g through empty space at a speed of 35 km/s a. With no forces acting on the spac
ID: 154621 • Letter: G
Question
g through empty space at a speed of 35 km/s a. With no forces acting on the spacecraft, how will ts speed change over 14 time? How do you know? (1 points) b. By magic, a large planet appears directly behind the spacecraft What effect will the planet's gravity have on the spacecraft's motion? (Consider both speed and direction.) (1 point) c. The planet has a mass equal to 6x1024 kg and is located 108 m behind the spacecraft, which has a mass of 1000 kg. Ignoring the gravitational constant G, what is the gravitational force exerted on the spacecraft by the planet? (2 points)Explanation / Answer
a) If a spacecaft moves through space, it maintains a constant speed until any forces act to change its speed.
For acceleration or deceleration of any object, force is needed. From the start of its journey a force was needed to accelerate it to its present velocity 35 km/s after which the action of the force has stopped. But the object is moving through an empty space where no external force is acting upon, so the velocity will remain constant.
b) The gravitational forces of the planet will come into play and the spacecraft will decelerate and may start to move in the opposite direction i.e., towards the planet behind the spacecraft.
c) Gravitational force, Fg = G x Mp x Ms / R2
[ where, Mp = Mass of the planet (6x1024Kg), Ms = Mass of the spacecraft (1000 kg). R= Distance between the planet and spacecraft (108 m), G= Gravitational constant (to be ignored as per the question) = 1 m3 kg-1 s-2]
Therefore, Gravitational force exerted on the spacecraft by the planet,
Fg = Mp x Ms / R2 = (6x1024) x (1000) / (108 )2 kg-m/s2
= 6.24 x 1011 kg-m/s2
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