Gravitation Definition and 918 Threads

Homework Statement The moon has a mass of approximately 7.34x1022kg and a radius of about 1785 km. Determine the strength of the gravitational field on or near the surface of the moon. Homework Equations I have made a list of equations that are relevant for this entire module on...

Homework Statement Neptune is about 17.2 times the mass of Earth. Satellite N orbits Neptune with the same orbital radius as satellite E that orbits the Earth. Determine which satellite has the smaller period. Support your answer with appropriate calculations. Homework Equations I have...

Homework Statement An astronaut weighs 833N on the surface of the Earth. Determine the weight of the astronaut on Planet Z if the planet's mass is 50.0 times the mass of the Earth and has a radius of 10.0 times the radius of the Earth. Homework Equations Kepler's 3rd law...

Homework Statement The moon orbits the Earth at a distance of 3.84x108m from the centre of Earth. The moon has a period of about 27.3 days. From these values, determine the mass of the Earth. Homework Equations Kepler's 3rd law: (Ta/Tb)2=(Ra/Rb)3 motion of planets must conform to...

Homework Statement Two satellites are orbiting around the Earth. One satellite has a period of 1.5 h and is 250 km above the Earth's surface. The second satellite has a period of 7.5 h. Using Kepler's Laws and the fact that the Earth's radius is 6.38x106 m determine the height of the second...

Homework Statement There is a point on the line between the centres of the Earth and the moon where their gravitational fields have equal magnitude but are in opposite directions, effectively creating a point of zero gravity. Calculate the distance of this point from the centre of the earth...

Homework Statement The Earth has a mass of 5.98x10^24 kg and the moon has a mass of 7.35x10^22 kg. The distance from the centre of the moon to the centre of the Earth is 3.84x10^8 m. A rocket with a total mass of 1200 kg is 3.0x10^8 m from the centre of the Earth and directly in between Earth...

Homework Statement The gravitational field g due to a point mass M may be obtained by analogy with the electric field by writing an expression for the gravitational force on a test mass, and dividing by the magnitude of the test mass, m. Show that Gauss' law for the gravitational field reads...

So I was looking at the equation for Gravitation potential energy U = - Gm1m2/r This implies the energy is 0 as r→∞ However, if I lift a book above my head, wouldn't it have more potential energy than if it was lying on the ground, meaning as r (h) increases, potential energy increases? Where...

Hello, Is there any research available as to whether Newtons Law F = mg should include horizontal surface area as a factor (ie the surface area of opposing masses). Example a pole weighing exactly the same seems heavier when held at one end horizontally to the ground, compared to holding it...

I have a bit of intuition on microscopic structures, so I "easily" understand things such as chemistry, nuclear and particle physics and the such. I'm no expert in these subject or anything but I do have a easier time learning it. But I REALLY have a hard time understanding some...

Homework Statement The sun mass MS = 2.0 E30 kg revolves around the center of the milky way which has a total extension of 2.2 E20 m. The sun takes 2.5 E8 years to complete one revolution. Estimate the number of star in our galaxy based on this data. Suppose that the distribution is...

I'm taking a course in general relativity, it's a beautiful theory and I personally have no reason to doubt it's validity. However, I also recently stumbled upon and alternative theory of gravitation which was worked out by Oleg Jefimenko and is published in the following book...

Homework Statement What is the change in gravitational potential energy of a 64.5-kg astronaut, lifted from Earth’s surface into a circular orbit of altitude 4.40 3 102 km? The Attempt at a Solution Ok, i know to find this i have to find the gravitational energy on Earth using...

Okay, i know people saw that Earth is pulling everything towards each other and infact every other object is attracting each other. So there must be a force. But how did they discover the law i.e. F = GMm / r^2. They must have done some experiements to figure out this law and determine the...

Hello, I am trying to work out this exercise for my personal research connected with my bachelor thesis. The task is to compare equations (25.42) and (25.47) and express $u_0$ in terms of \tilde{L}. I have so far put the two equations together getting \begin{equation}...

Dear Sir, My name is Ashish R. Sai I am from India.I just appeared for 11th std.A few days ago I went through Gravitation.I completed my assignment.After completing assignments,I tried to find the gravitation between the moon and earth. During this i got a few doubts in this...

**Bonus Question** Gravitation A 1000kg rocket sits on the surface of a Earth like (same mass and radius - no atmosphere) planet. When fired, the rocket engines produce a force of 25 000N. The rocket is designed to reach an altitude of 580 km before the fuel runs out. If 1/2 of the rockets...

Newton Law Gravitation - Multiple choice question?? Homework Statement Newton’s law of gravitation can be applied to the Earth-Moon system. Which of the following statements is not correct? A The value of G at the surface of the Moon is the same as that at the surface of the Earth...

Homework Statement Three objects of equal mass (m) are located at three corners of a square of edge length , as shown in the figure below. Find the magnitude and direction of the gravitational field at the fourth corner due to these objects. (Use any variable or symbol stated above along...

Homework Statement In the Bohr model of the hydrogen atom, the electron revolves around the nucleus. If the radius of the orbit is 5.8 z 10^-11 m and the electron makes 6.6 x 10^15 r/s, find; a) the acceleration of the electron b) the magnitude of the gravitational force of attraction...

Homework Statement is there a point between the Earth and the moon for which the net gravitational force on an object is zero? Where is this point located? Note that the mass of the Earth is 5.98x10^24 kg, the mass of the moon is 7.35x10^22kg, and the distance between the centres of Earth...

Derive "Focusing Theorem" in Gravitation by MTW I followed the logic in Chapter 22.5 from Misner&Thorne&Wheeler, trying to derive the focusing theorem, i.e. equation(22.37). The problem that blocks me is the derivation of (22.36) for the cross section area. I already find the equation for...

I know physical bodies with mass cause gravitation. But do massless particles, like photons, also cause gravitation ? I know they're affected by gravity, but would a cloud of photons bend space by itself? Thank you

Why is gravitation still considered a Fundamental Force when General Relativity says that it is a geometric effect of inertia and space-time curvature?

Homework Statement A 70 kg bungee jumper jumps from a bridge. She is tied to a bungee cord whose unstretched length is 13 m , and falls a total of 37 m . Calculate the spring stiffness constant of the bungee cord, assuming Hooke's law applies. 88 N/M Calculate the maximum...

Lets suppose that we setup two instances involving two masses m1 and m2. m1 > m2 Case 1. The two bodies are separated by a distance r = 20. Case 2. The two bodies are separated by a distance r = 10. Suppose that in both setups, we were to release all restraining forces on these two...

Homework Statement "At what height above planet B's surface (in meters) does the gravitational field intensity become 0.6 times its value on the surface of planet B, given that the radius of planet B is 6.40 x 10^3 km and that its mass is 5.97 x 10^24 kg? Homework Equations g=Gm/r^2...

At t = 0 a star of mass 5.0×1030 kg has velocity < 6.0×10^4, 7.0×10^4, -7.0×10^4 > m/s and is located at < 1.00×10^12, -4.00×10^12, 4.00×10^12 > m relative to the center of a cluster of stars. There is only one nearby star that exerts a significant force on the first star. The mass of the second...

Homework Statement Please refer to the figures. (The first one is multiple-choice, the latter is structured). Homework Equations For the first problem: u = √(2gH) x = uxsinθt + \frac{1}{2}gsinθt2 uycosθt = \frac{1}{2}gcosθt2 and maybe others u = initial velocity x = x-displacement...

Homework Statement I need to show that the first equation becomes the last. First sub in for r1 and r2 and then use the binomial theorem to expand to first order in d. Then use the assumption that d<<r1 and r2. To show it reduces to the last eqn **In the first eqn it is NOT r3 is should be r2...

My book says r^3/t^2 was found constant by Kepler. What this constant is called? How is acceleration equal to v^2/r in case of circular motion? Why is rate of change of momentum or say product of mass and acceleration equal to force? Why not was it ma^2? How was it proved that it...

We know that 1. Mass causes bend in space-time and this is the how gravitation occurs. 2. The formula for gravitation (per the universal law of gravitation) is product of masses divided by the square of the distance between them and multiplied by the universal gravitation constant. I...

Homework Statement Homework Equations 2ΔEk=-ΔEp The Attempt at a Solution -Gm1m2(1/r1-1/r2)-Q=mv2 plug in given values solve for v. my answer is 5.35x106m/s given answer is 2100m/s

Gravitational waves are generated when the mass quadrupole moment changes in time. We also know motion of mass contributes to its gravitation. Does the producing process of gravitational waves, which involves mass in accelerated motion, produce gravitation as well? If so, is it of less, equal...

while in downward motion or in an orbit astronomers experience weightlessness their apparent weight (the mass they feel is m = (g - a) where g is acceleration due to gravity and a is acceleration with which the person is going downwards. now my question is what will the person feel if a>g?

if the Earth stops rotating , the value of 'g' will increase by Rω2 at the equator but will remain same at the poles.how does it happen?could you please explain me this?

Homework Statement A space vehicle of mass 555kg, experiences a gravitational pull from Earth of 255N. The mass of Earth is 5.98x10 (to the power of 24) kg.How far is the vehicle a) from the center of the Earth, and b) above the surface of the Earth? Homework Equations FG = GM1M2/d squaredThe...

Its interesting that eventhough gravitation is a force, it cannot be measured. Literatures says that only gravitational gradient can be measured from gravity tensor is to be computed and by applying mathemaatical operations, derive the gravitational vector. Can anyone help me to understand...

Homework Statement Mars has a diameter of .54 times that of Earth and a mass of .11 times that of Earth. Suppose a rover was launched on Earth with the mass of 525 kg. Remember that g is -9.80 m/s/s A) How much does the rover weigh on Earth? B) How much does it weigh on Mars?Homework Equations...

Homework Statement See Attachment Calculate the force of gravity on the point mass due to the line mass in terms of the gravitational constant G, m, M, D, and L. The line mass has a uniform density. Homework Equations The Attempt at a Solution Ok so apparently I'm suppose to...

Homework Statement The question is presented as picture. Homework Equations We do not have the radius of the cavity and the position of the m. How can we find the force acted on it? The Attempt at a Solution r=1/(M-m)*Ʃmr=1/(M-m)*4/3ρR'^3*r where m is the mass of cavity ,R' is the...

a 120kg person stands on the surface of an asteroid of radius 600m. the person leaves the surface with 15J of kinetic energy and reached a maximum height of 300m above the asteroid's surface. what is the mass of the asteroid. i am stuck please help me with the problem. 15-GMm/r(i) = 0 -...

Universe with only "e+", "e-", photons, and gravitation? In theory could we have a universe with only electrically charged spin 1/2 particles and antiparticles of mass m and electrical charge e and that interacted only gravitationally and electromagnetically? If so could we fine tune things...

Hello! I need to find the relation between E^{2}-B^{2} and F_{\mu\nu} F^{\mu\nu} Actually, I need to use this relation to determine that the first is a scalar. What I can't understand is how these notations match the formal definition: If I multiply a matrix by another (same size) I should...

Homework Statement How deep would a mine shaft have to be for the gravitational acceleration at the bottom to be reduced by a factor of 5 from its value on the Earth's surface? Homework Equations g=r(GME/RE3) G = 6.67 * 10-11 ME = 5.97 * 1024 kg RE = 6.38 * 106 m The Attempt at a...

Gravitation Potential Energy Problem of WHY? Homework Statement Energy is required to move a 1540 kg mass from the Earth’s surface to an altitude 3.12 times the Earth’s radius RE. What amount of energy is required to accomplish this move? The acceleration of gravity is 9.8 m/s^{2}...

Hello! I fail to understand this question... I don't even know how to approach it... Given: m\frac{d^{2}x^{\mu}} {d\tau^{2}} =e{F^{\mu}_{nu}} \frac{dx^{\nu}} {d\tau} I have to define u^{\mu}= \frac {dx^{\mu}} {d\tau^2} and obtain: u^0= cosh(\frac {eE\tau} {m}) u^0(0)+ sinh(\frac {eE\tau}...

Homework Statement Standing on the surface of a small spherical moon whose radius is 6.00*104 m and whose mass is 7.50*1018 kg, an astronaut throws a rock of mass 2.05 kg straight upward with an initial speed 38.5 m/s. (This moon is too small to have an atmosphere.) What maximum height above...

I've worked out the inverse square law using centripetal acceleration and Kepler's law. But I can't quite see how Newton worked out for sure that the force is directly proportional to both masses. I know it's pretty intuitive, but I thought maybe there was a mathematical way of confirming that...