I have a few problems that I'm stuck on... If you can help with any/all of the it would be amazing! Here they are:
2. The first Death Star was 160-km in diameter with a mass of 2.4×1012 kg. Calculate the speed in m/s that the Millennium Falcon would need to reach to escape the gravitational pull of the Death Star.
3. The Earth has a mean radius of 6378 km and completes one rotation in 24 hours. Calculate the angular velocity in rad/s of the Earth’s equator.
2. The first Death Star was 160-km in diameter with a mass of 2.4×1012 kg. Calculate the speed in m/s that the Millennium Falcon would need to reach to escape the gravitational pull of the Death Star.
3. The Earth has a mean radius of 6378 km and completes one rotation in 24 hours. Calculate the angular velocity in rad/s of the Earth’s equator.
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Hello
to lave the gravitation field, the kinetic energy must equal the potential energy at height R (R = radius of star) :
1/2 mv^2 = GMm/R
v^2 = 2GM/R =2* 6,674*10^-11 (m3/(kg*s^2))*2,4*10^12 (kg) /8*10^4 (m)
v^2 = 0,004
v = 0,0632 m/s ( not really much, is it? But plug in the data of the earth, R = 6,37*10^6 m, M = 6*10^24 kg , then you come to 11000 m/s, which is the right value.)
ω = 2pi/(24*60^2) = 7,27*10^-5 rad/s (does not depend on the radius, is everywhere the same value)
Regards
to lave the gravitation field, the kinetic energy must equal the potential energy at height R (R = radius of star) :
1/2 mv^2 = GMm/R
v^2 = 2GM/R =2* 6,674*10^-11 (m3/(kg*s^2))*2,4*10^12 (kg) /8*10^4 (m)
v^2 = 0,004
v = 0,0632 m/s ( not really much, is it? But plug in the data of the earth, R = 6,37*10^6 m, M = 6*10^24 kg , then you come to 11000 m/s, which is the right value.)
ω = 2pi/(24*60^2) = 7,27*10^-5 rad/s (does not depend on the radius, is everywhere the same value)
Regards