A orbiting satellite stays over a certain spot on the equator of (rotating) Pluto. What is the altitude of the orbit (called a "synchronous orbit")?
Do I use T^2=4pi^2/GM x r^3?
yes. Pluto's rotation period is 6.39 (earth) days. You will also need its mass.
then how do i get the altitude after i solve for r subtract the radius of pluto?
yes, altitude=r-radiuspluto
Yes, you can use the formula T^2 = (4π^2 / GM) x r^3 to determine the altitude of a satellite in a synchronous orbit around Pluto. Let's break down the formula step by step:
T^2: This represents the orbital period of the satellite, i.e., the time it takes for the satellite to complete one orbit around Pluto.
G: This represents the gravitational constant, which is approximately 6.67430 x 10^-11 m^3 kg^-1 s^-2.
M: This represents the mass of Pluto, which is approximately 1.303 x 10^22 kg.
r: This represents the radius of the satellite's orbit. Since the satellite is in a synchronous orbit over the equator, we can consider the radius as the distance between the center of Pluto and the equator.
To solve for the altitude of the synchronous orbit, we need to rearrange the formula. Here's a step-by-step guide on how to do this:
1. Rearrange the formula to solve for the radius, r:
r = (G x M x T^2 / 4π^2)^(1/3)
2. Substitute the known values:
- Plug in the value of the gravitational constant, G.
- Plug in the mass of Pluto, M.
- Plug in the desired orbital period, T, for a synchronous orbit (usually equal to the rotational period of the planet).
3. Calculate the radius, r, by evaluating the expression using a calculator.
The resulting radius will give you the distance from the center of Pluto to the satellite in the synchronous orbit. However, to determine the altitude of the orbit, you have to subtract the radius of Pluto from the value you calculated.