find the speed and period of a satellite that would orbit Mars 203 km above its surface.
mv^2/r=GMm/r^2
solve for m. r is 203km+radiusMars
change r to meters. You will have to look up the Mass of Mars, Mm
what is mv?
To find the speed and period of a satellite orbiting Mars, we need to use the following formula:
v = (G * M)^(1/2) / r^(1/2)
Where:
v = velocity of the satellite
G = gravitational constant (6.67430 × 10^-11 m^3 kg^-1 s^-2)
M = mass of the planet (in this case, Mars)
r = radius of the orbit (203 km above the surface of Mars)
First, let's convert the radius to meters:
203 km = 203,000 m
The mass of Mars is approximately 0.64171 × 10^24 kg.
Now, we can calculate the speed (v):
v = (6.67430 × 10^-11 m^3 kg^-1 s^-2 * 0.64171 × 10^24 kg)^(1/2) / (203,000 m)^(1/2)
v ≈ 3240.95 m/s
So, the velocity of the satellite would be approximately 3240.95 m/s.
To find the period (T), we can use the following formula:
T = (2π * r) / v
T = (2 * 3.14159 * (203,000 m)) / 3240.95 m/s
T ≈ 3817.66 s
So, the period of the satellite would be approximately 3817.66 seconds.