I didnt know under what category to post this so here goes...
I have formulas but confusd which to use when. pls help. Maybe u can direct which formula to use and i will proceed from there.

Uranus orbits the Sun with an orbital radius of 2.56 x 107 m. Given that the mass of the Sun 1.99 x 1030 kg, calculate the period of Uranus’s orbit in seconds.



Venus orbits the Sun with an orbital radius of 6.05 x 106 m. Given that the mass of the Sun is 1.99 x 1030 kg, calculate the orbital velocity of Venus



Calculate the force of gravitational attraction between two spheres of mass 50.0 kg and 75.0 kg that are 20.8 m apart

A satellite orbits Pluto 1.20 x 105 m above its surface. Given that the mass of Pluto is 1.25 x 1022 kg and the radius of Pluto is 1.20 x 108 m, calculate the period of orbit of the satellite in seconds.


The Moon has an orbital period of 27.3 days around Earth and a mean distance of 3.84 ´ 105 km from Earth’s center. Use Kepler’s laws to find the orbital period of an artificial satellite orbiting Earth at a distance of 2.55 x104 km from the center of Earth

The distance between Pluto and the Sun is 57.2 times more than the distance between the Sun and Earth. Calculate the time taken by Pluto to orbit the Sun in Earth days.

Find the magnitude of the force required to accelerate an electron of mass 5.30 x 10 -3 kg from rest to a speed of 0.8 x 1010 m/s for a distance of 2.50 cm?

What have you been able to do with them?

For example, the first and second problems deal with circular motion with a constant speed. So it's a good bet that the centripetal force will come into play. In this case there is only one force on Uranus (gravity) so that must be the net force. Thus
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Which leads to
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Now that you have [LaTeX Error: Can't write to directory] the rest is simple. Just find T:
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Try that on problem 2 and let us know where you are with the other problems.

-Dan

__________________
"I must not fear. Fear is the mind killer. Fear is the little death that brings total obliteration. I will face my fear. I will permit it to pass over me and through me. And when it has gone I will turn the inner eye to see its path. Where the fear has gone there will be nothing. Only I will remain." - The Litany Against Fear, "Dune" by Frank Herbert

For #5 [Ta/Tb]^2 = [ra/rb]^3 ??
For #4 find r by adding the height of satellite to earth radius first, then solve for period using your formula for #2&3 ??
For 3#3 - i have no idea where to start
For #6 & #7 is it like #5?
For #8 - i have no clue

Find the magnitude of the force required to accelerate an electron of mass 5.30 x 10 -3 kg from rest to a speed of 0.8 x 1010 m/s for a distance of 2.50 cm?

The wording of the problem is slightly dicey. I think it should be in a distance and not for , else some data is missing.
Assuming it is in, use v^2 = 0^2 + 2 a s to get tha accln a and then
F = ma

Calculate the force of gravitational attraction between two spheres of mass 50.0 kg and 75.0 kg that are 20.8 m apart

What is the problem with this one? It is a straightforward application of Newton's law of gravitation which you have already used!

A satellite orbits Pluto 1.20 x 105 m above its surface. Given that the mass of Pluto is 1.25 x 1022 kg and the radius of Pluto is 1.20 x 108 m, calculate the period of orbit of the satellite in seconds.

For #4 find r by adding the height of satellite to earth radius first, then solve for period using your formula for #2&3 ??

That looks OK.

For #8 - i have no clue .I find only 7 problems!


The Moon has an orbital period of 27.3 days around Earth and a mean distance of 3.84 ´ 105 km from Earth’s center. Use Kepler’s laws to find the orbital period of an artificial satellite orbiting Earth at a distance of 2.55 x104 km from the center of Earth

The distance between Pluto and the Sun is 57.2 times more than the distance between the Sun and Earth. Calculate the time taken by Pluto to orbit the Sun in Earth days.


For #5 [Ta/Tb]^2 = [ra/rb]^3 ??

For both 5 and 6

For 7 ; the electron problem, i have already posted.

Uranus orbits the Sun with an orbital radius of 2.56 x 107 m. Given that the mass of the Sun 1.99 x 1030 kg, calculate the period of Uranus’s orbit in seconds.

Should I use this formula T = 2 pi x square root of r^3/Gm ? (not the one topsquark gave bcuz there's no mass given for Uranus?

Venus orbits the Sun with an orbital radius of 6.05 x 106 m. Given that the mass of the Sun is 1.99 x 1030 kg, calculate the orbital velocity of Venus

Should I use V = square root of Gm/r ?

In fact Topsquark has explained it very well. Look at the formula below. You will find that the mass of Uranus cancels out from both sides and hence you dont need it. In all such problems the mass of the planet satelite etc. will cancel out and the period is independent of it.



From this find w , then use w = 2 pi/T.

For the other question also use v = r w