Mysterious Planet: Approximating its Density

In summary, the conversation discusses how to calculate the approximate density of a strange new planet with no atmosphere, using the period of a satellite orbiting closely to its surface. It is suggested to equate the gravitational force to the centripetal force and solve for density as a function of period.
  • #1
tandoorichicken
245
0
A strange new planet that has no atmosphere has a satellite that orbits very close to the planet's surface with a period of 1.50 hours. What is the approximate density of the planet? (Assume that the radius of orbit equals the radius of the planet.)
 
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  • #2
Maybe I'm wrong...but it sounds like something is missing here:
It only gives you the time it takes to complete a revolution?
I would think u either need to know the planet's radius, mass, or ship velocity to calculate the density...

Because, say a person drives a car around the Earth's equator, and someone else flies a plane around the same distance. Without knowing velocity of the objects, the period of each revolution would be different, even though its the same planet, hence same density...
 
  • #3
How about just equating the gravitational force to the centripetal force?
[itex] \frac{mGM}{R^2} = m\omega^2R [/itex]

and since [itex] \rho = \frac{M}{R^3} [/itex] and v = Rω and [itex] T = \frac{2\pi}{\omega} [/itex] you can solve for density as a function of period. So I think:

[itex] \rho = \frac{1}{G}\left(\frac{2\pi}{T}\right)^2 [/itex]
 

1. What is the purpose of approximating a planet's density?

The density of a planet can provide important information about its composition and internal structure. By calculating the density, scientists can better understand the planet's formation and evolution, as well as its potential habitability.

2. How is a planet's density approximated?

The density of a planet is approximated by using its mass and volume. The mass can be determined through the planet's gravitational pull, while the volume can be estimated through measurements of the planet's size or by analyzing its gravitational effects on nearby objects. These values are then used to calculate the density using the formula D = M/V.

3. What factors can affect a planet's density?

The density of a planet can be affected by a variety of factors, such as its composition, size, and distance from its host star. Planets with higher metal content tend to have higher densities, while planets with more gas and ice tend to have lower densities. Additionally, larger planets tend to have higher densities due to increased gravitational compression.

4. How does a planet's density relate to its gravity?

The density of a planet is directly related to its gravity. Planets with higher densities have stronger gravitational pulls, while planets with lower densities have weaker gravitational pulls. This is because density is a measure of the amount of mass within a given volume, and gravity is a force that is dependent on an object's mass.

5. How does the density of Earth compare to other planets in our solar system?

The density of Earth is 5.51 grams per cubic centimeter, making it the densest planet in our solar system. This is due to its relatively high metal content and size. Other planets, such as Jupiter and Saturn, have lower densities due to their large gas and ice layers. Mercury, on the other hand, has a higher density than Earth, but it is also significantly smaller in size.

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