Initial speed of an object launched from Mars

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  • #1
marjine
10
1
Homework Statement
The radius of Mars (from the center of just above the atmosphere) is 3400 km, and its mass is 6 × 1023 kg. An object is launched straight up from just above the atmosphere of Mars. What initial speed (vi) is needed so that when the object is far from Mars, its final speed (vf) is 500 m/s?
Relevant Equations
G = 6.7E-11
Conservation of energy principle: U1 + K1 = U2 + K2
U1 = -GMm/r
K1 = (1/2)mvi^2
U2 = as r approaches infinity, U2 approaches zero
K2 = (1/2)mvf^2

(1/2)mvi^2 - GMm/r = (1/2)mvf^2 + 0

vi = √(vf^2 + (2GMm)/r) = √(250,000 + 2(6.7 E-11)(6 E23)/3400) = 153776.815

But that is not the correct answer, can anybody see my mistake/misunderstanding?
 
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  • #2
The radius (r) is given in km, isn't it?
 
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  • #3
nasu said:
The radius (r) is given in km, isn't it?
omg... converted it to m and fixed it, thank you so much
 
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FAQ: Initial speed of an object launched from Mars

What factors determine the initial speed of an object launched from Mars?

The initial speed of an object launched from Mars is determined by several factors including the gravitational pull of Mars, the desired final orbit or destination, atmospheric drag, and the efficiency of the propulsion system used for the launch.

How does Mars' gravity affect the initial launch speed?

Mars' gravity is about 38% that of Earth's. This means that the escape velocity required to overcome Mars' gravitational pull is lower than that of Earth. Specifically, the escape velocity on Mars is approximately 5 km/s compared to Earth's 11.2 km/s.

What is the escape velocity from Mars?

The escape velocity from Mars is approximately 5 kilometers per second (km/s). This is the minimum speed needed for an object to break free from Mars' gravitational influence without further propulsion.

How does Mars' thin atmosphere impact the launch speed?

Mars has a much thinner atmosphere compared to Earth, which means there is less atmospheric drag acting on a launched object. This can be advantageous because it requires less energy to overcome atmospheric resistance, allowing for potentially lower initial speeds for the same trajectory.

What initial speed is required to send a spacecraft from Mars to Earth?

The initial speed required to send a spacecraft from Mars to Earth depends on the specific mission profile and launch window. Generally, a spacecraft would need to reach a speed that allows it to enter a transfer orbit, such as a Hohmann transfer orbit, which typically requires an initial speed slightly higher than Mars' escape velocity, around 5.5 to 6 km/s.

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