Calculating Orbit Time of a Hypothetical Planet in the Asteroid Belt

In summary, the asteroid belt between Mars and Jupiter is made up of fragments from a destroyed planet. The radius of the asteroid belt is three times larger than the distance between the Sun and Earth. Using this information, we can calculate the hypothetical planet's orbital period using the equation T=TE sqrt((a/r)^3), where TE is the orbital period of Earth. However, we do not have enough information to deduce the mass of this planet.
  • #1
Phys221
1
0
Just looking for a place to start, not all the work.

Homework Statement


3 The asteroid belt between Mars and Jupiter consists of many fragments (which some
space scientists think came from a planet that once orbited the Sun but was destroyed).
(a) If the radius of the asteroid belt (where the orbit of the planet would have been) is
about three times larger than the distance between the Sun than the Earth, how long
would it have taken this hypothetical planet to orbit the Sun? (b) Can we use these data to
deduce the mass of this planet

Homework Equations


T=1.4sqrt((a/r)^3) this is for Earth.
sqrt = square root

The Attempt at a Solution


No idea where to start. I'm assuming we say it has the same density as Earth.

Thanks in advance.
 
Last edited:
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  • #2
Phys221 said:
...

Homework Equations


T=TE sqrt((a/r)^3)...
"a" is the radius of the hypothetical planet.

Where does the 1.4 come from?
 

Related to Calculating Orbit Time of a Hypothetical Planet in the Asteroid Belt

1. How do you calculate the orbit time of a hypothetical planet in the asteroid belt?

The orbit time of a planet in the asteroid belt can be calculated using Kepler's third law, which states that the square of the orbital period is proportional to the cube of the semi-major axis. This means that if we know the semi-major axis of the planet's orbit, we can use this equation to calculate the orbit time.

2. What is the semi-major axis of a planet's orbit?

The semi-major axis is a measure of the average distance between a planet and the sun. In order to calculate the orbit time of a hypothetical planet in the asteroid belt, we would need to know the semi-major axis of its orbit.

3. How is the semi-major axis of a planet's orbit determined?

The semi-major axis of a planet's orbit can be determined using observations of the planet's position in the sky over a period of time. By tracking the planet's movement and using mathematical calculations, astronomers can determine the semi-major axis of its orbit.

4. Can the orbit time of a hypothetical planet in the asteroid belt change?

Yes, the orbit time of a planet in the asteroid belt can change due to gravitational interactions with other objects in the solar system. These interactions can cause the planet's orbit to become more elliptical or change its orientation, which can alter the orbit time.

5. How accurate are calculations of the orbit time of a hypothetical planet in the asteroid belt?

The accuracy of these calculations depends on the accuracy of the data used, such as the planet's position and velocity. With precise measurements, the calculated orbit time can be very accurate. However, factors like gravitational interactions with other objects can also affect the accuracy of the calculation.

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