A satellite orbits a planet at 4000m/s, and the acceleration of gravity (centripetal acceleration) on the satellite is 0.58m/s2. What is the diameter of the orbit of the satellite? (Enter your answer in scientific notation utilizing "e" format and rounding the decimal value to one decimal place.)

For this problem, I used the formula r = v^2/g. When I plugged in 4000/0.58, I got 6.8e10^3, but I wasn't correct. Please help!

To find the diameter of the satellite's orbit, you can use the formula for centripetal acceleration:

a = v^2 / r

Where:
a is the centripetal acceleration (0.58 m/s^2)
v is the velocity of the satellite (4000 m/s)
r is the radius of the orbit (which is half of the diameter)

Rearranging the formula, we have:

r = v^2 / a

Let's plug in the given values:

r = (4000 m/s)^2 / 0.58 m/s^2
r = 16000000 m^2/s^2 / 0.58 m/s^2
r = 27586206.9 m

Now, we need to find the diameter. Recall that the diameter is twice the radius:

d = 2 * r
d = 2 * 27586206.9 m
d = 55172413.8 m

To express the diameter in scientific notation, we can round it to one decimal place:

d ≈ 5.5e7 m

Therefore, the diameter of the satellite's orbit is approximately 5.5e7 meters.

you need ti multiply your answer by two because its asking for diameter. The answer you got is jut the radius