A hypothetical spherical planet consists entirely of iron (p=7860kg/m^3). Calculate the period of a satellite that orbits just above its surface.

I really can't solve this! No other information was provided. Please and thank you

Time required for 1 revolution,

T= (2πr^(3/2))/√(G∙M) (p. 146 of 7th ed Cutnell & Johnson)

Volume of a sphere,
V=4πr^3 (book inside cover)

Formula for mass density,
M=ρ∙V (p.321)

Where
T: the time period
G: universal gravitational constant, 6.673 E-11 (N∙m^2)/kg^2
note: N=(kg∙m)/s
r: distance from center of planet to satellite, aka planet’s radius
ρ: mass density of planet.
Iron density = 7860 kg/m^3
V: Volume of planet

Substitute formula for volume of a sphere into equation for mass:
M = ρ∙ 4πr^3
Then substitute this into the equation for time period
T= (2πr^(3/2))/√(G∙ρ∙ 4πr^3)
The r^(3/2) in the numerator cancels the √(r^3) in the denominator,
So the equation simplifies to
T= 2π/√(G∙ρ∙4π)
Plug in the known value of G and given value of ρ.
For a planet made of iron, satellite period
T ≈ 2447.39 seconds

To calculate the period of a satellite orbiting just above the surface of a hypothetical spherical planet made entirely of iron, you need to know the radius of the planet. Since no other information was provided, we'll have to make an assumption about the radius. Let's assume the radius of the planet is denoted as "r".

The period of a satellite orbiting a planet can be calculated using Kepler's Third Law of Planetary Motion, which states that the square of the period (T) is proportional to the cube of the average distance (r) between the satellite and the center of the planet. Mathematically, this can be expressed as:

T^2 = k * r^3

where k is the gravitational constant. In this case, we can use the following expression:

T^2 = (4π^2 / GM) * r^3

Where:
G is the universal gravitational constant (6.67 x 10^-11 N m^2/kg^2)
M is the mass of the planet (ρV, where ρ is the density of iron and V is the volume of the planet)

To proceed with the calculation, we need to find the mass of the planet. The mass (M) can be calculated using the formula:

M = ρ * V

Let's denote the mass of the planet as "M" and the density of iron as "ρ".

Now, to get the volume of the planet (V), we need the formula of volume for a sphere:

V = (4/3) * π * r^3

Substituting the volume (V) formula into the mass (M) formula:

M = ρ * [ (4/3) * π * r^3 ]

So now we have all the necessary equations to calculate the period (T) of the satellite orbiting just above the surface of the planet. Given that no further information is provided about the radius (r), we can't calculate the specific period. However, if you have a specific radius value for the planet, you can plug it into the above equations to obtain the period.

To calculate the period of a satellite that orbits just above the surface of a hypothetical spherical planet, there are a few key pieces of information you need to know:

1. Mass of the planet: We are given that the planet consists entirely of iron, but the mass is not provided. Without this information, it is impossible to calculate the satellite's period accurately.

2. Radius of the planet: The radius of the planet is also not provided. The period of a satellite depends on the mass of the planet and its radius, as well as the gravitational constant.

3. Gravitational constant: The gravitational constant (G) is a fundamental constant in physics, and its value is approximately 6.674 × 10^(-11) N(m/kg)^2. This constant determines the strength of the gravitational force between two objects.

Without the necessary information, we cannot proceed with the calculation.

As I told you a few days ago, you can't solve it unless you know the radius of the sphere. if that was all the information you were provided, complain to your teacher. Perhaps you were supposed to assume it has the same raius as earth, but they should have said so. In that case, the orbital period is (as it is for earth, which has similar average density) about 90 minutes.