Using Kepler's Third Law to find mass

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To estimate the mass of the fictional planet Snazbort using Kepler's Third Law, the orbital period of its moon Pingdol (7.68 days) and its semimajor axis (92.53×10^9) are crucial. The equation T^2=4π^2*a^3/(GM) is used, where T must be converted to seconds for accurate calculations. There was initial confusion regarding the value of G and the proper units for the semimajor axis. Ultimately, the correct approach involves ensuring all units are consistent, particularly converting the orbital period from days to seconds. Accurate unit conversion is essential for solving the problem correctly.
Allen L
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Homework Statement


The fictional planet Snazbort has a fictional moon Pingdol. Pingdol has an orbital period of 7.68 days and a semimajor axis of 92.53×109. Use Kepler's Third Law to estimate the mass of Snazbort.

Homework Equations


T^2=4pi^2*a^3/(GM)

where 2a is the length of major axis
T is the time required for it to travel once around its elliptical orbit
G is gravitational constant
M is mass

The Attempt at a Solution


I've tried plugging in the numbers and I can't seem to figure out how I'm supposed to enter them. I'm also not entirely sure how I even get G. The G I used is from another question.

If it helps at all, the screenshot is here along with my "best" attempt.
http://i.imgur.com/jVZP7u8.png

EDIT: I got the answer. I was supposed to change T into seconds -_-
 
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Allen L said:
Pingdol has an orbital period of 7.68 days and a semimajor axis of 92.53×109
Is that semimajor axis supposed to be 92.53 X 109? What are the units?

It's important to keep track of the units, which maybe you've already found out with the days vs. seconds units in T.
 
Question: A clock's minute hand has length 4 and its hour hand has length 3. What is the distance between the tips at the moment when it is increasing most rapidly?(Putnam Exam Question) Answer: Making assumption that both the hands moves at constant angular velocities, the answer is ## \sqrt{7} .## But don't you think this assumption is somewhat doubtful and wrong?

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