# Finding the Density of a Planet using Time

• lanzjohn
In summary: Your homework statement is that a satellite is in a circular orbit very close to the surface of a spherical planet. The period of the orbit is T = 2.52 hours. The gravitational constant G has units of length3/(mass*time2). So T2/G has units of time2/(length3/(mass*time2)) or mass*time4*length-3.
lanzjohn

## Homework Statement

A satellite is in a circular orbit very close to the surface of a spherical planet. The period of the orbit is T = 2.52 hours.
What is density (mass/volume) of the planet? Assume that the planet has a uniform density.

Hint: "very close to the surface" means that Rorbit = Rplanet

## The Attempt at a Solution

[PLAIN]http://img692.imageshack.us/img692/4624/34096608.png

Where did I go wrong. I feel like its my terrible algebra skillzz?

Thanks guys

Last edited by a moderator:
Check your units. What are the units of $(4\pi T^2)/(4/3G)$?

ohh I just have to change hours to seconds? Well that would make sense then my number won't be as big, which is a good sign. Okay thanks. ill try that orr maybe not..

Why would I have to change the units of G? T I understand.

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Yes, you have to do that, but that is not what I was talking about. You have as an answer

$$\rho = \frac{4\pi T^2}{G 4/3}$$

Numbers such as 3, 4, and pi are unitless. So let's throw them away:

$$\rho \propto \frac{T^2}{G}$$

The left-hand side is supposed to be a density with units of mass / volume = mass / length3 = mass * length-3. To have a consistent result, the right-hand side must have the same units. The period T has units of time while the gravitational constant G has units of length3/(mass*time2). Thus T2/G has units of time2/(length3/(mass*time2)) or mass*time4*length-3. Those are not the units of density.

Your units are inconsistent. That always means your result is garbage. Always.

Ok bare with me here,

So are you saying that my

d=t^2/G is wrong? I understand now how the units don't match up. But where did I go wrong?

At your second step you have M T^2 = (something)

At the bottom of the first column you have M = (something) T^2
You can just divide both sides of the first equation by T^2 instead of whatever
it is you did

## 1. What is the formula for finding the density of a planet using time?

The formula for finding the density of a planet using time is density = mass / (4/3 * π * radius3).

## 2. Why is time used in finding the density of a planet?

Time is used because it is a crucial component in determining the orbital period of a planet, which is necessary in the formula for finding density.

## 3. How is the time of orbit measured in finding the density of a planet?

The time of orbit is measured by tracking the amount of time it takes for a planet to complete one full orbit around its star.

## 4. Can the density of a planet be calculated using time alone?

No, the density of a planet cannot be calculated using time alone. Other factors, such as mass and radius, are also needed to accurately determine the density.

## 5. How does finding the density of a planet using time contribute to our understanding of the planet?

By finding the density of a planet, we can gain insight into its composition, structure, and formation. This information can help us understand the planet's history and potential for supporting life.

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