A satellite orbits Neptune 4000km above its surface. given the mass of Neptune is 1.02x10^26 kg and the radius of Neptune is 2.48x10^7m, Calculate the orbital speed of the satellite
Neptune's gravity provides the centripetal force
the orbital altitude is not significant compared with Neptune's radius
m v^2 / r = G M m / r^2
v^2 = G M / r
... = 6.67E-11 * 1.02E26 / (2.48E7)^2
result (v) is in m/s
To calculate the orbital speed of the satellite around Neptune, we can use the following formula:
v = sqrt(G * M / r)
where:
v = orbital speed
G = gravitational constant (6.67430 x 10^-11 m^3 kg^-1 s^-2)
M = mass of Neptune
r = orbital radius (distance from the center of Neptune)
Now, plugging in the values:
M = 1.02 x 10^26 kg
r = 2.48 x 10^7 m
v = sqrt((6.67430 x 10^-11 m^3 kg^-1 s^-2) * (1.02 x 10^26 kg) / (2.48 x 10^7 m))
Let's calculate this:
v = sqrt((6.67430 x 1.02 x 10^15) / 2.48)
v = sqrt(1.076016 x 10^16 / 2.48)
v = sqrt(4.34065 x 10^15)
v ≈ 6.59 x 10^7 m/s
Therefore, the orbital speed of the satellite around Neptune is approximately 6.59 x 10^7 m/s.
To calculate the orbital speed of the satellite orbiting Neptune, we can use the following formula:
v = √(GM/r)
Where:
v is the orbital speed,
G is the gravitational constant (approximately 6.67 × 10^-11 m^3 kg^-1 s^-2),
M is the mass of Neptune, and
r is the distance between the satellite and the center of Neptune.
First, convert the distance between the satellite and the center of Neptune from kilometers to meters:
r = 4000 km = 4000000 m
Now, substitute the values into the formula:
v = √((6.67 × 10^-11 m^3 kg^-1 s^-2) × (1.02 × 10^26 kg) / (4000000 m))
Simplifying the equation:
v = √(2.63 × 10^5 m^3 s^-2 kg^-1)
Take the square root to find the orbital speed:
v ≈ 512.76 m/s
Therefore, the orbital speed of the satellite around Neptune is approximately 512.76 m/s.