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placebooooo
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Homework Statement
Question 1: 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")? (The radius of Pluto is 1150 km.)
Question 2:A orbiting satellite stays over a certain spot on the equator of (rotating) Venus. What is the altitude of the orbit (called a "synchronous orbit")? (The radius of Venus is 6050 km.)
Homework Equations
Kepler's law of periods:
T^3 = (r^3)(4pi^2)/GM
The Attempt at a Solution
Hi everyone, these two problems have been boggling me so bad. This is part of some online homework due midnight and these are the only two problems I was not able to do. I also have only one submission for each as I have no idea what I am doing wrong. I searched the forums and found a very similar question with a different planet and followed their work, but was too afraid to punch in my answer. I would love it if someone can confirm my work for me please. Here is my work:
T^3 = (r^3)(4pi^2)/GM
I solved for r:
r = [ (T^2)(G)(M)/(4pi^2) ]^1/3
For pluto, my first question, I used G = 6.67x10^-11, T = 6.39 days = 552096, and Mass of pluto, M= 1.309x10^22kg. I plugged in all of these values into my previous equation and got:
r = 18890566.49 m = 18890.56km
Then, h = r - r pluto = 18890.56 - 1150 = 17740.56km (final answer).
For venus, I did the same but instead I used the following values:
T = 116days and 18 hours = 10264800seconds
M =4.867x10^24 kg
Do the same as above, I got r = 953329010.5 m = 953329km
h = r - r venus = 953329km - 6050km = 947279km
Each question is qorth 13% of this homework assignment and would love it if someone could confirm whether these are correct or not. I really appreciate it.