# Newton's Law of Universal Gravitation, Satellites & Orbits, Kepler's Law of Planetary

1. Apr 30, 2012

### axedodger

Having significant issues with solving these problems. Any help is appreciated. Thanks to all who can help!

1. How large must the coefficient of static friction be between the tires and the road if a car is to round a level curve of radius 75 m at a speed of 90 km/h?

I used the equation: μs = v^2/gr

answer: 0.85 was told it was wrong? alternatives?

2. Calculate the force of Earth's gravity (in N) on a spacecraft 12,800 km (2 Earth radii) above the Earth's surface if its mass is 1600 kg.

Note: Your answer is assumed to be reduced to the highest power possible.

I am terrible with powers of 10. Any help is appreciated.

I used eq. F = G m(satellite)m(earth)/2r^2

I also tried F = G m(satellite)m(earth)/3r^2

3. A certain neutron star has five times the mass of our sun packed into a sphere about 10 km in radius. Estimate the surface gravity on this monster (in m/s2).

Note: Your answer is assumed to be reduced to the highest power possible.

Don't even knwo where to begin with this problem.

4. A space shuttle releases a satellite into a circular orbit 650 km above the Earth. How fast must the shuttle be moving (relative to Earth) when the release occurs (in m/s)?

equation used: V = √Gm(earth)/r

also go an answer of v = 23819 m/s

5. During an Apollo lunar landing mission, the command module continued to orbit the Moon at an altitude of about 100 km. How long did it take to go around Moon once (in seconds)?

Don't know where to begin here either.

THANKS TO ALL WHO CAN HELP!

Last edited: Apr 30, 2012
2. Apr 30, 2012

### HallsofIvy

Staff Emeritus
Re: Newton's Law of Universal Gravitation, Satellites & Orbits, Kepler's Law of Plane

What is "s" here? Why did you use that equation? What was your reasoning?

I don't see that "powers of 10" have anything to do with this.
$$F= \frac{GmM}{r^2}$$
You know that the acceleration due to gravity at the surface of the earth is -9.88 m/s^2 so $GM/R^2= 9.88$ where R is the radius of the earth. replace R with 2R.

Again, you know that $GM/R^2= 9.88$. Replace M by 5 M and replace R by (10/640000)R.

The distance from the center of the earth is 6400+ 650 km. What is the circumference of a circle of that radius? What is the speed of a satellite that goes that far in 24 hours?

Much the same as (4). What is the circumference of a circle of radius the radius of the moon plus 100?

You really need to show some of YOUR work in the future.

3. Apr 30, 2012

### axedodger

Re: Newton's Law of Universal Gravitation, Satellites & Orbits, Kepler's Law of Plane

sorry question 1 ... μs = coefficient of static friction

I used μs = v^2/gr because that is the equation derived from μ(static)mg = mv^2/r

Last edited: Apr 30, 2012
4. Apr 30, 2012

### axedodger

Re: Newton's Law of Universal Gravitation, Satellites & Orbits, Kepler's Law of Plane

I edited the work to show what I knew(which was limited).