You are on Mars 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 Mars is 6.42x10^23 kg and the radius of Mars is 3.40x10^6 m)
km/s
Please someone also help me on this.I really don't know how to do this.Thank you.
PE at surface= GMm/r
PE mars= GMmars*m/rm
PE earth= GMe*m/re
so on mars, you have to overcome the PE at the surface, or
1/2 m v^2=GMmars*m/rmars
velocity= sqrt(2G*MassMars/radiusMars)
To calculate the minimum launch speed required to ensure that a probe does not fall back to the surface of Mars, we need to consider the escape velocity of Mars. Escape velocity is the minimum speed needed to break free from the gravitational pull of a celestial body, in this case, Mars.
The formula for escape velocity is:
escape velocity (v) = √(2 * G * M / r)
where G is the gravitational constant (approximately 6.67 × 10^-11 N*m^2/kg^2), M is the mass of Mars (6.42 × 10^23 kg), and r is the radius of Mars (3.40 × 10^6 m).
Now, let's substitute these values into the formula and solve for the escape velocity:
v = √(2 * 6.67 × 10^-11 N*m^2/kg^2 * 6.42 × 10^23 kg / 3.40 × 10^6 m)
Simplifying the calculation:
v = √(8.97 × 10^4 m^2/s^2)
v ≈ 299.5 m/s
Now, we need to convert this value to km/s. There are 1000 meters in a kilometer, so we divide the velocity by 1000:
v = 299.5 m/s ÷ 1000 = 0.2995 km/s
Therefore, the minimum launch speed required is approximately 0.2995 km/s to ensure that the probe does not fall back to the surface of Mars.