Problem 13.66 Part A While visiting Planet Physics, you toss a rock straight up
ID: 1786749 • Letter: P
Question
Problem 13.66 Part A While visiting Planet Physics, you toss a rock straight up at 14 m/s and catch it 2.6 s later. While you visit the surface, your cruise ship orbits at an altitude equal to the planet's radius every 250 min What is the mass of Planet Physics? Express your answer to two significant figures and include the appropriate units. M= Submit My Answers Give Up Part B What is the radius of Planet Physics? Express your answer to two significant figures and include the appropriate units Submit My Answers Give UpExplanation / Answer
flight time t = 2·V·sin/g
2.6 s = 2 * 14m/s * sin90º / g
g = 10.77 m/s²
And we know from Newton's law of Gravitation,
g = GM / R²
ii) For "orbit", centripetal acceleration = gravitational acceleration, or
²r = (2/T)²r = 4²r / T² = v²/r = GM/r²
where the first four terms are all expressions for centripetal acceleration
and G = Newton's gravitational constant = 6.674e11 N·m²/kg²
and M = mass of central body
and r = orbit radius
and T = period
and v = orbit velocity
4²r / T² = GM/r² rearranges to
T² = 4²r³ / GM
(250*60 s)² = 4²(2R)³ / GM
712 415 s² = R³ / GM
Multiply these two results:
g * T² = GM/R² * R³ / GM
10.77m/s² * 712415s² = R
R = 7.67e6 m radius
i) Now plug that into either equation above to find the mass:
712415 s² = (7.67e6m)³ / (6.674e11N·m²/kg² * M)
M = 9.496e24 kg mass