that of Mars, so it's farther away from the sun. Since the new asteroid has a longer period than either Mars or Ceres, it's farther out than either, but Ceres would be between them. Therefore, the new asteroid is closer to Ceres.

This assumes the asteroid has a realtively circular orbit, and is not so eccentric that it actually crosses Mars' orbit, something like Pluto crossing Neptune's orbit. If it does, it's possible that the asteroid may make a closer approach to Mars than it ever does to Ceres.

Answer 2

The easiest approach to this problem is Kepler's 3rd Law of Planetary motion which is r^3 = T^2 where r is the average radius of the object's orbit in astronomical units (au's) and T is the time for one orbit in years.

Since we need to find the orbit, I would take the cube root of both sides of the equation above, so

r = T^(2/3)

Plugging in the values given...

New asteroid r = 5.63^(2/3) = 3.16 au
Mars r = 1.8809^(2/3) = 1.52 au
Ceres r = 4.603^*(2/3) = 2.77 au

So the new asteroid orbits closer to Ceres than Mars.

Answer 3

For most all objects, the orbital period is related to the size of the orbit by the equation:

Kepler's Third Law:
T = a^(3/2)
T in years
a is semi-major axis of orbit, in AU
(1 AU = Earth-Sun distance)

Flip this around, and you get
T^(2/3) = a

You should be able to do the math from here, I hope ...

Like one of the commentators said, this does not give the distance between the objects; it does give one part of the size of the orbit. The semi-minor distance is one of the other parameters, and you don't give enough information to calculate that. I guess you're supposed to assume that the orbits are circular.

Generally, you need 6 parameters to describe an orbit fully.
(More if the object is a comet or rocket, since they put out gas that pushes on them. And to be picky about it, 6 parameters are enough only for the 2-body situation (Sun + planet or asteroid).)

Answer 4

Nearer to Ceres, I would say.

The further away an object is from the Sun, the greater the orbit, and the slower the speed at which it revolves around the Sun.

Answer 5

I think you have to take into consideration the shape of the orbit. orbits are elliptical and not proper circular. Considering this, the question might not make sense. You can always tell the distance between the two objects in a given situation, but it is hard to give an answer that would be valid during the whole orbit.

Answer 6

Treating it as a 2-physique subject (solar and planet), the orbit must be an ellipse. 3 factors uniquely ascertain the formulation of an ellipse. you are able to ascertain the formulation via fixing 3 simultaneous equations. (They coach you the thank you to try this for the time of severe college algebra.) The orbital era for a small physique orbiting a vital physique is given via the formulation on the link under. If the recent planet has close encounters with different planets, the mathematics gets complicated. that's often solved via numerical prognosis. a working laptop or workstation simulates the trajectory and makes small ameliorations till the blunders turns into 0.

Answer 7

closer to ceres
by logics, not physics