Astronomic gravitation problems

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In summary: The L1 point is between the Sun and Jupiter, and is a point where the gravitational pull of the Sun and Jupiter cancel each other out, allowing for an object to orbit there without being pulled towards either body. It is also known as the "inner" Lagrange point.
  • #1
philadelphia
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1. If the INternational space station has an orbital velocity of 9,000 m/s. find the time (in minutes) it takes to make one complete orbit.

Relevant equations
F = mv2/ R = m4[pi]2R / T2

The attempt at a solution
Is this the way to solve for T?
Do I use Earth mass and Earth R b/c that all the question says?


2. A martian day is 1.03 Earth days. At what altitude above Mars should a communications satelite be placed such that it always stay over the same spot above the surface of Mars (answer in units of miles. 1000m = 0.62 miles

Relevant equations
F = ma = m4[pi]2R / T2
a= GM/R2

The attempt at a solution
I know how to solve the problem but what kinda threw me off are the martian days given...
Is T 354.36 days that is 365/1.03
If it is, can i find "a" after the "m" cancel, than solve for R which is (mar's radius + Mars altitude)


3. find the lagrange Point between the sun and Jupiter. In between what two planets will you find this point?

Jupiter:
mass: 1.9x1027 kg

Sun:
mass: 1.99x1030

distance betwwen sun and Jupiter: 778x106 km

Relevant equations
Im really not sure what is lagrange point equation, is it... GMsunmjupiter/ r
r is the distance of Jupiter- sun ?
 
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  • #2
You have the velocity and and hence you have

mv²/r = Gravitational force = GMm/r²

This yields v² = GM/r

What you don't know from that equation is r. But you want to calculate it, because v/r = ω

and ω = 2πf = 2π/T or

T = 2π/ω = 2πr/v
 

1. What is astrometric gravitation?

Astrometric gravitation is the study of how objects in space interact with each other due to the force of gravity. This includes the motion of planets, stars, and galaxies, as well as the effects of gravity on light and other forms of radiation.

2. How does the force of gravity affect celestial bodies?

The force of gravity between two celestial bodies depends on their masses and the distance between them. The greater the mass and the closer the distance, the stronger the force of gravity. This can lead to the formation of orbits, tides, and other gravitational interactions.

3. What is the difference between Newton's law of universal gravitation and Einstein's theory of general relativity?

Newton's law of universal gravitation states that the force of gravity between two objects is directly proportional to their masses and inversely proportional to the square of the distance between them. Einstein's theory of general relativity, on the other hand, describes gravity as the curvature of spacetime caused by the presence of mass and energy.

4. How do scientists use astrometric gravitation to study the universe?

Scientists use astrometric gravitation to understand the structure and dynamics of the universe. By measuring the gravitational interactions between celestial bodies, they can determine their masses, distances, and movements, which can provide insights into the evolution of the universe and the distribution of matter in it.

5. Can astrometric gravitation be used to predict future celestial events?

Yes, astrometric gravitation can be used to predict future celestial events such as planetary movements, eclipses, and gravitational interactions between galaxies. By understanding the forces of gravity at play, scientists can make accurate predictions about the future of the universe.

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