Imagine an arbitrary point in space. It is within the gravitational potential of every mass (although billions of ly away) in the entire universe.

Since every mass adds a tiny fraction, what is the total gravitational potential energy in this point?

Edit:

Let point masses be located distance $r_i$ from the point and have masses $m_i$, then the 'potential' is

$$\Phi = - G \sum_{i} \frac{m_i}{r_i}.$$

I'm looking for this value averaged over all points in space. How does this depend on the shape of our universe or can we measure it?

• For example gravity on my location is given by $$ 9.81 m/s^2 \text{(earth )} + 6 mm/s^2 \text{(sun)} + 200 pm/s^2 \text{(milky way)} + ? \text{(rest of the universe)}.$$

Imagine an arbitrary point in space. It is within the gravitational 'potential' of every mass (although billions of ly away) in the entire universe.

Since every mass adds a tiny fraction, what is the total gravitational 'potential' energy in this point?

Edit:

Let point masses be located distance $r_i$ from the point and have masses $m_i$, then the 'potential' is

$$\Phi = - G \sum_{i} \frac{m_i}{r_i}.$$

I'm looking for this value averaged over all points in space. How does this depend on the shape of our universe or can we measure it?

• For example gravity on my location is given by $$ 9.81 m/s^2 \text{(earth )} + 6 mm/s^2 \text{(sun)} + 200 pm/s^2 \text{(milky way)} + ? \text{(rest of the universe)}.$$

Imagine an arbitrary point in space. It is within the gravitational potential of every mass (although billions of ly away) in the entire universe.

Since every mass adds a tiny fraction, what is the total gravitational potential energy in this point?

Edit:

Let point masses be located distance $r_i$ from the point and have masses $m_i$, then the 'potential' is

$$\Phi = - G \sum_{i} \frac{m_i}{r_i}.$$

I'm looking for this value averaged over all points in space.

• For example gravity on my location is given by $$ 9.81 m/s^2 \text{(earth )} + 6 mm/s^2 \text{(sun)} + 200 pm/s^2 \text{(milky way)} + ? \text{(rest of the universe)}.$$

Imagine an arbitrary point in space. It is within the gravitational potential of every mass (although billions of ly away) in the entire universe.

Since every mass adds a tiny fraction, what is the total gravitational potential energy in this point?

Edit:

Let point masses be located distance $r_i$ from the point and have masses $m_i$, then the 'potential' is

$$\Phi = - G \sum_{i} \frac{m_i}{r_i}.$$

I'm looking for this value averaged over all points in space. How does this depend on the shape of our universe or can we measure it?

• For example gravity on my location is given by $$ 9.81 m/s^2 \text{(earth )} + 6 mm/s^2 \text{(sun)} + 200 pm/s^2 \text{(milky way)} + ? \text{(rest of the universe)}.$$

Imagine an arbitrary point in space. It is within the gravitational potential of every mass (although billions of ly away) in the entire universe.

Since every mass adds a tiny fraction, what is the total gravitational potential energy in this point?

Edit:

Let point masses be located distance $r_i$ from the point and have masses $m_i$, then the 'potential' is

$$\Phi = - G \sum_{i} \frac{m_i}{r_i}.$$

I'm looking for this value averaged over all points in space.

Imagine an arbitrary point in space. It is within the gravitational potential of every mass (although billions of ly away) in the entire universe.

Since every mass adds a tiny fraction, what is the total gravitational potential energy in this point?

Edit:

Let point masses be located distance $r_i$ from the point and have masses $m_i$, then the 'potential' is

$$\Phi = - G \sum_{i} \frac{m_i}{r_i}.$$

I'm looking for this value averaged over all points in space.

• For example gravity on my location is given by $$ 9.81 m/s^2 \text{(earth )} + 6 mm/s^2 \text{(sun)} + 200 pm/s^2 \text{(milky way)} + ? \text{(rest of the universe)}.$$