need help with HOW to solve this question: calculate the orbital velocity of earth satellite orbit 400mi.?

Question

above the earth. I need to know How to solve this and where can I look to solve this type of question in the future. Also truck traveling with an initial speed of 33.0ft/s accelerates until it reaches a speed of 77.0ft/s if the acceleration is 4.00ft/s2 how much time is required to reach final speed. I think the answer to 2nd one is 11 sec. however I am not sure I set the problem up right or used correct formula.Note: an answer won't do me any good if I don't know how to solve one like it in the future.Also, if you wanted to know your weight on the moon, would you take your weight in pounds X 9.80 and then divide by 1/6?

Answer 1

You want to learn about the Vis Viva equation.

V = { GM (2/r - 1/a) }^0.5

Where...
V = the orbital speed
GM = the mass times the gravitational constant
r = the current distance between the satellite and the center of the Earth
a = the semimajor axis of the satellite orbit

For Earth,
GM = 3.986E+14 m^3 sec^(-2)

400 miles is equal to 643737.6 meters, but this is the ALTITUDE, not the orbital RADIUS.

r = altitude + Rearth
Rearth = 6378000 meters
r = 7021737.6 meters

For a circular orbit r=a, so the speed would be
V = { GM / r }^0.5
V = 7534 m/sec

You got the truck problem right. The formula is
vf = v0 + g t
t = (vf - v0) / g
v0 = 33
vf = 77
g = 4

I used "g" for the acceleration to avoid getting it confused with the semimajor axis in the first part.

You would take your mass in kilograms (which is the same anywhere) and multiply it by the gravitational acceleration you feel. You calculate the acceleration as follows:

g = GM / r^2

For Earth,
GM = 3.986E+14 m^3 sec^(-2)
r = 6378000 meters
g = 9.80 m/sec^2

For the moon,
GM = 4.922E+12 m^3 sec^(-2)
r = 1738000 meters
g = 1.63 m/sec^2

The ratio of surface gravities is 6.01.

Answer 2

Yes, it's 11 sec. V2 = V1 + at or t = (V2-V1)/a

Your weight on the Moon is times 1/6, not divided by 1/6. Think about it, you would weigh less, not more. The 9.80 doesn't belong here. It is used to figure the force in Newtons that a mass exerts on the Earth. Weight is already a force.

The orbital problem is more complicated and since you are not sure of the 2 much easier problems I think it would be hard to understand the equations. However, if you just want to get the answer, convert to kilometers and use this link.

Answer 3

Wow. You want to know it all.
Let's start easy. Your answer to the truck problem is right. You should have used the equation: vf=v0+at, where vf is 77, v0 is 33, and a is 4.
Next, to find your weight on the moon, you only need to divide your weight on earth by 6. But the physics answer is as follows. Your weight on earth (in N) is found by multiplying your mass by the acceleration due to gravity (g). On the moon, your mass is the same, but (g) is roughly 1/6 of earth's.
I'm not sure your first problem. I know that the velocity needed to stay in orbit is ONLY related to g (9.8) and the distance from the center (Radius of earth +400miles). Sorry that is all i know

Answer 4

For the orbital problem, you know the earths angular velocity. Convert it to rad/unit time. You know the earth's radius. Add 400 to it, and viola, v = angular velocity times distance.