All Questions
41
questions
1
vote
2
answers
98
views
How to calculate equilibrium height of tidal bulge?
I am trying to model the shape of the tidal bulge caused by the moon.
I asked GPT for a formula and it gave me equilibrium tidal bulge height as
$$\frac{2 R_{earth} G M_{moon}}{3 r^3 \Delta g}$$
and ...
- 5,148
0
votes
2
answers
3k
views
Gravitational potential energy inside of a solid sphere [duplicate]
I am self-studying classical mechanics. I came across a problem which required me to calculate the gravitational potential inside of a sphere. I found in one of my textbooks that the potential energy ...
- 23
2
votes
2
answers
146
views
A simple proof that under Newtonian gravity rotating massive bodies are ellipsoids?
Here is my attempt at deriving the shape of an idealized rotating massive body under Newtonian gravity, assuming that the gravity force points towards the center of mass and shape of the body is ...
- 513
1
vote
1
answer
71
views
How do we find the centripetal forces of 3 planets revolving around a point given that they have the same mass?
Let's say we have three planets revolving around a point. We know that the force of gravity acting on all of these planets can be taken from $g = G{m_1m_2 \over r^2}$. We can derive the velocity of ...
0
votes
1
answer
121
views
Body falling through Earth
Imagine a body with mass $m$ moves through a pipe through the centre of earth. The gravitational force is given by $\vec{F}=-C \vec{r}$ where $C$ is constant. I want to determine the 1D equation of ...
- 15
0
votes
2
answers
753
views
How to derive Kepler's third law of planetary motion using angular momentum of Earth around the Sun?
While I was trying to derive Kepler's third law of planetary motion, I tried the gravitational force for the Earth method which goes something like this:
$$\frac{mv^2}{r}=\frac{GMm}{r^2}$$
$$\...
- 115
1
vote
1
answer
48
views
Why can we not take gravity to act at the center of mass in this case? [closed]
I found this problem when I was trying to prove that the gravitational attraction on an object is the gravitational attraction on the center of mass of that object (I had doubts on it). And in doing ...
- 1,189
1
vote
1
answer
2k
views
Gravitational potential at the centre of Earth [duplicate]
Why does gravitational potential at the centre of the Earth is finite i.e. $V_c=\frac{3}{2} V_s$, as at the centre $r$ becomes zero so applying $V = \frac{GM}{r}$ the result must be infinity.
- 149
0
votes
0
answers
22
views
Why does the mass of small objects not cause them to "pull" Earth towards them as slightly different speeds, as they fall to Earth? [duplicate]
Debate over dinner: we read on Wikipedia that objects fall at the same speed towards Earth regardless of mass. Then we remember seeing on TV ages ago an astronaut dropping a feather and bowling ball ...
- 133
-2
votes
1
answer
919
views
How to integrate acceleration due to gravity with height? [duplicate]
If I project a body at a very large velocity such that it reaches a height h which is comparable to Earth's radius, then how to derive an equation for 'h' in terms of initial velocity 'u' and other ...
- 1
0
votes
2
answers
111
views
How does the gravitational acceleration on a surface of planet change, if its radius shrinks while retaining the same mass? [closed]
If the radius of the earth were to shrink by $1$%
while its mass remained the same,
then how would the acceleration due to gravity on the earth's surface increase by $2$%?
0
votes
2
answers
165
views
How far can you pee on the moon vs. mars? [closed]
Let's suppose you are at Elon Musk's Future Mars colony and you drank too much beer, how far can you pee on Mars if you can pee one meter on earth?
If the next day you get on the shuttle to the ...
- 11
1
vote
2
answers
680
views
Accurate Equation for Earth's Gravitational Binding Energy
This is a relatively important question for anyone who can answer it. I am trying to find the equation that accurately solves for Earth's Gravitational Binding Energy. The information below is from ...
- 273
0
votes
0
answers
98
views
How fast would the Earth have to spin to lose the atmosphere?
I have read these questions:
How fast would the Earth need to spin for us to feel weightless?
Why can't we feel the Earth (or being in any non-inertial frame) rotating?
And it made me curious. Is ...
- 29k
0
votes
4
answers
7k
views
What is acceleration due to gravity at the centre of the earth? [duplicate]
When I asked my teacher that what is the acceleration at the centre of earth, he replied that it is 0 as when we move inside the earth, the effective mass decreases i.e. the mass that exerts ...
- 592