You are on Pluto and would like to send a probe into space so that it does not fall back to the surface. What minimum launch speed do you need? (The mass of Pluto is 1.3x^22 kg and the radius of Pluto is 1.18x10^6 m).
Answer in km/s.
I have used the velocity of escape = (square root of) 2(g)(m1)(m2)/r but keep getting the wrong answer.
1.21e5 km/s and 4.7e3 km/s are two of the answers I've been getting. Help?
PE at surface=KE at launch
GMp/radius = 1/2 v^2
v= sqrt(2GMp/r) where G is 6.67E-11
v=sqrt(2*6.67E-11*1.3E22)/1.18E6)
You seem to have difficulty operating your calculator. Put this into the Google search window:
sqrt(2*6.67E-11*1.3E22/1.18E6)
Hmm. I wonder how I can correct my poor usage. Thank you very much!
To determine the minimum launch speed required for a probe to escape Pluto's gravitational pull, you can use the formula for escape velocity, which is given by:
v_escape = sqrt((2 * G * m_p) / r_p)
Where:
- v_escape is the escape velocity
- G is the gravitational constant (approximately 6.67 x 10^-11 m^3/(kg * s^2))
- m_p is the mass of Pluto
- r_p is the radius of Pluto
Let's calculate the escape velocity step by step using the given values:
Step 1: Convert the mass of Pluto and the radius to SI units
Mass of Pluto (m_p) = 1.3 x 10^22 kg
Radius of Pluto (r_p) = 1.18 x 10^6 m
Step 2: Plug the values into the formula
v_escape = sqrt((2 * G * m_p) / r_p)
v_escape = sqrt((2 * (6.67 x 10^-11) * (1.3 x 10^22)) / (1.18 x 10^6))
Note: It is crucial to use the correct scientific notation when entering the values into the calculator to avoid calculation errors.
Step 3: Calculate the result
v_escape = sqrt((2 * 8.81 x 10^11) / (1.18 x 10^6))
v_escape = sqrt(1.989 x 10^6)
v_escape ≈ 1,408.37 m/s
To convert this velocity to km/s, divide by 1000:
v_escape ≈ 1.40837 km/s
Therefore, according to the calculations, the minimum launch speed required for the probe to escape Pluto's gravity is approximately 1.408 km/s.